The weight percent of sucrose (formula weight = 342 g `"mol"^(-1)` in an aqueous solution is 3.42. The density of the solution is 1 g `mL^(-1)`, the concentration of sucrose in the solution in mol `L^(-1)` is

Options

A. 0.01
B. 0.1
C. 1
D. 10

Explanation

To find the concentration of sucrose in the solution in mol/L, we can follow these steps:

### Step 1: Understand the Given Information
- Weight percent of sucrose = 3.42%
- Molar mass of sucrose = 342 g/mol
- Density of the solution = 1 g/mL

### Step 2: Calculate the Mass of Sucrose in 100 g of Solution
Since the weight percent is given as 3.42%, this means that in 100 g of the solution, there are 3.42 g of sucrose.

### Step 3: Calculate the Volume of the Solution
Using the density of the solution, we can find the volume. The density is given as 1 g/mL, which means:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{100 \text{ g}}{1 \text{ g/mL}} = 100 \text{ mL} \]
To convert this volume into liters:
\[ 100 \text{ mL} = \frac{100}{1000} \text{ L} = 0.1 \text{ L} \]

### Step 4: Calculate the Number of Moles of Sucrose
To find the number of moles of sucrose, we use the formula:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{3.42 \text{ g}}{342 \text{ g/mol}} = 0.01 \text{ mol} \]

### Step 5: Calculate the Concentration in mol/L
Now, we can find the concentration (molarity) of sucrose in the solution:
\[ \text{Concentration (C)} = \frac{\text{Number of moles}}{\text{Volume in L}} = \frac{0.01 \text{ mol}}{0.1 \text{ L}} = 0.1 \text{ mol/L} \]

### Final Answer
The concentration of sucrose in the solution is **0.1 mol/L**.

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