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 54.0 g of the salt will be

Explanation

To solve the problem step by step, we need to find the volume of the salt solution that contains 54.0 g of NaCl, given that the density of the solution is 1.13 g/cm³ and it contains 18% NaCl by weight.

### Step 1: Understand the relationship between mass, volume, and density
The density (d) of a solution is defined as:
\[ d = \frac{\text{mass of solution}}{\text{volume of solution}} \]

From this, we can express the mass of the solution (m) as:
\[ m = d \times V \]
where \( V \) is the volume of the solution.

### Step 2: Calculate the mass of the solution
Let the volume of the solution be \( V \) cm³. Given the density of the solution is 1.13 g/cm³, the mass of the solution can be expressed as:
\[ \text{mass of solution} = 1.13 \times V \]

### Step 3: Relate the mass of NaCl to the mass of the solution
The problem states that the solution contains 18% NaCl by weight. This means:
\[ \text{mass of NaCl} = 0.18 \times \text{mass of solution} \]

Since we know the mass of NaCl is 54.0 g, we can set up the equation:
\[ 54.0 = 0.18 \times (1.13 \times V) \]

### Step 4: Solve for the volume \( V \)
Now we can solve for \( V \):
1. Substitute the mass of the solution:
\[ 54.0 = 0.18 \times (1.13 \times V) \]
2. Rearranging gives:
\[ 54.0 = 0.2034 \times V \]
3. Now, solve for \( V \):
\[ V = \frac{54.0}{0.2034} \]
4. Calculate \( V \):
\[ V \approx 265.0 \, \text{cm}^3 \]

### Final Answer
The volume of the solution containing 54.0 g of NaCl is approximately **265.0 cm³**.

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