Health Education Systems Inc (HESI) A2 Exam Quiz: Balancing Chemical Equations
20 questions · exam conditions
0:00
Balancing Chemical EquationsQuestion 1 of 20

The decomposition reaction KClO3→KCl+O2KClO_3 \rightarrow KCl + O_2 is to be balanced. If the coefficient of KClO3KClO_3 is chosen to be 2, what must be the coefficient of O2O_2 to maintain proper stoichiometric balance?

2
3
4
6
← Back to quizzes

Health Education Systems Inc (HESI) A2 Exam Quiz

Health Education Systems Inc (HESI) A2 Exam Quiz: Balancing Chemical Equations

Practice Balancing Chemical Equations in Health Education Systems Inc (HESI) A2 Exam with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Balancing Chemical Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for Health Education Systems Inc (HESI) A2 Exam.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

The decomposition reaction KClO3→KCl+O2KClO_3 \rightarrow KCl + O_2 is to be balanced. If the coefficient of KClO3KClO_3 is chosen to be 2, what must be the coefficient of O2O_2 to maintain proper stoichiometric balance?

  1. 2
  2. 3 (correct answer)
  3. 4
  4. 6
Explanation: With coefficient 2 for KClO3KClO_3, we have 2KClO3→2KCl+xO22KClO_3 \rightarrow 2KCl + xO_2. The left side contains 2(3) = 6 oxygen atoms. Since each O2O_2 molecule contains 2 oxygen atoms, we need x = 6/2 = 3. The balanced equation is 2KClO3→2KCl+3O22KClO_3 \rightarrow 2KCl + 3O_2. Choice A (2) incorrectly matches the coefficient of KClO3KClO_3. Choice C (4) overcounts oxygen requirements. Choice D (6) uses the total number of oxygen atoms instead of O2O_2 molecules.

Question 2

A redox reaction is represented as: MnO4−+Fe2++H+→Mn2++Fe3++H2OMnO_4^- + Fe^{2+} + H^+ \rightarrow Mn^{2+} + Fe^{3+} + H_2O. When balanced in acidic solution using the smallest integer coefficients, how many H+H^+ ions are required per MnO4−MnO_4^- ion?

  1. 5
  2. 8 (correct answer)
  3. 10
  4. 16
Explanation: The balanced equation is: MnO4−+5Fe2++8H+→Mn2++5Fe3++4H2OMnO_4^- + 5Fe^{2+} + 8H^+ \rightarrow Mn^{2+} + 5Fe^{3+} + 4H_2O. For each MnO4−MnO_4^-, 8 H+H^+ ions are needed. Choice A (5) confuses the coefficient with the number of electrons transferred. Choice C (10) might come from adding H⁺ coefficients incorrectly. Choice D (16) represents doubling the correct answer.

Question 3

When solid potassium chlorate (KClO₃) is heated, it decomposes into solid potassium chloride (KCl) and oxygen gas (O₂). What is the sum of all coefficients when this decomposition reaction is balanced using the lowest whole-number ratio?

  1. 3
  2. 4
  3. 5
  4. 7 (correct answer)
Explanation: When you encounter chemical decomposition reactions, you need to balance the equation by ensuring equal numbers of each type of atom on both sides. This tests your understanding of conservation of mass and stoichiometry. Start with the unbalanced equation: KClO3→KCl+O2\text{KClO}_3 \rightarrow \text{KCl} + \text{O}_2 Count atoms on each side. The left side has 1 K, 1 Cl, and 3 O atoms. The right side has 1 K, 1 Cl, and 2 O atoms. The oxygen atoms don't balance (3 ≠ 2). To balance oxygen, find the least common multiple of 3 and 2, which is 6. You need 6 oxygen atoms on each side. Place a 2 in front of KClO₃ (giving 6 O atoms) and a 3 in front of O₂ (also giving 6 O atoms): 2KClO3→KCl+3O22\text{KClO}_3 \rightarrow \text{KCl} + 3\text{O}_2 Now the left side has 2 K and 2 Cl atoms, but the right side has only 1 K and 1 Cl. Add a 2 in front of KCl: 2KClO3→2KCl+3O22\text{KClO}_3 \rightarrow 2\text{KCl} + 3\text{O}_2 The balanced equation has coefficients 2, 2, and 3, which sum to 7. Choice A (3) likely comes from counting only the oxygen coefficients. Choice B (4) might result from adding 2 + 2 while forgetting the oxygen coefficient. Choice C (5) could come from miscounting or partial balancing attempts. Remember: always verify your balanced equation by counting each type of atom on both sides, then sum all coefficients including the implied "1" values.

