Calculate the per cent concentration of a `9.28N` NaOH solution of density `1.31g//mL`.

Answer

To calculate the percent concentration of a 9.28N NaOH solution with a density of 1.31 g/mL, we can follow these steps:

### Step 1: Identify the given values
- Normality (N) of NaOH solution = 9.28 N
- Density of the solution = 1.31 g/mL
- Molar mass of NaOH = 40 g/mol
- Valence factor (n-factor) of NaOH = 1

### Step 2: Convert Normality to Gram Equivalents
Normality (N) is defined as the number of gram equivalents of solute per liter of solution. Since the valence factor of NaOH is 1, the gram equivalent weight of NaOH is equal to its molar mass.

\[ \text{Gram equivalent weight of NaOH} = \frac{\text{Molar mass}}{\text{n-factor}} = \frac{40 \, \text{g/mol}}{1} = 40 \, \text{g/equiv} \]

### Step 3: Calculate the number of gram equivalents in 1 liter of solution
Using the formula for normality:

\[ \text{Normality} = \frac{\text{Number of gram equivalents}}{\text{Volume in liters}} \]

For 1 liter of solution:

\[ 9.28 = \frac{\text{Number of gram equivalents}}{1} \]

Thus, the number of gram equivalents in 1 liter of solution is 9.28 equivalents.

### Step 4: Calculate the weight of NaOH in grams
To find the weight of NaOH in grams, we multiply the number of gram equivalents by the gram equivalent weight:

\[ \text{Weight of NaOH} = \text{Number of gram equivalents} \times \text{Gram equivalent weight} \]
\[ \text{Weight of NaOH} = 9.28 \times 40 = 371.2 \, \text{g} \]

### Step 5: Calculate the total weight of the solution
Since the density of the solution is given as 1.31 g/mL, we can calculate the total weight of 1 liter (1000 mL) of the solution:

\[ \text{Total weight of solution} = \text{Density} \times \text{Volume} = 1.31 \, \text{g/mL} \times 1000 \, \text{mL} = 1310 \, \text{g} \]

### Step 6: Calculate the mass percentage concentration
The mass percentage concentration is calculated using the formula:

\[ \text{Mass percentage} = \left( \frac{\text{Weight of solute}}{\text{Total weight of solution}} \right) \times 100 \]
\[ \text{Mass percentage} = \left( \frac{371.2 \, \text{g}}{1310 \, \text{g}} \right) \times 100 \approx 28.3\% \]

### Final Answer
The percent concentration of the 9.28N NaOH solution is approximately **28.3%**.

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