Question

The rms speed of CH4 is 3.8 x 104 cm s. The total kinetic energy of a mixture of 0.8 moles of CH4
and 0.2 moles of C4H10 is
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Answer 1

Explanation:

We know that average kinetic energy of gas molecules is (3/2)nRT,

n = number of moles of gas, R = gas constant, T = temperature of gas.

So, kinetic energy of 0.8 mol CH4 gas is (3/2)(0.8)RT and that of 0.2 mol C4H10 is (3/2)(0.2)RT.

We need to calculate RT.

We know that rms speed of gas molecules is \sqrt{3RT/M} = \sqrt{3RT/16} for CH4 gas. (M is molar mass of gas)

\sqrt{3RT/16} = 3.8 x 102 in SI units. Square both sides.

3RT/16 = 14.44 x 104 \Rightarrow RT = 14.44 x 104 x 16/3.

So, average kinetic energy of 0.8 mol CH4 = (3/2)(0.8)(14.44 x 104 x 16/3) J = 924160 J = 924.16 kJ

and that of 0.2 mol C4H10 = (3/2)(0.2)(14.44 x 104 x 16/3) J = 231040 J = 231.04 kJ.