Question

x ml of 0.1 M NaOH solution is diluted with distilled water to get 250 ml of 0.01 M solution. The value of x (in ml) is

• A. 12.5
• B. 25
• C. 37.5
• D. 50

Hint:

The dilution formula \(M_1V_1 = M_2V_2\) is fundamental for solving problems involving the dilution of solutions. As long as the units of volume (\(V_1\) and \(V_2\)) are the same (e.g., both in ml or both in L), you don't need to convert them.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This is a dilution problem. A concentrated solution of NaOH is diluted with water to a larger volume and lower concentration. We need to find the initial volume of the concentrated solution.

Step 2: Key Formula or Approach:
When a solution is diluted, the amount (moles) of solute remains constant. This is expressed by the dilution equation:
\[ M_1 V_1 = M_2 V_2 \]
where \(M_1\) and \(V_1\) are the initial molarity and volume, and \(M_2\) and \(V_2\) are the final molarity and volume.

Step 3: Detailed Explanation:
Let's identify the given values:
- Initial Molarity, \(M_1 = 0.1\) M
- Initial Volume, \(V_1 = x\) ml (this is what we need to find)
- Final Molarity, \(M_2 = 0.01\) M
- Final Volume, \(V_2 = 250\) ml
Now, substitute these values into the dilution equation:
\[ M_1 V_1 = M_2 V_2 \]
\[ (0.1 \text{ M}) \times (x \text{ ml}) = (0.01 \text{ M}) \times (250 \text{ ml}) \]
Now, solve for \(x\):
\[ 0.1 \cdot x = 2.5 \]
\[ x = \frac{2.5}{0.1} = 25 \]
The value of x is 25 ml.

Step 4: Final Answer:
The value of x is 25 ml.