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

Hint- In order to deal with this question, we will use the concept as minimum molar mass means that at least one atom of Mg should be present in one molecule of the given compound. And one atom of Mg and N weight is 24 and 14g respectively, use these things to get the answer.

Complete step-by-step answer:
Given that
A compound contains $6\% $ Mg by mass
This can be considered the same as 6g of Mg in 100g of compound.
Minimum molar mass of the compound is $n \times {10^2}g/mol$
We know that
Min. molar mass means the compound will contain at least one atom of Mg.
$
  6gm{\text{ of }}Mg \to 100gm{\text{ of compound}} \\
   \Rightarrow 1gm{\text{ of }}Mg \to \dfrac{{100}}{6}gm{\text{ of compound}} \\
 $
One atom of Mg weights 24g
$
   \Rightarrow 24gm{\text{ of }}Mg \to \dfrac{{100 \times 24}}{6}gm{\text{ of compound}} \\
   \Rightarrow 24gm{\text{ of }}Mg \to 400gm{\text{ of compound}} \\
 $
Therefore, the minimum molar mass of the compound is $400gm/mole$
Or
 \[
  400gm/mole = n \times {10^2}g/mol \\
   \Rightarrow 4 \times {10^2}gm/mole = n \times {10^2}g/mol \\
   \Rightarrow n = 4 \\
 \]
Therefore the value of n is 4.
Now for the value of m:
Given that Caffeine has a Molar weight of 194u
And has $30\% $ by mass of nitrogen
 $30g$ of nitrogen in $100g$ of caffeine
\[
   \Rightarrow 100gm{\text{ of Caffeine}} \to 30gm{\text{ of nitrogen}} \\
   \Rightarrow 1gm{\text{ of Caffeine}} \to \dfrac{{30}}{{100}}gm{\text{ of nitrogen}} \\
   \Rightarrow 194gm{\text{ of Caffeine}} \to \dfrac{{30 \times 194}}{{100}}gm{\text{ of nitrogen}} \\
   \Rightarrow 194gm{\text{ of Caffeine}} \to 58.2gm{\text{ of nitrogen}} \\
 \]
No. of atoms of \[{N_2}\] in one molecule of caffeine is m.
Also we know that one atom of nitrogen weighs 14g
So let us find the number of atoms in 58.2gm
\[
   \Rightarrow 58.2gm{\text{ of Nitrogen}} \to \dfrac{{58.2}}{{14}}{\text{atoms of nitrogen}} \\
   \Rightarrow 58.2gm{\text{ of Nitrogen}} \to 4.1{\text{atoms of nitrogen}} \\
 \]
No. of atoms of \[{N_2}\] in one molecule of caffeine is \[m = 4.1\]
So, the value of m is almost equal to 4.
Further we will find the ratio $m/n$:
$
   \Rightarrow \dfrac{m}{n} = \dfrac{{4.1}}{4} \approx \dfrac{1}{1} \\
   \Rightarrow m:n = 1:1 \\
 $
Hence, the required ratio is 1:1
So, the correct answer is option B.

Note- The molar mass is known as the mass of a sample of that compound expressed in moles, divided by the volume of material in that sample. The molar mass is a substance's weight, not its molecular structure. In order to solve such types of problems students must remember the atomic weight of some common elements and also must know how to find the atomic weight from the periodic table.