### Question 1.12

NCERT Class XI Chemistry

If the density of methanol is 0.793 kg L-1, what is its volume needed for making 2.5 L of its 0.25 M solution?

### Outline and Hint(Ans: 25.2 ml)

(detailed solution given after the video below)

Molecular formula of methanol is CH3OH.

First use the definition of molarity (= moles/vol in liters) to calculate the required number of moles of methanol.

Then use the molar mass of methanol to get grams.

Finally use the formula mass = vol x density to get the volume.

Answer is 25.2 ml.

detailed solution given after the video below### Video Explanation

(detailed solution given after this video)

Please watch this youtube video for a quick explanation of the solution:

### Solution in Detail

$ \begin{aligned} &\underline{\underline{\text{Step 1: Calculate molar mass of methanol}}}\\\\ &\text{methanol is CH}_3\text{OH} \equiv \text{CH}_4\text{O}\\ &12.00 + (1.008 \times 4) + 16.00\\ &= 32.032 \text{ g/mol}\\\\ &\underline{\underline{\text{Step 2: mass of methanol}}}\\\\ &\frac{\text{no. of moles}}{\text{vol. of solution in litres}} = \text{Molarity}\\\\ &\therefore \frac{n}{2.5} = 0.25 \text{ M} \\\\ &\therefore n = 2.5 \times 0.25 = 0.625 \text{ moles} \\\\ &\therefore \text{mass} = n \times \text{molar mass}\\ &= 0.625 \times 32.032 =20.02 \text{ grams (4 SF)}\\\\ &\underline{\underline{\text{Step 3: Calculate volume of methanol}}}\\\\ &\text{vol} = \frac{\text{mass}}{\text{density}}\\\\ &= \frac{20.02 \text{ g}}{0.793 \text{ kg/L}}\\\\ &= \frac{20.02 \text{ g}}{793 \text{ g/L}}\\\\ &= 0.0252 \text{ L (3 SF)}\:\underline{Ans} \end{aligned} $

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