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 30.0 g of the salt will be

Explanation

To solve the problem, we need to find the volume of the salt solution that contains 30.0 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. **Identify the Given Information:**
- Density of the salt solution (d) = 1.13 g/cm³
- Percentage of NaCl by weight = 18%
- Mass of NaCl (m_NaCl) = 30.0 g

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

3. **Calculate the Mass of NaCl in the Solution:**
- The mass of NaCl in the solution is given as 18% of the total mass of the solution:
\[ \text{Mass of NaCl} = \frac{18}{100} \times \text{Mass of solution} \]
- Substituting the expression for the mass of the solution:
\[ 30.0 = \frac{18}{100} \times (1.13 \times V) \]

4. **Rearrange the Equation:**
- Rearranging gives:
\[ 30.0 = 0.18 \times 1.13 \times V \]
- Simplifying further:
\[ 30.0 = 0.2034 \times V \]

5. **Solve for Volume (V):**
- Now, isolate \( V \):
\[ V = \frac{30.0}{0.2034} \]
- Calculating this gives:
\[ V \approx 147.3 \text{ cm}^3 \]

### Final Answer:
The volume of the solution containing 30.0 g of NaCl is approximately **147.3 cm³**.