Question

A compound of Mg contains 6% Mg by mass. Minimum molar mass of the compound is $n\times {10}^2$ g/mol. Caffeine has a molecular weight of 194. It contains about 30% by mass of nitrogen. The number of atoms of nitrogen in one molecule of it is m. Give the value of m/n.

• A. 1:2
• B. 1:1
• C. 2:1
• D. 3:2

Answer 1

Answer: (B)

1:1

$\to$A comnpound contains $6$% Mg by mass

$6$g of Mg in $100$g of compound.

$\to$Minimum molar mass of the compound is $n\times {10}^{2}g/mol$

Min. molar mass means that at least one atom of Mg should be present in the compound.

$6gofMg⟶100gofcompound1gofMg⟶\frac{100}{6}gofcompound$

One atom of Mg weighs $24g$

$24gofMg⟶\frac{100\times 24}{6}gofcompound24g⟶400g$

Therefore, the minimum molar mass of the compound is $400g/mole$

or $4\times {10}^{2}g/mole=n\times {10}^{2}g/molen=4$

Caffeine$\to$Mol.wt.$\to 194$

$30$% by mass of nitrogen

$30g$ of nitrogen in $100g$ of caffience

i.e.$100gofCaffeine⟶30gofnitrogen1gofCaffeine⟶\frac{30}{100}gofnitrogen194gofCaffeine⟶\frac{30}{100}\times 194gofnitrogen⟶58.2gofnitrogen$

No. of atoms of $N_2$ in one molecule of it is m.

One atom of N weighs $⟶14g$

$58.2gofN⟶\frac{58.2}{14}=4.1$

No. of atoms of $N_2$ in one molecule of it is $4.1=m$

Value of $\frac{m}{n}=\frac{4.1}{4}=\frac{1}{1}=1:1$