Two rigid, identical cubic boxes each have a volume of . Box 1 contains helium gas at…

CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures

Problem

Two rigid, identical cubic boxes each have a volume of

0.010\,\text{m}^{3}

. Box 1 contains helium gas at a pressure of

1.0\times10^{5}\,\text{Pa}

and a mass density of

0.20\,\text{kg\,m}^{-3}

. Box 2 contains argon gas at the same pressure but at a mass density of

1.40\,\text{kg\,m}^{-3}

. The molar masses are

4.00\,\text{g\,mol}^{-1}

for helium and

40.0\,\text{g\,mol}^{-1}

for argon. Treat both gases as ideal and monatomic. Boltzmann’s constant:

k_{B}=1.38\times10^{-23}\,\text{J\,K}^{-1}

. (a) Derive an expression for the absolute temperature

T

of an ideal gas in terms of its pressure

P

, mass density

\rho

, and molecular mass

m

(mass of a single atom). Show all algebraic steps. (b) Using your expression from part (a), calculate the ratio

T_{\text{He}}/T_{\text{Ar}}

of the temperatures in the two boxes. (c) Determine the numerical value of the ratio of the root-mean-square speeds

v_{\text{rms,He}}/v_{\text{rms,Ar}}

of atoms in the two boxes. (d) Discuss whether the average translational kinetic energy per atom is the same or different for the two gases, and support your conclusion with reasoning based on your previous results.

Related theory

Browse the problem library