A solution containing 0.1 g of a non – volatile organic substance P (molecular mass 100) in 100g of benzene raise the boiling point of benzene by $0.2 ° C,$ while a solution containing 0.1 g of another non – volatile substance Q in the same amount of benzene raise the boiling point of benzene by $0.4 ° C .$ What is the ratio of molecular masses of P and Q?

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1:4

1:2

4:1

2:1

answer is B.

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Detailed Solution

$\frac{{(Δ T)}_{p}}{{(Δ T)}_{Q}} = \frac{K_{b} \times {(\frac{w_{g} \times 100}{m_{B} \times w_{A}})}_{p}}{K_{b} \times {(\frac{w_{B} \times 100}{m_{B} \times w_{A}})}_{Q}} \frac{0.2}{0.4} = \frac{{(\frac{0.1 \times 1000}{100 \times 1000})}_{p}}{{(\frac{0.1 \times 1000}{100 \times m_{B}})}_{Q}}$

$\frac{1}{2} = \frac{{(m_{B})}_{Q}}{100}$

$m_{B} = 50$

$∴ {(m_{B})}_{p} : {(m_{B})}_{Q} = 100 : 50 = 2 : 1]$

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