The density of a salt solution is 1.13g`cm^(−3)` and it contains 20% of NaCI by weight The volume of the solution containing 18.0 g of the salt will be

Options

A. 79.6`cm^3`
B. 94.4`cm^3`
C. 80.6`cm^3`
D. None of these

Explanation

To solve the problem, we need to find the volume of a salt solution that contains 18.0 g of NaCl, given that the density of the solution is 1.13 g/cm³ and it contains 20% NaCl by weight.

### Step-by-step Solution:

1. **Understand the Given Information**:
- Density of the solution (d) = 1.13 g/cm³
- Percentage of NaCl by weight = 20%
- Mass of NaCl (salt) = 18.0 g

2. **Let the Volume of the Solution be \( x \) cm³**:
- The mass of the solution can be calculated using the formula:
\[ \text{Mass of solution} = \text{Density} \times \text{Volume} = 1.13 \times x \text{ g} \]

3. **Calculate the Mass of NaCl in the Solution**:
- Since the solution is 20% NaCl by weight, we can express the mass of NaCl in terms of the mass of the solution:
\[ \text{Mass of NaCl} = \frac{20}{100} \times \text{Mass of solution} = 0.20 \times (1.13 \times x) \]
- Setting this equal to the given mass of NaCl (18.0 g):
\[ 0.20 \times (1.13 \times x) = 18.0 \]

4. **Solve for \( x \)**:
- Rearranging the equation:
\[ 1.13 \times x = \frac{18.0}{0.20} \]
- Calculate the right side:
\[ \frac{18.0}{0.20} = 90.0 \]
- Therefore:
\[ 1.13 \times x = 90.0 \]
- Now, solve for \( x \):
\[ x = \frac{90.0}{1.13} \approx 79.646 \text{ cm}^3 \]

5. **Final Result**:
- The volume of the solution containing 18.0 g of NaCl is approximately:
\[ x \approx 79.6 \text{ cm}^3 \]