86. The volume of 4 M NaOH (in ml) required to make 350 ml solution of 1.2 M NaOH is ________. (in integer)

Volume of 4 M NaOH Required to Prepare 350 mL of 1.2 M NaOH

Correct Answer

Answer: 105 mL

Understanding the Concept of Dilution

This problem is based on the principle of dilution. During dilution, the number of moles of solute remains constant because only solvent is added. As a result, the concentration decreases while the total volume increases.

The relationship between the initial and final solutions is given by the dilution equation.

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Formula Used

The dilution equation is:

M₁V₁ = M₂V₂

where:

• M₁ = Initial molarity = 4 M
• V₁ = Volume of stock solution required
• M₂ = Final molarity = 1.2 M
• V₂ = Final volume = 350 mL

Step-by-Step Calculation

Substitute the given values into the dilution equation:

4 × V₁ = 1.2 × 350

Calculate the right-hand side:

4 × V₁ = 420

Now divide both sides by 4:

V₁ = 420 ÷ 4 = 105 mL

Verification

The stock solution has a higher concentration (4 M) than the required solution (1.2 M). Therefore, only a portion of the stock solution is needed, followed by the addition of water until the total volume becomes 350 mL.

If 105 mL of 4 M NaOH is taken and diluted to a final volume of 350 mL, the resulting concentration is exactly 1.2 M.

Why This Method Works

Molarity represents the number of moles of solute present per litre of solution. During dilution, no NaOH is lost; only the volume changes. Hence, the total number of moles before and after dilution remains the same. This conservation of moles leads directly to the equation M₁V₁ = M₂V₂, making it one of the most frequently used formulas in analytical chemistry and competitive examinations.

Final Answer

The volume of 4 M NaOH required to prepare 350 mL of 1.2 M NaOH is:

105 mL