What is the volume ( in mL ) of 0.5 M NaOH required to prepare one litre of 0.2 M NaOH ?

Options

A. 200
B. 500
C. 400
D. 250

Answer

To solve the problem of determining the volume of 0.5 M NaOH required to prepare one liter of 0.2 M NaOH, we can follow these steps:

### Step 1: Understand the Molarity Formula
Molarity (M) is defined as the number of moles of solute divided by the volume of solution in liters. The formula is:
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]

### Step 2: Set Up the Equation for the Final Solution
We need to prepare 1 liter of a 0.2 M NaOH solution. Using the molarity formula, we can express the number of moles of NaOH needed:
\[ \text{Moles of NaOH} = \text{Molarity} \times \text{Volume} = 0.2 \, \text{M} \times 1 \, \text{L} = 0.2 \, \text{moles} \]

### Step 3: Relate the Moles to the Initial Concentration
We have a 0.5 M NaOH solution. Let \( V \) be the volume in liters of this solution that we need to use to get 0.2 moles of NaOH. Using the molarity formula again:
\[ \text{Moles of NaOH from 0.5 M solution} = 0.5 \, \text{M} \times V \]
Setting this equal to the moles needed:
\[ 0.5V = 0.2 \]

### Step 4: Solve for \( V \)
Now, we can solve for \( V \):
\[ V = \frac{0.2}{0.5} = 0.4 \, \text{L} \]

### Step 5: Convert Liters to Milliliters
Since the question asks for the volume in milliliters, we convert liters to milliliters:
\[ 0.4 \, \text{L} = 0.4 \times 1000 \, \text{mL} = 400 \, \text{mL} \]

### Final Answer
The volume of 0.5 M NaOH required to prepare one liter of 0.2 M NaOH is **400 mL**.

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