Wood's metal contains `50.0%` bismuth, `25.0%` lead, `12.5%` tin and `12.5%` cadmium by mass. What is the mole fraction of tin ?(\ (Atomic mass : `Bi=209, Pb=207, Sn=119, Cd=112)`

Options

A. `0.202`
B. `0.158`
C. `0.176`
D. `0.221`

Answer

To find the mole fraction of tin in Wood's metal, we will follow these steps:

### Step 1: Calculate the mass of each component in a 100 g sample
Since the percentages are given by mass, we can assume we have a 100 g sample of Wood's metal. This makes the calculations straightforward.

- Mass of bismuth (Bi) = 50.0 g
- Mass of lead (Pb) = 25.0 g
- Mass of tin (Sn) = 12.5 g
- Mass of cadmium (Cd) = 12.5 g

### Step 2: Calculate the number of moles of each component
To find the number of moles, we will use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

- Moles of bismuth (Bi):
\[ \text{Moles of Bi} = \frac{50.0 \, \text{g}}{209 \, \text{g/mol}} \approx 0.239 \, \text{mol} \]

- Moles of lead (Pb):
\[ \text{Moles of Pb} = \frac{25.0 \, \text{g}}{207 \, \text{g/mol}} \approx 0.121 \, \text{mol} \]

- Moles of tin (Sn):
\[ \text{Moles of Sn} = \frac{12.5 \, \text{g}}{119 \, \text{g/mol}} \approx 0.105 \, \text{mol} \]

- Moles of cadmium (Cd):
\[ \text{Moles of Cd} = \frac{12.5 \, \text{g}}{112 \, \text{g/mol}} \approx 0.112 \, \text{mol} \]

### Step 3: Calculate the total number of moles
Now, we will sum up the moles of all components:
\[ \text{Total moles} = \text{Moles of Bi} + \text{Moles of Pb} + \text{Moles of Sn} + \text{Moles of Cd} \]
\[ \text{Total moles} = 0.239 + 0.121 + 0.105 + 0.112 \approx 0.577 \, \text{mol} \]

### Step 4: Calculate the mole fraction of tin
The mole fraction of tin (Sn) is given by the formula:
\[ \text{Mole fraction of Sn} = \frac{\text{Moles of Sn}}{\text{Total moles}} \]
\[ \text{Mole fraction of Sn} = \frac{0.105}{0.577} \approx 0.182 \]

### Final Answer
The mole fraction of tin in Wood's metal is approximately **0.182**.

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