The vapour pressure of a solution having $2.0 g$ of solute $X$ (gram atomic mass $= 32 g m o l^{- 1}$ ) in $100 g$ of $C S_{2}$ (vapour pressure $= 854$ torr) is $848.9$ torr. The molecular formula of the solute is:

X

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X_{2}

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X_{4}

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X_{8}

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Solution

The correct option is D $X_{8}$
molar mass of $C S_{2} = 64 + 12 = 76$ g/mol

mole fraction: $\frac{100}{76} / \frac{100}{76} + \frac{2}{m}$

$∴ 848.9 = {\frac{1.316}{1.316 + 2 g / m}} \times 854$

$6.71 m = 1697.8$

$∴ m = 253.0$ g/mol

$∴ \frac{253}{32} = 7.9 = 8$

$∴ 8$ s atoms of the solute

Thus, the correct formula for solute is $X_{8}$

Hence, the correct option is $D$

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The vapour pressure of a solution having 2.0 g of solute X (gram atomic mass =32 g mol−1) in 100 g of CS2 (vapour pressure =854 torr) is 848.9 torr. The molecular formula of the solute is:

The correct option is D X8molar mass of CS2=64+12=76 g/molmole fraction: 10076/10076+2m∴848.9={1.3161.316+2g/m}×8546.71m=1697.8∴m=253.0g/mol∴25332=7.9=8∴8s atoms of the soluteThus, the correct formula for solute is X8Hence, the correct option is D

The vapour pressure of a solution having $2.0 g$ of solute $X$ (gram atomic mass $= 32 g m o l^{- 1}$ ) in $100 g$ of $C S_{2}$ (vapour pressure $= 854$ torr) is $848.9$ torr. The molecular formula of the solute is: