Question

Equal weights of methane and hydrogen are mixed in an
empty container at 25ºC. The fraction of the total pressure
exerted by hydrogen is :
(a) 1/2
(b) 8/9
(c) 1/9
(d) 16/17

Answer 1

Answer:

8/9 is the fraction of total pressure

Answer 2

(b) $\frac{8}{9}$

Explanation:

Atomic mass of H₂ is = (2×1) =2

Atomic mass of CH₄ is= 12+(4×1)=12+4 =16

Since equal weights of methane and hydrogen are mixed.

Let m gram of hydrogen and methane are mixed.

Molar mass of H₂ is = $m\times \frac{1 \textrm{mole of}H_2}{2}$  =   $\frac{m}{2}$ mole of H₂

Molar mass of CH₄ is $=m \times \frac{1 \textrm{ mole of} CH_4}{16}$ = $\frac{m}{16}$ mole of CH₄

Therefore the total number of mole =($\frac{m}{2}$  +  $\frac{m}{16}$) moles $= \frac{9m}{16}$ moles

Mole fraction of H₂ is $=\frac{\textrm{no. of mole of } H_2}{\textrm{total no. of mole}}$

                                   $=\frac{\frac{m}{2} }{\frac{9m}{16} }$

                                  $=\frac{8}{9}$

By definition  of partial pressure of hydrogen gas is

$P_{H_2}= \textrm{mole fraction of }H_2 \times P_{\textrm{total pressure}}$

$\Rightarrow P_{H_2}= \frac{8}{9} \times P_{\textrm{total pressure}}$