Chemistry · Learn by Concept

Chemistry Help: Use Mole Ratios

Review real example questions for Use Mole Ratios in Chemistry.

Question 1 / 10

0 of 10 answered

Consider the balanced equation: $6CO_2 + 6H_2O \rightarrow C_6H_{12}O_6 + 6O_2$ If a plant uses $12 \text{ mol}$ of $CO_2$ in photosynthesis, how many moles of $O_2$ are produced (assuming enough $H_2O$ is available)?

All questions

Question 1

$2 \text{ mol}$
$72 \text{ mol}$
$6 \text{ mol}$
$12 \text{ mol}$ (correct answer)

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , if given 5 moles of $\text{O}_2$ and asked to find moles of $\text{H}_2\text{O}$ , the mole ratio conversion factor is $(2 \text{ moles } \text{H}_2\text{O} / 1 \text{ mole } \text{O}_2)$ from the coefficients, so $5 \text{ moles } \text{O}_2 \times (2 \text{ moles } \text{H}_2\text{O} / 1 \text{ mole } \text{O}_2) = 10 \text{ moles } \text{H}_2\text{O}$ . The "moles $\text{O}_2$ " units cancel, leaving "moles $\text{H}_2\text{O}$ "—dimensional analysis ensures you set up the fraction correctly! For this specific question, with the balanced equation $6\text{CO}_2 + 6\text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2$ and 12 mol of $\text{CO}_2$ given, the conversion factor to find moles of $\text{O}_2$ is $(6 \text{ mol } \text{O}_2 / 6 \text{ mol } \text{CO}_2)$ , so $12 \text{ mol } \text{CO}_2 \times (6/6) = 12 \text{ mol } \text{O}_2$ . Choice D correctly calculates the moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. A common distractor like choice B (72 mol) might result from multiplying coefficients unnecessarily, like 6×12, but stick to the ratio and given moles only. The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: (coefficient of wanted substance / coefficient of given substance). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$ . Given: 9 moles $\text{H}_2$ . Find: moles $\text{NH}_3$ . Coefficients: $\text{H}_2$ has 3, $\text{NH}_3$ has 2. Conversion factor: $(2 \text{ moles } \text{NH}_3 / 3 \text{ moles } \text{H}_2)$ . Calculation: $9 \text{ moles } \text{H}_2 \times (2/3) = 6 \text{ moles } \text{NH}_3$ . Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for $\text{H}_2$ : $\text{NH}_3$ ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.

Question 2

Aluminum reacts with chlorine gas to form aluminum chloride: $2\text{Al} + 3\text{Cl}_2 \rightarrow 2\text{AlCl}_3$ If $4.0\ \text{mol}$ of $\text{Al}$ react completely, how many moles of $\text{Cl}_2$ are needed?

$6.0\ \text{mol}$ (correct answer)
$8.0\ \text{mol}$
$3.0\ \text{mol}$
$2.0\ \text{mol}$

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , if given 5 moles of $\text{O}_2$ and asked to find moles of $\text{H}_2\text{O}$ , the mole ratio conversion factor is $(2 \text{ moles } \text{H}_2\text{O} / 1 \text{ mole } \text{O}_2)$ from the coefficients, so 5 moles $\text{O}_2$ × $(2 \text{ moles } \text{H}_2\text{O} / 1 \text{ mole } \text{O}_2)$ = 10 moles $\text{H}_2\text{O}$ . The "moles $\text{O}_2$ " units cancel, leaving "moles $\text{H}_2\text{O}$ "—dimensional analysis ensures you set up the fraction correctly! In this case, for $2\text{Al} + 3\text{Cl}_2 \rightarrow 2\text{AlCl}_3$ with 4.0 mol Al given and Cl2 wanted, the conversion factor is $(3 \text{ mol } \text{Cl}_2 / 2 \text{ mol } \text{Al})$ , so 4.0 mol Al × $(3/2)$ = 6.0 mol Cl2. Choice A correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. Choice B might result from using $(2/3)$ instead of $(3/2)$ , inverting the ratio, but check by seeing if the proportion matches the coefficients. The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: (coefficient of wanted substance / coefficient of given substance). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$ . Given: 9 moles H2. Find: moles NH3. Coefficients: H2 has 3, NH3 has 2. Conversion factor: $(2 \text{ moles } \text{NH}_3 / 3 \text{ moles } \text{H}_2)$ . Calculation: 9 moles H2 × $(2/3)$ = 6 moles NH3. Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for H2:NH3 ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.

