There are two containers of equal volumes, each filled with a different gas. Bot

Question

There are two containers of equal volumes, each filled with a different gas. Both containers have the same number of moles of gas and are at the same temperature. The molecules of gas in container 1 are four times more massive than the molecules of gas in container 2. The number of moles in container 2 is increased until it is a factor of 4 larger than the number of moles in container 1. The volume and temperature of container 2 remain unchanged. After increasing the number of moles in container 2: Which container, 1 or 2, has a higher pressure, or are they the same? Which container, 1 or 2, has a higher average (rms) speed of gas molecules, or are they the same? Which container, 1 or 2, has a higher average kinetic energy of gas molecules, or are they the same? Which container, 1 or 2, has a higher thermal energy, or are they the same?

Explanation / Answer

Ideal Gas Law : PV = nRT

n = number of moles

P1*V1 = n1*R*T1

and P2*V2 = n2*R*T2

Now, after number of moles is increased in container 2,

n2 > n1

V2 = V1 = V , T2 = T1 = T

So, P1*V = n1*R*T

and P2*V = n2*RT

So, P1/P2 = n1/n2

Now, as n2 > n1

So, n1/n2 < 1

So, P1/P2 < 1

So, P1 < P2

So, container 2 has higher pressure than container 1 <----- answer

avg speed of molecules, v = sqrt(3RT/M)

R = Molar Gas constant

M = molar mass

Now, as the Temperature(T) is constant as well as R

So, v is inversely proportional to sqrt(M)

So, container 2 will have higher average speed of molecules <------answer

KEavg = (3/2)*k*T

as KEavg is directly related to T only , container 1 and 2 have same average KE <------answer

Thermal energy = KEavg * number of moles

Now, number of moles in container 2 is greater than in container 1, so Thermal enrgy in container 2 is greater <----answer

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