Question

A vessel of volume 20 litres contains a mixture of hydrogen and helium at temperature of ${27}^{o}C$ and pressure 2.0 atm.The mass of the mixture is 5g.Assuming the gases to be ideal,the ratioof the mass of hydrogen to that of helium in the given mixture will be approximately:

• A. 1:2
• B. 2:3
• C. 2:1
• D. 2:5

Answer 1

The correct option is A 1:2

$n_1$ moles of hydrogen and $n_2$ moles of helium

$m_1=n_1\ast M_1$

$m_2=n_2\ast M_2$

where M is the molar mass.

Total mass $=m_1+m_2=5gm$

$=n_1\ast M_1+n_2\ast M_2=5gm$.....$\left(i\right)$

Total moles $=n_1+n_2=n\left(say\right)$.........$\left(ii\right)$

From equation $\left(i\right)$ and $\left(ii\right)$ we can say,

$n_1=\frac{n{M}_2-5}{M_2-M_1}$

$n_2=\frac{5-n{M}_1}{M_2-M_1}$

From ideal gas equation,

$PV=nRT$

$=2\ast 20=0\ast 0.0821\ast 293$

$n=1.66$

$\frac{m_1}{m_2}$= $\frac{M_1}{M_2}$ $\times \frac{n{M}_2-5}{5-n{M}_1}$

Putting the values of $n=1.66$, $M_1=2$ and $M_2=4$, we get as,

$\frac{m_1}{m_2}=0.5=1:2$