Question 3

Consider the balanced equation: $CaCO_3 \rightarrow CaO + CO_2$ If $7.5 \text{ mol}$ of $CaCO_3$ decompose completely, how many moles of $CO_2$ are produced?

$15.0 \text{ mol}$
$7.5 \text{ mol}$ (correct answer)
$3.75 \text{ mol}$
$8.5 \text{ mol}$

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , if given 5 moles of $\text{O}_2$ and asked to find moles of $\text{H}_2\text{O}$ , the mole ratio conversion factor is $(2 \text{ moles } \text{H}_2\text{O} / 1 \text{ mole } \text{O}_2)$ from the coefficients, so 5 moles $\text{O}_2$ × $(2 \text{ moles } \text{H}_2\text{O} / 1 \text{ mole } \text{O}_2)$ = 10 moles $\text{H}_2\text{O}$ . The "moles $\text{O}_2$ " units cancel, leaving "moles $\text{H}_2\text{O}$ "—dimensional analysis ensures you set up the fraction correctly! For this specific question, with the balanced equation $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$ and 7.5 mol of $\text{CaCO}_3$ given, the conversion factor to find moles of $\text{CO}_2$ is $(1 \text{ mol } \text{CO}_2 / 1 \text{ mol } \text{CaCO}_3)$ , so 7.5 mol $\text{CaCO}_3$ × $(1/1)$ = 7.5 mol $\text{CO}_2$ . Choice B correctly calculates the moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. A common distractor like choice A (15.0 mol) might result from doubling the amount or using a wrong coefficient, but confirm it's a 1:1 ratio here. The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: (coefficient of wanted substance / coefficient of given substance). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$ . Given: 9 moles $\text{H}_2$ . Find: moles $\text{NH}_3$ . Coefficients: $\text{H}_2$ has 3, $\text{NH}_3$ has 2. Conversion factor: $(2 \text{ moles } \text{NH}_3 / 3 \text{ moles } \text{H}_2)$ . Calculation: 9 moles $\text{H}_2$ × $(2/3)$ = 6 moles $\text{NH}_3$ . Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for $\text{H}_2$ : $\text{NH}_3$ ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.

Question 4

Consider the balanced equation: $C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O$ If $2.0\ \text{mol}$ of $C_3H_8$ burn completely, how many moles of $CO_2$ are produced?

$\tfrac{2}{3}\ \text{mol}$
$6.0\ \text{mol}$ (correct answer)
$10.0\ \text{mol}$
$3.0\ \text{mol}$

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from $2H_2 + O_2 \rightarrow 2H_2O$ , if given 5 moles of O2 and asked to find moles of H2O, the mole ratio conversion factor is $(2 \text{ moles H}_2\text{O} / 1 \text{ mole O}_2)$ from the coefficients, so 5 moles O2 × $(2 \text{ moles H}_2\text{O} / 1 \text{ mole O}_2)$ = 10 moles H2O. The "moles O2" units cancel, leaving "moles H2O"—dimensional analysis ensures you set up the fraction correctly! For this specific question, with the balanced equation $C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O$ and 2.0 mol of C3H8 given, the conversion factor to find moles of CO2 is $(3 \text{ mol CO}_2 / 1 \text{ mol C}_3\text{H}_8)$ , so 2.0 mol C3H8 × $(3/1)$ = 6.0 mol CO2. Choice B correctly calculates the moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. A common distractor like choice A ( $\tfrac{2}{3} \text{ mol}$ ) might result from inverting the ratio to (1/3) or a calculation error, but always put the wanted on top to avoid inversion mistakes. The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: (coefficient of wanted substance / coefficient of given substance). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: $N_2 + 3H_2 \rightarrow 2NH_3$ . Given: 9 moles H2. Find: moles NH3. Coefficients: H2 has 3, NH3 has 2. Conversion factor: $(2 \text{ moles NH}_3 / 3 \text{ moles H}_2)$ . Calculation: 9 moles H2 × $(2/3)$ = 6 moles NH3. Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for H2:NH3 ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.