Question 4

When butane (C₄H₁₀) undergoes complete combustion with oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O), the equation must be balanced. What is the sum of all coefficients in the final balanced chemical equation using the smallest possible whole numbers?

  1. 17
  2. 23
  3. 33 (correct answer)
  4. 35
Explanation: When you encounter combustion reactions, you're balancing a hydrocarbon with oxygen to produce carbon dioxide and water. The key is working systematically through each element. Start with the unbalanced equation: C4H10+O2→CO2+H2O\text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} Balance carbon first: butane has 4 carbon atoms, so you need 4 CO₂ molecules. Next, balance hydrogen: butane has 10 hydrogen atoms, so you need 5 H₂O molecules (since each water has 2 hydrogens). Your equation now reads: C4H10+O2→4CO2+5H2O\text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2\text{O} Finally, balance oxygen: the products contain 8 oxygen atoms (from 4 CO₂) plus 5 oxygen atoms (from 5 H₂O) = 13 total oxygen atoms. Since O₂ molecules contain 2 oxygen atoms each, you need 6.5 O₂ molecules. To eliminate the fraction, multiply all coefficients by 2: 2C4H10+13O2→8CO2+10H2O2\text{C}_4\text{H}_{10} + 13\text{O}_2 \rightarrow 8\text{CO}_2 + 10\text{H}_2\text{O} Adding all coefficients: 2 + 13 + 8 + 10 = 33, making C correct. Choice A (17) likely comes from forgetting to double all coefficients to eliminate fractions. Choice B (23) might result from miscounting oxygen atoms. Choice D (35) could stem from arithmetic errors when summing the final coefficients. Remember: always check that your coefficients use the smallest whole numbers possible, and verify your work by ensuring atoms balance on both sides.

Question 5

The overall process of photosynthesis is represented by the unbalanced equation: CO₂ + H₂O → C₆H₁₂O₆ + O₂. Which of the following represents the correctly balanced chemical equation for this essential biological process?

  1. 6CO₂ + H₂O → C₆H₁₂O₆ + 3O₂
  2. 6CO₂ + 6H₂O → C₆H₁₂O₆ + O₂
  3. 12CO₂ + 6H₂O → 2C₆H₁₂O₆ + 6O₂
  4. 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ (correct answer)
Explanation: When you encounter chemical equation balancing questions, remember that atoms cannot be created or destroyed - you must have equal numbers of each type of atom on both sides of the equation. This fundamental principle of chemistry is essential for understanding biological processes like photosynthesis. To balance the photosynthesis equation, count atoms systematically. Start with the most complex molecule, glucose (C₆H₁₂O₆), which contains 6 carbon, 12 hydrogen, and 6 oxygen atoms. Working backwards, you need 6 CO₂ molecules to provide the 6 carbon atoms. For the 12 hydrogen atoms in glucose, you need 6 H₂O molecules (since each water molecule contributes 2 hydrogens). Now count the oxygen atoms on the reactant side: 6 CO₂ contributes 12 oxygens, and 6 H₂O contributes 6 oxygens, totaling 18. On the product side, glucose contains 6 oxygens, leaving 12 that must appear as O₂ gas. Since each O₂ molecule contains 2 oxygen atoms, you need 6 O₂ molecules. This gives us: 6CO2+6H2O→C6H12O6+6O26CO_2 + 6H_2O \rightarrow C_6H_{12}O_6 + 6O_2 Answer A is wrong because it uses only 1 H₂O, providing insufficient hydrogen atoms. Answer B fails because it produces only 1 O₂, leaving oxygen unbalanced. Answer C incorrectly doubles the entire equation, making it unnecessarily complex while changing the stoichiometric relationships. Study tip: Always balance equations by counting atoms of each element separately. Start with the most complex molecule and work systematically through carbon, hydrogen, then oxygen - this approach prevents errors on HESI chemistry questions.

Question 6

When phosphoric acid (H₃PO₄) is completely neutralized by sodium hydroxide (NaOH), the products are sodium phosphate (Na₃PO₄) and water. After balancing the equation with the lowest whole-number coefficients, what is the ratio of the coefficient of sodium hydroxide to the coefficient of water?

