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 26.0 g of the salt will be

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the given data
- Density of the salt solution = 1.13 g/cm³
- Percentage of NaCl by weight in the solution = 20%
- Mass of NaCl in the solution = 26 g

### Step 2: Set up the equation for the mass of the solution
Let the volume of the solution be \( x \) cm³. The mass of the solution can be calculated using the formula:
\[ \text{Mass of solution} = \text{Density} \times \text{Volume} \]
Thus, the mass of the solution is:
\[ \text{Mass of solution} = 1.13 \, \text{g/cm}^3 \times x \, \text{cm}^3 = 1.13x \, \text{g} \]

### Step 3: Relate the mass of NaCl to the mass of the solution
Since the solution contains 20% NaCl by weight, we can express the mass of NaCl in terms of the mass of the solution:
\[ \text{Mass of NaCl} = \frac{20}{100} \times \text{Mass of solution} \]
Substituting the mass of the solution:
\[ 26 \, \text{g} = \frac{20}{100} \times 1.13x \]

### Step 4: Solve the equation for \( x \)
Now, we can solve for \( x \):
\[ 26 = 0.2 \times 1.13x \]
\[ 26 = 0.226x \]
To isolate \( x \), divide both sides by 0.226:
\[ x = \frac{26}{0.226} \]
Calculating this gives:
\[ x \approx 115.93 \, \text{cm}^3 \]

### Step 5: Final Calculation
To find the volume of the solution containing 26 g of NaCl, we can also multiply by 5 (since 20% means that for every 20 g of NaCl, there are 100 g of solution):
\[ \text{Volume of solution} = 5 \times 26 \, \text{g} = 130 \, \text{g} \]
Now, converting this mass to volume using the density:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{130 \, \text{g}}{1.13 \, \text{g/cm}^3} \approx 115.93 \, \text{cm}^3 \]

### Conclusion
The volume of the solution containing 26.0 g of NaCl is approximately **115.93 cm³**.

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