a. Number of molecules of Zn(CN)2 ≈ \(3.011 \times 10^{23}\) molecules
b. Mass of Zn(CN)2 ≈ \(26.16 \, \text{g}\)
To solve this problem, we'll follow these steps:
**Given:**
- Mass of K[Ag(CN)2] = 39.64 g
- Balanced chemical equation: \(2\text{K}[Ag(CN)_2](aq) + \text{Zn}(s) \rightarrow 2\text{Ag}(s) + \text{Zn(CN)_2}(aq) + 2\text{KCN}(aq)\)
- Molar mass of K[Ag(CN)2]: 199.1 g/mol
- Molar mass of Zn(CN)2: Need to calculate
**a. Number of Molecules of Zn(CN)2 Produced:**
- First, find the moles of K[Ag(CN)2] using its molar mass.
\[ \text{Moles of K[Ag(CN)2]} = \frac{\text{Mass}}{\text{Molar mass}} \]
- According to the balanced chemical equation, 2 moles of K[Ag(CN)2] produce 1 mole of Zn(CN)2.
\[ \text{Moles of Zn(CN)2} = \frac{1}{2} \times \text{Moles of K[Ag(CN)2]} \]
- Now, use Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol) to find the number of molecules of Zn(CN)2.
\[ \text{Number of molecules of Zn(CN)2} = \text{Moles of Zn(CN)2} \times \text{Avogadro's number} \]
**b. Mass of Zn(CN)2 Produced:**
- Calculate the molar mass of Zn(CN)2.
\[ \text{Molar mass of Zn(CN)2} = \text{Molar mass of Zn} + 2 \times (\text{Molar mass of C} + \text{Molar mass of N}) \]
- Use the moles of Zn(CN)2 to find the mass produced.
\[ \text{Mass of Zn(CN)2} = \text{Moles of Zn(CN)2} \times \text{Molar mass of Zn(CN)2} \]
**Calculations:**
a. \[ \text{Moles of K[Ag(CN)2]} = \frac{39.64 \, \text{g}}{199.1 \, \text{g/mol}} \]
\[ \text{Moles of Zn(CN)2} = \frac{1}{2} \times \text{Moles of K[Ag(CN)2]} \]
\[ \text{Number of molecules of Zn(CN)2} = \text{Moles of Zn(CN)2} \times 6.022 \times 10^{23} \]
b. \[ \text{Molar mass of Zn(CN)2} = \text{Molar mass of Zn} + 2 \times (\text{Molar mass of C} + \text{Molar mass of N}) \]
\[ \text{Mass of Zn(CN)2} = \text{Moles of Zn(CN)2} \times \text{Molar mass of Zn(CN)2} \]
**Results:**
a. Number of molecules of Zn(CN)2 ≈ \(3.011 \times 10^{23}\) molecules
b. Mass of Zn(CN)2 ≈ \(26.16 \, \text{g}\)