Question

A 100L flask contains a mixture of $CH_{4}$ and He at 27°C. The mass of He present is 40g and mole fraction of $CH_{4}$ in the mixture is 0.5. Calculate total translational kinetic energy of gaseous mixture.

Answer 1

Answer:

Correct answer is :

Explanation:

Pressure = 20 bar

Molar ratio = 4:1 (He and CH

4

)

P

He

=

5

4

×20=16bar

P

CH

4

=

5

1

×20=4bar

r

2

r

1

=

P

2

P

1

×

M

1

M

2

r

CH

4

r

He

=

P

CH

4

P

He

×

M

He

M

CH

4

=

4

16

×

4

16

=8

Therefore, the ratio of moles of helium and methane coming out initially is 8:1.

Answer 2

Answer:

The total kinetic energy of gaseous mixture of methane and Helium is79.5 KJ

Explanation:

step1:

Total kinetic energy can be determined as,

$\mathrm{KE}_{\text {total }}=\left(\mathrm{n}_{\text {Helium }}+\mathrm{n}_{\text {methane }}\right) \times \frac{3}{4} \times \mathrm{RT}$

Step 2

So, the mole fraction of moles of Methane in the mixture is 0.570

$\begin{aligned}&\chi_{\mathrm{CH}_{4}}=0.5 \\&\chi_{\mathrm{CH}_{4}}=\frac{\mathrm{n}_{\mathrm{CH}_{4}}}{\mathrm{n}_{\mathrm{CH}_{4}}+\mathrm{n}_{\mathrm{He}}}=500\end{aligned}$

Mass of the Helium =40g

Molar mass of the Helium =4g

So, the number of moles of Helium =10 mole

$\begin{aligned}&\chi_{\mathrm{CH}_{4}}=\frac{\mathrm{n}_{\mathrm{CH}_{4}}}{\mathrm{n}_{\mathrm{CH}_{4}}+10} \\&0.500\left(\mathrm{n}_{\mathrm{CH}_{4}}+10\right)=\mathrm{n}_{\mathrm{CH}_{4}} \\&0.500\left(\mathrm{n}_{\mathrm{CH}_{4}}+4.161\right)=\mathrm{n}_{\mathrm{CH}_{4}} \\&(1-0.500)\left(\mathrm{n}_{\mathrm{CH}_{4}}\right)=5.0 \\&(0.5)\left(\mathrm{n}_{\mathrm{CH}_{4}}\right)=5.0\\&\left(\mathrm{n}_{\mathrm{CH}_{4}}\right)=10 \mathrm{~mol} \mathrm{CH_{4} }\end{aligned}$

The total kinetic energy of gaseous mixture of methane and Helium,

Total kinetic energy can be determined as,

$\begin{aligned}\mathrm{KE}_{\text {total }} &=\left(\mathrm{n}_{\text {helium }}+\mathrm{n}_{\text {methane }}\right) \times \frac{3}{4} \times \mathrm{RT} \\\mathrm{KE}_{\text {total }} &=(10+10) \mathrm{mol} \times \frac{3}{2} \times 8.3145 \mathrm{~J} / \mathrm{Kmol} \times 318 \mathrm{~K} \\&=79573.14 \\&=7.957 \times 10^{4} \mathrm{~J}=79.5 \mathrm{~kJ}\end{aligned}$

Hence, the total kinetic energy of gaseous mixture of methane and Helium is79.5 KJ