Question 5

Aluminum reacts with chlorine to form aluminum chloride: $\mathrm{2Al + 3Cl_2 \rightarrow 2AlCl_3}$ If $3.0 \, \text{mol}$ of $\mathrm{Cl_2}$ react completely, how many moles of $\mathrm{AlCl_3}$ form?

$2.0 \, \text{mol}$ (correct answer)
$4.5 \, \text{mol}$
$1.5 \, \text{mol}$
$3.0 \, \text{mol}$

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , if given 5 moles of O2 and asked to find moles of H2O, the mole ratio conversion factor is ( $\frac{2 \text{ moles H}_2\text{O}}{1 \text{ mole O}_2}$ ) from the coefficients, so 5 moles O2 × ( $\frac{2 \text{ moles H}_2\text{O}}{1 \text{ mole O}_2}$ ) = 10 moles H2O. The "moles O2" units cancel, leaving "moles H2O"—dimensional analysis ensures you set up the fraction correctly! For this problem, with $2\text{Al} + 3\text{Cl}_2 \rightarrow 2\text{AlCl}_3$ and 3.0 mol Cl2 given to find mol AlCl3, the conversion factor is ( $\frac{2 \text{ mol AlCl}_3}{3 \text{ mol Cl}_2}$ ), so 3.0 mol Cl2 × ( $\frac{2}{3}$ ) = 2.0 mol AlCl3. Choice A correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. Choice C could result from using $\frac{3}{2}$ instead, inverting the fraction, but always verify with the proportion check to catch that—excellent effort! The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: ( $\frac{\text{coefficient of wanted substance}}{\text{coefficient of given substance}}$ ). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$ . Given: 9 moles H2. Find: moles NH3. Coefficients: H2 has 3, NH3 has 2. Conversion factor: ( $\frac{2 \text{ moles NH}_3}{3 \text{ moles H}_2}$ ). Calculation: 9 moles H2 × ( $\frac{2}{3}$ ) = 6 moles NH3. Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for H2:NH3 ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.

Question 6

Photosynthesis can be represented by $\mathrm{6CO_2 + 6H_2O \rightarrow C_6H_{12}O_6 + 6O_2}$ If a plant uses $12\ \text{mol}$ of $\mathrm{CO_2}$ , how many moles of $\mathrm{O_2}$ are produced (assume enough water is available)?

$1\ \text{mol}$
$72\ \text{mol}$
$6\ \text{mol}$
$12\ \text{mol}$ (correct answer)

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , if given 5 moles of O2 and asked to find moles of H2O, the mole ratio conversion factor is $(2\ \text{moles H}_2\text{O} / 1\ \text{mole O}_2)$ from the coefficients, so $5\ \text{moles O}_2 \times (2\ \text{moles H}_2\text{O} / 1\ \text{mole O}_2) = 10\ \text{moles H}_2\text{O}$ . The "moles O2" units cancel, leaving "moles H2O"—dimensional analysis ensures you set up the fraction correctly! For this problem, with $6\mathrm{CO_2} + 6\mathrm{H_2O} \rightarrow \mathrm{C_6H_{12}O_6} + 6\mathrm{O_2}$ and 12 mol CO2 given to find mol O2, the conversion factor is $(6\ \text{mol O}_2 / 6\ \text{mol CO}_2)$ , so $12\ \text{mol CO}_2 \times (6/6) = 12\ \text{mol O}_2$ . Choice D correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. Choice B might arise from confusing with other ratios or arithmetic errors, but since it's 1:1 simplified, it's direct—keep practicing these larger coefficients! The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: (coefficient of wanted substance / coefficient of given substance). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: $N_2 + 3H_2 \rightarrow 2NH_3$ . Given: 9 moles H2. Find: moles NH3. Coefficients: H2 has 3, NH3 has 2. Conversion factor: $(2\ \text{moles NH}_3 / 3\ \text{moles H}_2)$ . Calculation: $9\ \text{moles H}_2 \times (2/3) = 6\ \text{moles NH}_3$ . Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for H2:NH3 ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.