  1. 1:1 (correct answer)
  2. 1:3
  3. 2:3
  4. 3:1
Explanation: When you encounter acid-base neutralization problems, you need to balance the chemical equation first, then examine the coefficients to find the requested ratio. Let's balance the neutralization of phosphoric acid with sodium hydroxide. Start with the unbalanced equation: H3PO4+NaOH→Na3PO4+H2O\text{H}_3\text{PO}_4 + \text{NaOH} \rightarrow \text{Na}_3\text{PO}_4 + \text{H}_2\text{O} Since phosphoric acid (H₃PO₄) has three hydrogen atoms and sodium phosphate (Na₃PO₄) contains three sodium atoms, you need three NaOH molecules to provide enough sodium and hydroxide ions. The three H⁺ ions from the acid combine with three OH⁻ ions from the base to form three water molecules: H3PO4+3NaOH→Na3PO4+3H2O\text{H}_3\text{PO}_4 + 3\text{NaOH} \rightarrow \text{Na}_3\text{PO}_4 + 3\text{H}_2\text{O} The coefficient of NaOH is 3, and the coefficient of water is 3. Therefore, the ratio is 3:3, which simplifies to 1:1, making choice A correct. Choice B (1:3) incorrectly suggests one NaOH produces three waters, ignoring the actual stoichiometry. Choice C (2:3) might result from miscounting atoms or confusing this with a different acid. Choice D (3:1) reverses the ratio by putting NaOH first instead of recognizing that equal coefficients create a 1:1 ratio. Remember that in neutralization reactions, the number of H⁺ ions from the acid must equal the number of OH⁻ ions from the base. Count carefully and always reduce ratios to their simplest form.

Question 7

The combustion of ethanol (C₂H₅OH) is an important biochemical reaction. The unbalanced equation is: C₂H₅OH + O₂ → CO₂ + H₂O. When balanced using the smallest whole numbers, what is the coefficient for oxygen (O₂)?

  1. 2
  2. 3 (correct answer)
  3. 5
  4. 7
Explanation: When you encounter chemical equation balancing problems, you're applying the law of conservation of mass—atoms can't be created or destroyed, so you need equal numbers of each type of atom on both sides of the equation. Start by counting atoms in the unbalanced equation: C2H5OH+O2→CO2+H2O\text{C}_2\text{H}_5\text{OH} + \text{O}_2 → \text{CO}_2 + \text{H}_2\text{O}. The reactant side has 2 carbons, 6 hydrogens, and 1 oxygen (in ethanol). Begin balancing with the most complex molecule—ethanol. Since ethanol has 2 carbons, you need 2 CO2\text{CO}_2 molecules on the product side. Since ethanol has 6 hydrogens, you need 3 H2O\text{H}_2\text{O} molecules (each water has 2 hydrogens). This gives you: C2H5OH+O2→2CO2+3H2O\text{C}_2\text{H}_5\text{OH} + \text{O}_2 → 2\text{CO}_2 + 3\text{H}_2\text{O} Now count oxygen atoms on the product side: 4 from 2CO22\text{CO}_2 plus 3 from 3H2O3\text{H}_2\text{O} equals 7 total oxygen atoms needed. The reactant side already has 1 oxygen from ethanol, so you need 6 more from O2\text{O}_2 molecules. Since each O2\text{O}_2 provides 2 oxygen atoms, you need 3 O2\text{O}_2 molecules. Choice A (2) would only provide 4 oxygen atoms from O2\text{O}_2, giving you 5 total—not enough. Choice C (5) would give you 10 oxygen atoms from O2\text{O}_2, totaling 11—too many. Choice D (7) would provide 14 oxygen atoms from O2\text{O}_2, totaling 15—far too many. Always balance carbon and hydrogen first, then use oxygen to complete the equation. This systematic approach prevents calculation errors.

Question 8

Stomach acid, which is primarily hydrochloric acid (HCl), is neutralized by milk of magnesia, which is magnesium hydroxide (Mg(OH)₂). The products are magnesium chloride and water. What is the sum of the coefficients of the products when the chemical equation is balanced?

