An alloy of gold and silver contains `38.5%` silver by mass and has a density of `14.6 g.mL^(-1)`. What is the molar concentration of silver in this alloy :

Options

A. `52.1 mol.L^(-1)`
B. `45.6 mol.L^(-1)`
C. `3.57 mol.L^(-1)`
D. `2.64 mol.L^(-1)`

Explanation

To find the molar concentration of silver in the alloy, we can follow these steps:

### Step 1: Determine the mass of silver in a given mass of the alloy.
Given that the alloy contains 38.5% silver by mass, we can assume a total mass of the alloy for our calculations. For simplicity, let's assume we have 100 g of the alloy.

\[ \text{Mass of silver} = 38.5\% \text{ of 100 g} = 38.5 \text{ g} \]

### Step 2: Calculate the number of moles of silver.
To find the number of moles of silver, we use the molar mass of silver (Ag), which is approximately 107.87 g/mol.

\[ \text{Number of moles of silver} = \frac{\text{mass of silver}}{\text{molar mass of silver}} = \frac{38.5 \text{ g}}{107.87 \text{ g/mol}} \approx 0.357 \text{ moles} \]

### Step 3: Calculate the volume of the alloy.
We know the density of the alloy is 14.6 g/mL. Using this, we can find the volume of the 100 g of alloy.

\[ \text{Volume of alloy} = \frac{\text{mass of alloy}}{\text{density}} = \frac{100 \text{ g}}{14.6 \text{ g/mL}} \approx 6.85 \text{ mL} \]

### Step 4: Convert the volume from mL to L.
Since molar concentration is expressed in moles per liter, we need to convert the volume from mL to L.

\[ \text{Volume in liters} = \frac{6.85 \text{ mL}}{1000} = 0.00685 \text{ L} \]

### Step 5: Calculate the molar concentration of silver.
Now we can calculate the molar concentration (C) of silver using the formula:

\[ C = \frac{\text{number of moles of silver}}{\text{volume in liters}} = \frac{0.357 \text{ moles}}{0.00685 \text{ L}} \approx 52.1 \text{ mol/L} \]

### Final Answer:
The molar concentration of silver in the alloy is approximately **52.1 mol/L**.

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