Question 7

For the combustion reaction $\mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O}$ if $3.0\ \text{mol}$ of $\mathrm{CH_4}$ burn completely, how many moles of $\mathrm{O_2}$ are required?

$1.5\ \text{mol}$
$3.0\ \text{mol}$
$5.0\ \text{mol}$
$6.0\ \text{mol}$ (correct answer)

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from 2H2 + O2 → 2H2O, if given 5 moles of O2 and asked to find moles of H2O, the mole ratio conversion factor is (2 moles H2O / 1 mole O2) from the coefficients, so 5 moles O2 × (2 moles H2O / 1 mole O2) = 10 moles H2O. The "moles O2" units cancel, leaving "moles H2O"—dimensional analysis ensures you set up the fraction correctly! For this problem, with CH4 + 2O2 → CO2 + 2H2O and 3.0 mol CH4 given to find mol O2, the conversion factor is (2 mol O2 / 1 mol CH4), so 3.0 mol CH4 × (2/1) = 6.0 mol O2. Choice D correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. A distractor like choice B could result from halving instead of multiplying by 2, but remember the ratio is 2:1, so double the moles of CH4—keep up the good work! The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: (coefficient of wanted substance / coefficient of given substance). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: N2 + 3H2 → 2NH3. Given: 9 moles H2. Find: moles NH3. Coefficients: H2 has 3, NH3 has 2. Conversion factor: (2 moles NH3 / 3 moles H2). Calculation: 9 moles H2 × (2/3) = 6 moles NH3. Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for H2:NH3 ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.

Question 8

Photosynthesis can be represented by the balanced equation: $6\text{CO}_2 + 6\text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2$ If a plant uses $12 \text{mol}$ of $\text{CO}_2$ completely, how many moles of $\text{O}_2$ are produced?

$2 \text{mol}$
$6 \text{mol}$
$12 \text{mol}$ (correct answer)
$72 \text{mol}$

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$ , if given 5 moles of O2 and asked to find moles of H2O, the mole ratio conversion factor is ( $2$ moles H2O / $1$ mole O2) from the coefficients, so 5 moles O2 × ( $2$ moles H2O / $1$ mole O2) = 10 moles H2O. The "moles O2" units cancel, leaving "moles H2O"—dimensional analysis ensures you set up the fraction correctly! In this case, for $6\text{CO}_2 + 6\text{H}_2\text{O} \rightarrow \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2$ with 12 mol CO2 given and O2 wanted, the conversion factor is ( $6$ mol O2 / $6$ mol CO2), so 12 mol CO2 × ( $6/6$ ) = 12 mol O2. Choice C correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. Choice D might result from multiplying by 6 without dividing, but remember to use the full ratio fraction. The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: ( $\text{coefficient of wanted substance} / \text{coefficient of given substance}$ ). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$ . Given: 9 moles H2. Find: moles NH3. Coefficients: H2 has 3, NH3 has 2. Conversion factor: ( $2$ moles NH3 / $3$ moles H2). Calculation: 9 moles H2 × ( $2/3$ ) = 6 moles NH3. Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for H2:NH3 ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.

Question 9

In the reaction $\mathrm{2KClO_3 \rightarrow 2KCl + 3O_2}$ how many moles of $\mathrm{O_2}$ are produced when $4.0\ \text{mol}$ of $\mathrm{KClO_3}$ decompose completely?