  1. 2
  2. 3 (correct answer)
  3. 4
  4. 5
Explanation: When you encounter chemical equation balancing problems, you're working with the law of conservation of mass—atoms can't be created or destroyed, only rearranged. This question tests your ability to balance equations and then count specific coefficients. Start by writing the unbalanced equation: HCl+Mg(OH)2→MgCl2+H2O\text{HCl} + \text{Mg(OH)}_2 \rightarrow \text{MgCl}_2 + \text{H}_2\text{O} To balance this, count atoms on each side. The left side has 1 H from HCl plus 2 H from Mg(OH)₂ (total 3 H), 1 Cl, 1 Mg, and 2 O. The right side needs the same totals. Since Mg(OH)₂ provides 2 OH⁻ ions, you need 2 HCl molecules to neutralize them: 2HCl+Mg(OH)2→MgCl2+2H2O2\text{HCl} + \text{Mg(OH)}_2 \rightarrow \text{MgCl}_2 + 2\text{H}_2\text{O} Verify: Left side has 2 H + 2 H = 4 H, 2 Cl, 1 Mg, 2 O. Right side has 4 H, 2 Cl, 1 Mg, 2 O. ✓ The question asks for the sum of coefficients of the products only. The products are MgCl₂ (coefficient = 1) and H₂O (coefficient = 2). Sum: 1 + 2 = 3. Choice A (2) only counts one product's coefficient. Choice C (4) likely includes all coefficients from both reactants and products. Choice D (5) adds all coefficients plus an extra error. Study tip: Always double-check what the question asks for—reactants, products, or all coefficients. Many students lose points by calculating correctly but answering the wrong question.

Question 9

A student incorrectly balances an equation by changing the chemical formulas of the substances instead of using coefficients. Which of the following principles of chemistry does this action violate?

  1. The Law of Multiple Proportions
  2. The Law of Definite Proportions (correct answer)
  3. The Law of Conservation of Energy
  4. The Ideal Gas Law
Explanation: When balancing chemical equations, you're working with fundamental laws that govern how matter behaves in chemical reactions. The key principle at stake here is that chemical compounds have fixed, definite compositions that cannot be altered. The Law of Definite Proportions states that a given chemical compound always contains the same elements in the same fixed ratio by mass. When you change a chemical formula (like turning H₂O into H₃O), you're creating an entirely different substance with different properties. This violates the law because you're no longer dealing with the original compound that has its definite, unchangeable composition. Water will always be H₂O - you can't make it H₃O and still call it water. Looking at the wrong answers: (A) The Law of Multiple Proportions deals with different compounds formed by the same elements (like CO and CO₂), not with changing formulas during balancing. (C) The Law of Conservation of Energy relates to energy transformations, not the composition of chemical formulas. (D) The Ideal Gas Law describes the behavior of gases under different conditions and has nothing to do with chemical equation balancing. The correct approach is to use coefficients (like 2H₂O) which change the number of molecules present but preserve each compound's definite composition. Study tip: Remember that chemical formulas are like molecular "fingerprints" - they're fixed identities that define what a substance actually is. Only coefficients can be adjusted during balancing, never the subscripts in formulas.

Question 10

When solid magnesium nitride (Mg₃N₂) reacts with liquid water, it produces solid magnesium hydroxide and ammonia gas (NH₃). What is the balancing coefficient for water in the final, balanced chemical equation?

  1. 2
  2. 3
  3. 6 (correct answer)
  4. 8
Explanation: When you encounter chemical equation balancing problems, you're applying the law of conservation of mass—atoms can't be created or destroyed, so the same number of each type of atom must appear on both sides of the equation. Start by writing the unbalanced equation: Mg3N2+H2O→Mg(OH)2+NH3\text{Mg}_3\text{N}_2 + \text{H}_2\text{O} \rightarrow \text{Mg(OH)}_2 + \text{NH}_3 Now systematically balance each element. Begin with the most complex compound, magnesium nitride. Since you have 3 magnesium atoms on the left, you need 3 Mg(OH)2\text{Mg(OH)}_2 on the right. For nitrogen, you have 2 nitrogen atoms on the left, so you need 2 NH3\text{NH}_3 molecules on the right. Your equation now looks like: Mg3N2+H2O→3Mg(OH)2+2NH3\text{Mg}_3\text{N}_2 + \text{H}_2\text{O} \rightarrow 3\text{Mg(OH)}_2 + 2\text{NH}_3 Count the hydrogen and oxygen atoms needed on the right side. You have 3×2=63 \times 2 = 6 OH groups (6 hydrogen, 6 oxygen) plus 2×3=62 \times 3 = 6 hydrogen atoms from ammonia, totaling 12 hydrogen atoms and 6 oxygen atoms. Since each water molecule provides 2 hydrogen and 1 oxygen, you need 6 water molecules to supply exactly what's needed. The balanced equation is: Mg3N2+6H2O→3Mg(OH)2+2NH3\text{Mg}_3\text{N}_2 + 6\text{H}_2\text{O} \rightarrow 3\text{Mg(OH)}_2 + 2\text{NH}_3 Option C (6) is correct. Option A (2) would provide insufficient hydrogen atoms. Option B (3) would also fall short of the required hydrogen. Option D (8) would provide excess atoms, violating conservation of mass. Study tip: Always balance the most complex polyatomic compounds first, then work toward simpler molecules like water. Double-check by counting each type of atom on both sides.

