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For equal volumes of N2(g) and CO2(g) maintained at 298 K and 1 atm pressure, which of the following statements are correct?

1. The average translational KE per molecule is the same for N2 and CO2
2. The rms speed remains same for both N2 and CO2.
3. The density of N2 is less than that of CO2.
4. The total translational KE of both N2 and CO2 is same.

Correct answer: The average translational KE per molecule is the same for N2 and CO2

Solution

At the same temperature, average translational KE per molecule = (3/2)kT is identical for both gases (A true). RMS speed = sqrt(3RT/M) differs because molar masses differ (B false). Since M(CO2)=44 > M(N2)=28, density of N2 < density of CO2 at same T,P (C true). Equal volumes at same T and P have equal number of molecules (PV=NkT), so total translational KE = N*(3/2)kT is the same (D true). Correct statements: A, C, D.

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