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 $\mathrm{O_2}$ and asked to find moles of $\mathrm{H_2O}$, the mole ratio conversion factor is $(2 \text{ moles } \mathrm{H_2O} / 1 \text{ mole } \mathrm{O_2})$ from the coefficients, so $5 \text{ moles } \mathrm{O_2} \times(2 \text{ moles } \mathrm{H_2O} / 1 \text{ mole } \mathrm{O_2}) = 10 \text{ moles } \mathrm{H_2O}$. The "moles $\mathrm{O_2}$" units cancel, leaving "moles $\mathrm{H_2O}$"—dimensional analysis ensures you set up the fraction correctly! For this problem, with $$2\mathrm{H_2O_2} \rightarrow 2\mathrm{H_2O} + \mathrm{O_2}$$ and 7.0 mol $\mathrm{H_2O_2}$ given to find mol $\mathrm{O_2}$, the conversion factor is $(1 \text{ mol } \mathrm{O_2} / 2 \text{ mol } \mathrm{H_2O_2})$, so $7.0 \text{ mol } \mathrm{H_2O_2} \times(1/2) = 3.5 \text{ mol } \mathrm{O_2}$. Choice B correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. Something like choice A might happen if you forget to halve and just use 2:1 incorrectly, but always divide by the given coefficient—you're doing great, just double-check the fraction setup! 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 $\mathrm{H_2}$. Find: moles $\mathrm{NH_3}$. Coefficients: $\mathrm{H_2}$ has 3, $\mathrm{NH_3}$ has 2. Conversion factor: $(2 \text{ moles } \mathrm{NH_3} / 3 \text{ moles } \mathrm{H_2})$. Calculation: $9 \text{ moles } \mathrm{H_2} \times(2/3) = 6 \text{ moles } \mathrm{NH_3}$. Check: 9:6 simplifies to 3:2, matching coefficient ratio 3:2 for $\mathrm{H_2}$:$\mathrm{NH_3}$ ✓. 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.

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.

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.

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 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! In this case, for $2\text{KClO}_3 \rightarrow 2\text{KCl} + 3\text{O}_2$ with 4.0 mol KClO3 given and O2 wanted, the conversion factor is $(3 \text{ mol O}_2 / 2 \text{ mol KClO}_3)$, 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 D might result from mistakenly using $(3/1)$ or ignoring the 2 for KClO3, but ensure both coefficients are used correctly. 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.

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.

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.

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 $4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3$ with 8.0 mol Fe given and $\text{Fe}_2\text{O}_3$ wanted, the conversion factor is $(2 \text{ mol } \text{Fe}_2\text{O}_3 / 4 \text{ mol } \text{Fe})$, so 8.0 mol Fe × $(2/4)$ = 4.0 mol $\text{Fe}_2\text{O}_3$. Choice C correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. Choice A might result from multiplying by $(4/2)$ instead of $(2/4)$, but always verify the ratio direction with the equation's 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 $\text{H}_2$. 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.

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 the equation 4Fe + 3O₂ → 2Fe₂O₃, we're given 6.0 mol Fe and need to find moles of Fe₂O₃ formed. The mole ratio conversion factor is (2 moles Fe₂O₃ / 4 moles Fe) from the coefficients, so: 6.0 mol Fe × (2 mol Fe₂O₃ / 4 mol Fe) = 6.0 × (2/4) = 6.0 × (1/2) = 3.0 mol Fe₂O₃. Choice A correctly calculates 3.0 mol by applying the 2:4 (or 1:2) coefficient ratio as a conversion factor and performing accurate arithmetic. Common errors include using the wrong ratio or multiplying by 2 instead of dividing, which would give 12.0 mol. 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. Quick verification: 6.0 mol Fe produces 3.0 mol Fe₂O₃, giving ratio 6:3 = 2:1, matching the coefficient ratio 4:2 = 2:1 for Fe:Fe₂O₃ ✓.

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 $$4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3$$ and 8.0 mol Fe given to find mol Fe2O3, the conversion factor is ($2 \text{ mol Fe}_2\text{O}_3 / 4 \text{ mol Fe}$), so $8.0 \text{ mol Fe} \times(2/4) = 4.0 \text{ mol Fe}_2\text{O}_3$. Choice C correctly calculates moles by applying the appropriate coefficient ratio as a conversion factor and performing accurate arithmetic. A distractor like choice D could stem from using only half the ratio or forgetting to simplify 2/4 to 1/2, but practice makes perfect—ensure the coefficients match exactly! 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: ($2 \text{ moles NH}_3 / 3 \text{ moles H}_2$). 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.

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.