To determine the mass of zinc carbonate (ZnCO₃) needed for the given reaction to produce 15.0 g of zinc chloride (ZnCl₂), follow these detailed steps:
1. Calculate the molar mass of ZnCl₂:
- Atomic masses (Ar): [tex]\( Zn = 65 \)[/tex], [tex]\( Cl = 35.5 \)[/tex]
- Molar mass of [tex]\(ZnCl_2\)[/tex]:
[tex]\[
65 + 2 \times 35.5 = 65 + 71 = 136 \text{ g/mol}
\][/tex]
2. Calculate the molar mass of ZnCO₃:
- Atomic masses (Ar): [tex]\( Zn = 65 \)[/tex], [tex]\( C = 12 \)[/tex], [tex]\( O = 16 \)[/tex]
- Molar mass of [tex]\(ZnCO_3\)[/tex]:
[tex]\[
65 + 12 + 3 \times 16 = 65 + 12 + 48 = 125 \text{ g/mol}
\][/tex]
3. Calculate the moles of ZnCl₂ needed:
- Desired mass of ZnCl₂: [tex]\( 15.0 \text{ g} \)[/tex]
- Moles of ZnCl₂:
[tex]\[
\text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{15.0 \text{ g}}{136 \text{ g/mol}} \approx 0.1103 \text{ mol}
\][/tex]
4. Calculate the mass of ZnCO₃ needed:
- Moles of ZnCO₃ needed is equal to moles of ZnCl₂ (1:1 ratio in the reaction):
[tex]\[
\text{mass} = \text{moles} \times \text{molar mass of ZnCO}_3 = 0.1103 \text{ mol} \times 125 \text{ g/mol} \approx 13.79 \text{ g}
\][/tex]
5. Determine the closest choice:
- Provided choices:
[tex]\[
A. \quad 11.0 \text{ g} \\
B. \quad 13.8 \text{ g} \\
C. \quad 15.0 \text{ g} \\
D. \quad 22.0 \text{ g}
\][/tex]
- The calculated mass of [tex]\( 13.79 \text{ g} \)[/tex] is closest to choice B: [tex]\( 13.8 \text{ g} \)[/tex].
Answer: B [tex]\(13.8 \text{ g}\)[/tex]