$6.0\ \text{mol}$ (correct answer)
$3.0\ \text{mol}$
$8.0\ \text{mol}$
$2.0\ \text{mol}$

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from 2H2 + O2 → 2H2O, if given 5 moles of O2 and asked to find moles of H2O, the mole ratio conversion factor is (2 moles H2O / 1 mole O2) from the coefficients, so 5 moles O2 × (2 moles H2O / 1 mole O2) = 10 moles H2O. The "moles O2" units cancel, leaving "moles H2O"—dimensional analysis ensures you set up the fraction correctly! For this problem, with 2KClO3 → 2KCl + 3O2 and 4.0 mol KClO3 given to find mol O2, the conversion factor is (3 mol O2 / 2 mol KClO3), so 4.0 mol KClO3 × (3/2) = 6.0 mol O2. Choice A correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. Choice B might occur if you use 2/3 instead of 3/2, inverting the ratio, but remember to put the wanted (O2) on top—nice catch if you spotted that! The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: (coefficient of wanted substance / coefficient of given substance). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: N2 + 3H2 → 2NH3. Given: 9 moles H2. Find: moles NH3. Coefficients: H2 has 3, NH3 has 2. Conversion factor: (2 moles NH3 / 3 moles H2). Calculation: 9 moles H2 × (2/3) = 6 moles NH3. Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for H2:NH3 ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.

Question 10

Calcium carbonate decomposes as shown: $\mathrm{CaCO_3 \rightarrow CaO + CO_2}$ If $0.75 \text{ mol}$ of $\mathrm{CaCO_3}$ decompose completely, how many moles of $\mathrm{CO_2}$ are produced?

$0.75 \text{ mol}$ (correct answer)
$1.50 \text{ mol}$
$0.25 \text{ mol}$
$0.50 \text{ mol}$

Explanation: This question tests your ability to use mole ratios from balanced equations as conversion factors to calculate how many moles of one substance react with or form from a given number of moles of another substance. Using mole ratios for stoichiometry calculations follows a simple pattern: from the balanced equation, create a conversion factor (fraction) using coefficients where the numerator is the coefficient of the substance you want to find and the denominator is the coefficient of the substance you're given, then multiply the given number of moles by this conversion factor. For example, from $2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$ , if given 5 moles of O2 and asked to find moles of H2O, the mole ratio conversion factor is $(2 \text{ moles H2O} / 1 \text{ mole O2})$ from the coefficients, so 5 moles O2 × $(2 \text{ moles H2O} / 1 \text{ mole O2}) = 10 \text{ moles H2O}$ . The "moles O2" units cancel, leaving "moles H2O"—dimensional analysis ensures you set up the fraction correctly! For this problem, with $\mathrm{CaCO_3} \rightarrow \mathrm{CaO} + \mathrm{CO_2}$ and 0.75 mol CaCO3 given to find mol CO2, the conversion factor is $(1 \text{ mol CO2} / 1 \text{ mol CaCO3})$ , so 0.75 mol CaCO3 × $(1/1) = 0.75 \text{ mol CO2}$ . Choice A correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. Choice D might come from misreading coefficients or adding extras, but it's a clean 1:1 ratio—you're on the right track! The mole ratio calculation recipe: (1) Write the balanced equation and identify the given substance and wanted substance. (2) Read their coefficients from the equation. (3) Set up conversion factor as fraction: (coefficient of wanted substance / coefficient of given substance). Put what you want on top, what you have on bottom! (4) Multiply: (given moles) × (conversion factor) = answer in moles. Example step-by-step: $\mathrm{N_2} + 3\mathrm{H_2} \rightarrow 2\mathrm{NH_3}$ . Given: 9 moles H2. Find: moles NH3. Coefficients: H2 has 3, NH3 has 2. Conversion factor: $(2 \text{ moles NH3} / 3 \text{ moles H2})$ . Calculation: 9 moles H2 × $(2/3) = 6 \text{ moles NH3}$ . Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for H2:NH3 ✓. Quick verification trick: after calculating, check if your answer maintains the coefficient ratio. If equation shows 2:1 ratio and you got 6 moles from 3 moles given, does 6:3 equal 2:1? Yes (both are 2:1), so answer likely correct! If equation shows 1:3 ratio and you got 9 moles from 3 moles, does 9:3 equal 1:3? No (9:3 = 3:1, not 1:3), so error occurred—probably inverted the ratio! This proportion check catches most mistakes and takes 3 seconds.