Question 11

Which of the following chemical equations is NOT correctly balanced?

  1. 2Na + 2H₂O → 2NaOH + H₂
  2. C₃H₈ + 5O₂ → 3CO₂ + 4H₂O
  3. 2KNO₃ → 2KNO₂ + O₂
  4. Fe₂O₃ + 2CO → 2Fe + 3CO₂ (correct answer)
Explanation: When you encounter chemical equation balancing questions, you need to verify that the number of atoms of each element is equal on both sides of the equation. This follows the law of conservation of mass - atoms cannot be created or destroyed in chemical reactions. Let's check each equation systematically. For option A (2Na + 2H₂O → 2NaOH + H₂), the left side has 2 Na, 4 H, and 2 O atoms, while the right side also has 2 Na, 4 H, and 2 O atoms - this balances correctly. Option B (C₃H₈ + 5O₂ → 3CO₂ + 4H₂O) shows 3 C, 8 H, and 10 O atoms on each side - also balanced. Option C (2KNO₃ → 2KNO₂ + O₂) has 2 K, 2 N, and 6 O atoms on both sides - correctly balanced. Option D (Fe₂O₃ + 2CO → 2Fe + 3CO₂) is the problem. On the left side, you have 2 Fe, 1 C, and 5 O atoms. On the right side, you have 2 Fe, 3 C, and 6 O atoms. The carbon and oxygen don't balance - you have unequal numbers on each side, violating conservation of mass. The correctly balanced version of equation D should be: Fe₂O₃ + 3CO → 2Fe + 3CO₂, which gives equal atoms on both sides. Study tip: Always count atoms element by element when checking balanced equations. Start with the most complex molecule first, then work systematically through each element. This methodical approach prevents overlooking imbalances that make equations incorrect.

Question 12

When the mineral antimony(III) sulfide (Sb₂S₃) is roasted in air (O₂), it forms antimony(III) oxide (Sb₂O₃) and sulfur dioxide (SO₂). When the equation for this process is balanced, what is the coefficient for sulfur dioxide?

  1. 2
  2. 3
  3. 6 (correct answer)
  4. 9
Explanation: When you encounter chemical equation balancing problems, you're applying the law of conservation of mass—atoms can't be created or destroyed, so the same number of each type of atom must appear on both sides of the equation. Start with the unbalanced equation: Sb2S3+O2→Sb2O3+SO2Sb_2S_3 + O_2 → Sb_2O_3 + SO_2 The most systematic approach is to balance the most complex molecule first. Since Sb2S3Sb_2S_3 contains both antimony and sulfur, start there. You have 2 antimony atoms and 3 sulfur atoms on the left side. For antimony: You need 2 antimony atoms on the right, and Sb2O3Sb_2O_3 already provides this, so its coefficient is 1. For sulfur: You have 3 sulfur atoms from Sb2S3Sb_2S_3, so you need 3 SO2SO_2 molecules on the right side to balance them. Now count oxygen atoms on the right: 3 from Sb2O3Sb_2O_3 plus 6 from 3SO23SO_2 equals 9 total oxygen atoms needed. Since O2O_2 provides 2 oxygen atoms per molecule, you need 92=4.5\frac{9}{2} = 4.5 O2O_2 molecules. To eliminate the fraction, multiply the entire equation by 2: 2Sb2S3+9O2→2Sb2O3+6SO22Sb_2S_3 + 9O_2 → 2Sb_2O_3 + 6SO_2 The coefficient for SO2SO_2 is 6, making C correct. Choice A (2) and B (3) are too small and likely come from not doubling the equation to eliminate fractions. Choice D (9) incorrectly uses the oxygen coefficient. Remember: always check your final answer by counting atoms on both sides to ensure they balance, and don't be afraid to use fractions initially—just clear them at the end.

