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Solutions question

2018 · 15 Apr · Shift 2 · Q12
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Solutions question

2018 · 15 Apr · Shift 2 · Q12

JEE MainChemistrySolutionsMCQ+4 / −1
Two 5 molal solutions are prepared by dissolving a non-electrolyte non-volatile solute separately in the solvents X and Y. The molecular weights of the solvents are Mx and My, respectively where Mx = 34{3 \over 4}43​ My. The relative lowering of vapor pressure of the solution in X is ''m'' times that of the solution in Y. Given that the number of moles of solute is very small in comparison to that of the solvent, the value of ''m'' is :
  1. A
    43{4 \over 3}34​
  2. B
    34{3 \over 4}43​
  3. C
    12{1 \over 2}21​
  4. D
    14{1 \over 4}41​
View written solutionFree

Correct answer: B

  1. Use relative lowering of vapour pressure

For a non-volatile solute, p0−pp0=xsolute\frac{p^0-p}{p^0}=x_{\text{solute}}p0p0−p​=xsolute​

When the number of moles of solute is very small compared to solvent, xsolute≈n2n1x_{\text{solute}} \approx \frac{n_2}{n_1}xsolute​≈n1​n2​​ where n2n_2n2​ = moles of solute and n1n_1n1​ = moles of solvent.

  1. Interpret 5 molal solution

A 5 molal solution means:

  • 555 moles of solute are dissolved in 111 kg of solvent.

So for both solvents X and Y, n2=5n_2=5n2​=5

  1. Moles of solvent in each case

If molecular weight of solvent X is MxM_xMx​ g/mol, then moles of solvent in 111 kg = n1(X)=1000Mxn_1(X)=\frac{1000}{M_x}n1​(X)=Mx​1000​

Similarly, n1(Y)=1000Myn_1(Y)=\frac{1000}{M_y}n1​(Y)=My​1000​

  1. Relative lowering for each solution

For solvent X, (p0−pp0)X≈51000/Mx=5Mx1000\left(\frac{p^0-p}{p^0}\right)_X \approx \frac{5}{1000/M_x}=\frac{5M_x}{1000}(p0p0−p​)X​≈1000/Mx​5​=10005Mx​​

For solvent Y, (p0−pp0)Y≈51000/My=5My1000\left(\frac{p^0-p}{p^0}\right)_Y \approx \frac{5}{1000/M_y}=\frac{5M_y}{1000}(p0p0−p​)Y​≈1000/My​5​=10005My​​

  1. Find the ratio mmm

Given the lowering in X is mmm times that in Y,

=\frac{5M_x/1000}{5M_y/1000} =\frac{M_x}{M_y}$$ Given, $$M_x=\frac{3}{4}M_y$$ Therefore, $$m=\frac{M_x}{M_y}=\frac{3}{4}$$ 6. **Check options** The correct option is: $$\boxed{\frac{3}{4}}$$ which is **Option B**.
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