Question

A metal $M$ (atomic weight $=111g$ and density $=12gc{m}^{-3})$ dissolves hydrogen gas $896$ times of its own volume at STP to form an interstitial hydride $M{H}_x$. Which of the following options is/are correct?

• A. The value of $x=0.74$
• B. The number of moles of metal is $0.108$
• C. The molarity of $H-$atoms in hydride is $6.67$
• D. The number of moles of hydrogen present in $1$ litre at STP is $80$

Answer 1

Answer: (A), (C), (D)

The correct options are
A The value of $x=0.74$
C The number of moles of hydrogen present in $1$ litre at STP is $80$
D The molarity of $H-$atoms in hydride is $6.67$

Let $1$ $\left(111g\right)$ mole of metal is present.
Its volume will be $\frac{111}{12}=9.25ml$
The volume of hydrogen dissolved is $896$ times the volume of metal. It is $896\times 9.25=8288$ mL or $8.288$ L.
At STP, it corresponds to $\frac{8.288}{22.4}=0.37$ moles of hydrogen gas or $2\times 0.37=0.74$ moles of $H$ atoms.
Thus 1 mole of metal contains $0.74$ moles of $H$ atoms.
(A) Hence, the value of $x$ is $0.74$.

(B) The number of moles of metal cannot be determined from the given data.

(D) Total volume is $9.25$ mL. The number of moles of $H$ atoms are 0.74.
The number of moles of hydrogen present in 1 L at STP are
$\frac{0.74}{9.25}\times 1000=80$.