Question 13

In a single replacement reaction, solid zinc reacts with aqueous hydrochloric acid to produce aqueous zinc chloride and hydrogen gas. The unbalanced equation is Zn + HCl → ZnCl₂ + H₂. When balanced, what is the ratio of the coefficient of HCl to the coefficient of Zn?

  1. 1:1
  2. 1:2
  3. 2:1 (correct answer)
  4. 2:2
Explanation: When you encounter chemical equation balancing problems, remember that atoms must be conserved—the same number of each type of atom must appear on both sides of the equation. Let's balance this single replacement reaction step by step. Start with the unbalanced equation: Zn+HCl→ZnCl2+H2\text{Zn} + \text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 First, count the atoms on each side. On the right side, you have 1 zinc atom in ZnCl₂, 2 chlorine atoms in ZnCl₂, and 2 hydrogen atoms in H₂. On the left side, you currently have 1 zinc atom, 1 hydrogen atom, and 1 chlorine atom. To balance the chlorine atoms, you need 2 HCl molecules on the left side. This gives you the balanced equation: Zn+2HCl→ZnCl2+H2\text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 Now verify: 1 Zn, 2 H, and 2 Cl on each side—perfectly balanced! The coefficient of HCl is 2, and the coefficient of Zn is 1 (understood when no number is written). Therefore, the ratio of HCl to Zn is 2:1. Choice A (1:1) assumes equal coefficients without balancing. Choice B (1:2) incorrectly reverses the ratio, perhaps from reading the question backwards. Choice D (2:2) might result from overthinking and unnecessarily doubling all coefficients, though this would technically be correct, it's not in simplest form and doesn't match the other ratios given. Study tip: Always balance equations systematically by starting with the most complex molecule, then work toward simpler ones. Double-check by counting atoms on both sides.

Question 14

Consider the double displacement reaction between aluminum sulfate and calcium hydroxide: Al₂(SO₄)₃ + Ca(OH)₂ → Al(OH)₃ + CaSO₄. When this equation is balanced with the lowest whole-number coefficients, what is the sum of the coefficients for the products?

  1. 4
  2. 5 (correct answer)
  3. 7
  4. 9
Explanation: When you encounter double displacement reactions, you're dealing with two ionic compounds swapping their ions to form two new compounds. The key skill being tested here is your ability to balance chemical equations using the lowest whole-number coefficients. To balance this equation, you need to ensure equal numbers of each type of atom on both sides. Start by counting atoms in the unbalanced equation: Al2(SO4)3+Ca(OH)2→Al(OH)3+CaSO4\text{Al}_2(\text{SO}_4)_3 + \text{Ca(OH)}_2 \rightarrow \text{Al(OH)}_3 + \text{CaSO}_4 The left side has 2 aluminum atoms, so you need 2 Al(OH)3\text{Al(OH)}_3 on the right. The left side has 3 sulfate groups, so you need 3 CaSO4\text{CaSO}_4 on the right. This means you need 3 calcium atoms on the left, requiring 3 Ca(OH)2\text{Ca(OH)}_2. The balanced equation becomes: Al2(SO4)3+3Ca(OH)2→2Al(OH)3+3CaSO4\text{Al}_2(\text{SO}_4)_3 + 3\text{Ca(OH)}_2 \rightarrow 2\text{Al(OH)}_3 + 3\text{CaSO}_4 The products are 2Al(OH)3+3CaSO42\text{Al(OH)}_3 + 3\text{CaSO}_4, so the sum of product coefficients is 2 + 3 = 5, making B correct. Choice A (4) likely comes from miscounting or forgetting one coefficient. Choice C (7) represents the sum of ALL coefficients (1 + 3 + 2 + 3 = 9, but students might miscount as 7). Choice D (9) is the sum of all coefficients in the equation, not just the products. Remember: when balancing equations, always double-check by counting each type of atom on both sides, and pay careful attention to whether the question asks for reactant coefficients, product coefficients, or total coefficients.

Question 15

Aqueous solutions of barium chloride (BaCl₂) and sodium sulfate (Na₂SO₄) react to form a precipitate of barium sulfate (BaSO₄) and aqueous sodium chloride (NaCl). What is the sum of the coefficients of the reactants when this equation is balanced?

