Question

A mixture of $1.65\times {10}^{21}$ molecules of X and $1.85\times {10}^{21}$ molecules of Y weighs $0.688$ g. If the molar mass of the Y is $187g{mol}^{-1}$, then the molar mass of X is :

Answer 1

$\because 6.023\times {10}^{23}$ molecules of X weigh $=$ a g (where a is mol. mass of X)

$\therefore 1.65\times {10}^{21}$ molecules of X weigh $=\frac{a\times 1.65\times {10}^{21}}{6.023\times {10}^{23}}g=2.7\times {10}^{-3}ag$

$\because 6.023\times {10}^{23}$ molecules of Y weigh $=$ $187$ g

$1.85\times {10}^{21}$ molecules of y weigh $=\frac{187\times 1.85\times {10}^{21}}{6.023\times {10}^{23}}g=57.44\times {10}^{-2}g$

$\therefore 0.27\times {10}^{-2}a+57.44\times {10}^{-2}=0.688$

$MolarmassofX,a=42$ g/mol.