Grade 12Physical Chemistry

Tthe rms speed of ch4 is 3.8x10 raised to 4 cm per second.The total kinetic energy of a mixture of 0.8 moles of ch4 and 0.2 moles of c4div0 is?

JRP

7 Years agoGrade 12

7 Years ago

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.

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