  1. 2 (correct answer)
  2. 3
  3. 4
  4. 5
Explanation: When you encounter chemical equation balancing problems, you're applying the law of conservation of mass—atoms can't be created or destroyed, so the same number of each type of atom must appear on both sides of the equation. Start by writing the unbalanced equation: BaCl2+Na2SO4→BaSO4+NaCl\text{BaCl}_2 + \text{Na}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + \text{NaCl} Now balance systematically. Begin with the most complex compound, barium sulfate. Since there's one Ba and one SO₄ unit on each side, those are already balanced. However, the reactant side has 2 Cl atoms (from BaCl₂) and 2 Na atoms (from Na₂SO₄), while the product side shows only 1 of each in NaCl. To balance, you need 2 NaCl molecules on the product side. The balanced equation becomes: BaCl2+Na2SO4→BaSO4+2NaCl\text{BaCl}_2 + \text{Na}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + 2\text{NaCl} The question asks specifically for the sum of coefficients of the reactants. The coefficient for BaCl₂ is 1 (when no coefficient is written, it's understood to be 1), and the coefficient for Na₂SO₄ is also 1. Therefore, 1 + 1 = 2. Choice A (2) correctly represents this sum. Choice B (3) might result from incorrectly including one product coefficient. Choice C (4) could come from adding all four coefficients in the entire equation (1+1+1+1). Choice D (5) has no clear mathematical basis from this equation. Remember: when balancing equations, invisible coefficients are always 1, and read questions carefully—they may ask only about reactants, products, or specific compounds.

Question 16

In the industrial production of iron, iron(III) oxide (Fe₂O₃) reacts with carbon monoxide gas (CO) to produce solid iron (Fe) and carbon dioxide gas (CO₂). When the equation for this reaction is balanced with the smallest whole-number coefficients, what is the coefficient for carbon monoxide?

  1. 1
  2. 2
  3. 3 (correct answer)
  4. 4
Explanation: When you encounter chemical equation balancing problems, you're applying the law of conservation of mass—atoms can neither be created nor destroyed, so you need equal numbers of each type of atom on both sides of the equation. Start by writing the unbalanced equation: Fe2O3+CO→Fe+CO2\text{Fe}_2\text{O}_3 + \text{CO} \rightarrow \text{Fe} + \text{CO}_2 Now systematically balance each element. Begin with the most complex compound, Fe₂O₃. Since it contains 2 iron atoms, you need 2 Fe on the product side: Fe2O3+CO→2Fe+CO2\text{Fe}_2\text{O}_3 + \text{CO} \rightarrow 2\text{Fe} + \text{CO}_2 Next, balance oxygen. Fe₂O₃ has 3 oxygen atoms, so you need 3 CO₂ molecules on the product side to account for these oxygens: Fe2O3+CO→2Fe+3CO2\text{Fe}_2\text{O}_3 + \text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2 Finally, balance carbon. With 3 CO₂ molecules containing 3 carbon atoms, you need 3 CO molecules on the reactant side: Fe2O3+3CO→2Fe+3CO2\text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2 The coefficient for CO is 3, making C correct. Choice A (1) represents the unbalanced equation. Choice B (2) might result from incorrectly trying to balance iron first without considering oxygen atoms from Fe₂O₃. Choice D (4) could come from miscounting oxygen atoms or attempting to balance carbon incorrectly. Always verify your final equation by counting atoms: 2 Fe, 6 O, and 3 C on each side confirms the equation is properly balanced with the smallest whole-number coefficients.

Question 17

When balancing the equation for the synthesis of ammonia from nitrogen and hydrogen (N₂ + H₂ → NH₃), a student determines the coefficients are 1, 3, and 2, respectively. Which fundamental law does this set of coefficients satisfy?

  1. The Law of Constant Composition
  2. The Law of Conservation of Mass (correct answer)
  3. Avogadro's Law
  4. The Law of Thermodynamics
Explanation: When you encounter chemical equation balancing questions, you're working with one of chemistry's most fundamental principles: atoms cannot be created or destroyed in ordinary chemical reactions. Let's examine the balanced equation: N2+3H2→2NH3N_2 + 3H_2 → 2NH_3. On the left side, you have 2 nitrogen atoms and 6 hydrogen atoms. On the right side, you have 2 nitrogen atoms (2 × 1) and 6 hydrogen atoms (2 × 3). The total number of each type of atom remains identical on both sides of the equation. This demonstrates the Law of Conservation of Mass (B) – matter is neither created nor destroyed, only rearranged. Choice A, the Law of Constant Composition, states that compounds always contain the same elements in the same proportions by mass. This doesn't relate to balancing equations but to compound composition. Choice C, Avogadro's Law, deals with the relationship between gas volume and the number of moles at constant temperature and pressure. While relevant to gas reactions, it's not what balancing coefficients directly demonstrates. Choice D, the Law of Thermodynamics, encompasses energy relationships in reactions, not the conservation of atoms during chemical changes. For HESI chemistry questions, remember that balanced chemical equations always reflect mass conservation. When you see coefficients in chemical equations, think "atom counting" – the coefficients ensure equal numbers of each element on both sides, satisfying the fundamental rule that atoms are conserved in chemical reactions.

