The density of a salt solution is 1.13g`cm^(−3)` and it contains 18% of NaCI by weight The volume of the solution containing 36.0 g of the salt will be

Explanation

To solve the problem, we need to find the volume of the salt solution that contains 36.0 g of NaCl, given that the density of the solution is 1.13 g/cm³ and it contains 18% NaCl by weight.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Density of the solution = 1.13 g/cm³
- Percentage of NaCl by weight = 18%
- Mass of NaCl = 36.0 g

2. **Set Up the Equation**:
- Let the volume of the solution be \( V \) cm³.
- The mass of the solution can be calculated using the formula:
\[ \text{Mass of solution} = \text{Volume} \times \text{Density} = V \times 1.13 \]

3. **Calculate the Mass of NaCl in the Solution**:
- Since the solution contains 18% NaCl by weight, we can express this as:
\[ \text{Mass of NaCl} = 0.18 \times \text{Mass of solution} \]
- Substituting the mass of the solution:
\[ 36.0 = 0.18 \times (1.13 \times V) \]

4. **Solve for Volume \( V \)**:
- Rearranging the equation gives:
\[ 36.0 = 0.18 \times 1.13 \times V \]
- Calculate \( 0.18 \times 1.13 \):
\[ 0.18 \times 1.13 = 0.2034 \]
- Now substitute this back into the equation:
\[ 36.0 = 0.2034 \times V \]
- To find \( V \), divide both sides by 0.2034:
\[ V = \frac{36.0}{0.2034} \approx 176.5 \text{ cm}^3 \]

5. **Final Answer**:
- The volume of the solution containing 36.0 g of NaCl is approximately **176.5 cm³**.