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 use the formula for molar concentration based on weight percentage and density. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Percentage of silver (by mass) = 38.5%
- Density of the alloy = 14.6 g/mL
- Molar mass of silver (Ag) = 108 g/mol

### Step 2: Use the formula for molar concentration
The formula for molar concentration (C) in terms of weight percentage (W) is given by:

\[ C = \frac{(\text{W by W percentage}) \times (\text{Density}) \times 10}{\text{Molar mass of the solute}} \]

### Step 3: Substitute the values into the formula
Now, substituting the values we have:

\[ C = \frac{(38.5) \times (14.6) \times 10}{108} \]

### Step 4: Calculate the numerator
First, calculate the numerator:

\[ 38.5 \times 14.6 \times 10 = 5631 \]

### Step 5: Calculate the molar concentration
Now, divide the result by the molar mass of silver:

\[ C = \frac{5631}{108} \approx 52.1 \text{ mol/L} \]

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

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