Question 18

Copper metal reacts with concentrated nitric acid according to the unbalanced equation: Cu(s) + HNO₃(aq) → Cu(NO₃)₂(aq) + NO₂(g) + H₂O(l). A key feature of this reaction is that the nitrogen from nitric acid ends up in two different products. When this complex equation is correctly balanced, what is the coefficient for nitric acid (HNO₃)?

  1. 2
  2. 3
  3. 4 (correct answer)
  4. 6
Explanation: When you encounter redox reactions involving acids like nitric acid, you're dealing with electron transfer where the acid serves both as a reactant and an oxidizing agent. The key insight here is that nitrogen appears in two different products, meaning you need to track where all the nitrogen atoms go. To balance this equation systematically, start by recognizing that copper is oxidized (Cu → Cu²⁺) while nitrogen in nitric acid is reduced (N⁵⁺ → N⁴⁺ in NO₂). The balanced equation is: Cu(s)+4HNO3(aq)→Cu(NO3)2(aq)+2NO2(g)+2H2O(l)\text{Cu}(s) + 4\text{HNO}_3(aq) → \text{Cu(NO}_3)_2(aq) + 2\text{NO}_2(g) + 2\text{H}_2\text{O}(l) Each copper atom loses 2 electrons, while each nitrogen atom in HNO₃ that becomes NO₂ gains 1 electron. You need 4 HNO₃ molecules total: 2 provide the nitrate ions for Cu(NO₃)₂, and 2 are reduced to form the NO₂ gas. Answer choice A (2) only accounts for the nitrate ions needed for the copper salt, ignoring the HNO₃ molecules that get reduced. Answer choice B (3) represents a common miscalculation where students partially account for both roles of nitric acid but miss the stoichiometric balance. Answer choice D (6) overcounts the nitric acid needed, likely from incorrectly balancing the electron transfer. For HESI chemistry questions involving complex redox reactions, always track each element separately and remember that acids can play multiple roles. Write out half-reactions when the electron transfer isn't immediately obvious.

Question 19

When balancing Al2S3+H2O→Al(OH)3+H2SAl_2S_3 + H_2O \rightarrow Al(OH)_3 + H_2S, a student finds that the ratio of coefficients for H2OH_2O to H2SH_2S is 2:1. If this ratio is correct, what is the coefficient for Al(OH)3Al(OH)_3 in the balanced equation?

  1. 1
  2. 2 (correct answer)
  3. 3
  4. 6
Explanation: The balanced equation is Al2S3+6H2O→2Al(OH)3+3H2SAl_2S_3 + 6H_2O \rightarrow 2Al(OH)_3 + 3H_2S. The ratio of H2OH_2O to H2SH_2S is 6:3 = 2:1, confirming the student's ratio. The coefficient for Al(OH)3Al(OH)_3 is 2. Choice A (1) fails to account for the 2 aluminum atoms in Al2S3Al_2S_3. Choice C (3) incorrectly matches the coefficient of H2SH_2S. Choice D (6) incorrectly uses the coefficient of H2OH_2O.

Question 20

Consider the unbalanced equation: Ca3(PO4)2+SiO2+C→CaSiO3+CO+P4Ca_3(PO_4)_2 + SiO_2 + C \rightarrow CaSiO_3 + CO + P_4. When this equation is balanced with the smallest integer coefficients, what is the coefficient of carbon (C)?

  1. 5
  2. 10 (correct answer)
  3. 15
  4. 20
Explanation: This is a complex industrial reaction. The balanced equation is: 2Ca3(PO4)2+6SiO2+10C→6CaSiO3+10CO+P42Ca_3(PO_4)_2 + 6SiO_2 + 10C \rightarrow 6CaSiO_3 + 10CO + P_4. The coefficient of C is 10. Choice A (5) comes from balancing with half the required scale. Choice C (15) results from overcounting the oxygen balance requirements. Choice D (20) comes from doubling the correct coefficient unnecessarily.