Questions 10-13 refer to the following information. Cu(s) + 4 HNO3(aq) → Cu(NO3)2(aq) + 2 NO2(g) + 2 — Stoichiometry Chemistry Question

STEPS:

1. Analyze the stoichiometry of the reaction:
Review the balanced chemical equation provided in the problem description:
$$\text{Cu}(s) + 4\ \text{HNO}_3(aq) \rightarrow \text{Cu(NO}_3)_2(aq) + 2\ \text{NO}_2(g) + 2\ \text{H}_2\text{O}(l)$$
The stoichiometric coefficient in front of solid copper, $\text{Cu}(s)$, is 1, and the coefficient in front of copper(II) nitrate, $\text{Cu(NO}_3)_2(aq)$, is also 1. This indicates a $1:1$ molar ratio between the reacting copper metal and the dissolved copper(II) nitrate product.
2. Determine the moles of copper metal in the original sample:
Because of the $1:1$ stoichiometry, if the reaction produces $0.010\text{ mol}$ of $\text{Cu(NO}_3)_2$, then the amount of copper metal that reacted must be exactly equal to that value:
$$\text{Moles of Cu} = \text{Moles of Cu(NO}_3)_2 = \mathbf{0.010\text{ mol}}$$
3. Calculate the mass of the reacting copper metal:
To convert moles of copper to grams, multiply by the molar mass of copper ($\text{Cu} \approx 63.55\text{ g/mol}$):
$$\text{Mass of Cu} = 0.010\text{ mol} \times 63.55\text{ g/mol} = \mathbf{0.636\text{ g}}$$
*(For rapid mental math or scratch work on the calculator-free multiple-choice section, rounding the molar mass of copper to $64\text{ g/mol}$ yields a very close approximation of $\mathbf{0.64\text{ g}}$).*
4. Calculate the mass percent of copper in the original mixture:
The original sample of the metal mixture (containing both copper and aluminum) had a total mass of $2.00\text{ g}$. Use the mass percent formula to find the percentage of copper by mass:
$$\text{Mass } \% \text{ of Cu} = \left( \frac{\text{Mass of Cu}}{\text{Total mass of sample}} \right) \times 100\%$$
$$\text{Mass } \% \text{ of Cu} = \left( \frac{0.636\text{ g}}{2.00\text{ g}} \right) \times 100\% = \mathbf{31.8\%}$$
5. Select the closest match among the options:
The calculated value of $31.8\%$ rounds perfectly to $32\%$, which corresponds to Option B.

*

WHY_OTHERS_WRONG:

• Option A is incorrect (16%): A student might arrive at this value if they make a stoichiometric error and assume a $1:2$ ratio between $\text{Cu}$ and $\text{Cu(NO}_3)_2$ (resulting in $0.0050\text{ mol}$ of $\text{Cu}$ and a mass of $0.32\text{ g}$), or if they calculate the mass of copper correctly as $0.32\text{ g}$ but divide by double the actual sample mass (e.g., dividing by $4.00\text{ g}$ instead of $2.00\text{ g}$).
• Option C is incorrect (64%): This value matches the numerical value of the molar mass of copper ($64\text{ g/mol}$). A student would make this error if they calculate the mass of copper in the sample as $0.64\text{ g}$ and then simply drop the decimal place to assume it represents $64\%$, completely forgetting to divide by the original sample mass of $2.00\text{ g}$.
• Option D is incorrect (96%): This option has no valid stoichiometric basis. It represents $3 \times 32\%$, which could result from tripling the correct answer, or it might be selected if a student confuses the mass percent of the unreacted aluminum in the mixture (which would be $100\% - 32\% = 68\%$) and performs an incorrect subtraction or ratio calculation.