Calculates the molarity and normality of a solution containing `0.5` g of `NaOH` dissolved in `500 ml` solution

Options

A. ` 0.0025 M,0.025 N `
B. ` 0.025 M,0.025 N `
C. ` 0.25 M, 0.25 N `
D. ` 0.025 M,0.0025 N `

Explanation

To calculate the molarity and normality of a solution containing 0.5 g of NaOH dissolved in 500 mL of solution, follow these steps:

### Step 1: Calculate the number of moles of NaOH

First, we need to find the molar mass of NaOH (Sodium Hydroxide):
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol

Molar mass of NaOH = 23 + 16 + 1 = 40 g/mol

Now, we can calculate the number of moles of NaOH in 0.5 g:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

\[ \text{Number of moles} = \frac{0.5 \, \text{g}}{40 \, \text{g/mol}} = 0.0125 \, \text{mol} \]

### Step 2: Calculate the volume of the solution in liters

Since the volume of the solution is given in milliliters, we need to convert it to liters:

\[ \text{Volume (L)} = \frac{500 \, \text{mL}}{1000} = 0.5 \, \text{L} \]

### Step 3: Calculate the molarity of the solution

Molarity (M) is defined as the number of moles of solute per liter of solution:

\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]

\[ \text{Molarity (M)} = \frac{0.0125 \, \text{mol}}{0.5 \, \text{L}} = 0.025 \, \text{M} \]

### Step 4: Calculate the normality of the solution

Normality (N) is defined as the number of equivalents of solute per liter of solution. For NaOH, which is a strong base, it provides one hydroxide ion (OH⁻) per molecule. Therefore, the number of equivalents is equal to the number of moles.

\[ \text{Normality (N)} = \text{Number of equivalents} \times \frac{1}{\text{Volume of solution in liters}} \]

Since NaOH provides one equivalent per mole:

\[ \text{Normality (N)} = \frac{0.0125 \, \text{equivalents}}{0.5 \, \text{L}} = 0.025 \, \text{N} \]

### Final Results

- Molarity of the solution = 0.025 M
- Normality of the solution = 0.025 N