How many grams of `40%` pure sodium hydroxide is dissolved in 0.5 M, 250ml `NaOH` solution?

Options

A. 5 gm
B. 2g
C. 12.5g
D. 4gm

Explanation

To solve the problem of how many grams of 40% pure sodium hydroxide (NaOH) is dissolved in a 0.5 M, 250 mL NaOH solution, we can follow these steps:

### Step 1: Calculate the number of moles of NaOH in the solution
We start with the formula for molarity (M):
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]

Given:
- Molarity (M) = 0.5 M
- Volume = 250 mL = 0.250 L

Using the formula, we can rearrange it to find the number of moles:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume} \]
\[ \text{Number of moles} = 0.5 \, \text{mol/L} \times 0.250 \, \text{L} = 0.125 \, \text{moles} \]

### Step 2: Calculate the mass of pure NaOH required
Next, we need to find the mass of NaOH corresponding to the number of moles calculated. The molar mass of NaOH is calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol

Thus, the molar mass of NaOH is:
\[ \text{Molar mass of NaOH} = 23 + 16 + 1 = 40 \, \text{g/mol} \]

Now, we can calculate the mass of pure NaOH:
\[ \text{Mass of NaOH} = \text{Number of moles} \times \text{Molar mass} \]
\[ \text{Mass of NaOH} = 0.125 \, \text{moles} \times 40 \, \text{g/mol} = 5 \, \text{g} \]

### Step 3: Calculate the mass of 40% pure NaOH
Since the NaOH we have is only 40% pure, we need to find out how much of the 40% solution corresponds to the 5 g of pure NaOH.

Let \( x \) be the mass of the 40% NaOH solution. The relationship can be expressed as:
\[ 0.40x = 5 \, \text{g} \]

Now, solving for \( x \):
\[ x = \frac{5 \, \text{g}}{0.40} = 12.5 \, \text{g} \]

### Final Answer
Therefore, the mass of the 40% pure sodium hydroxide that is dissolved in the solution is **12.5 grams**.

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