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At 287 K and 1.01 x 10^-2 atm, the density of a gas is 1.01 x 10^-5 g/cm^3.

(a) Find vrms for the gas molecules.

(b) Find the molar mass of the gas.
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What are our Givens

T = 287 Kelvin
P = 1.01 *10^-2 atm
D = 1.01 *10^-5 g/cm^3

We need to know

R = 8.314 J / kMole
vrsm = sqrt(3P/D) = sqrt(3RT/M)

(a) Find vrms for the gas molecules.
vrsm = sqrt(3P/D)
plug in the givens and evaluate
vrsm = sqrt(  (3 * 1.01 * 10^(-2)) / (1.01 * 10^(-5)) )

vrsm = sqrt(3000) = 54.77 m/s

(b) Find the molar mass of the gas.
Use sqrt(3P/D) = sqrt(3RT/M) to solve for M

sqrt(3P/D) = sqrt(3RT/M)
>> 3P/D = 3RT/M        (square both sides)
>> M/D = 3RT / 3P
>> M = DRT / P

Plug in your variables to M = DRT / P and evaluate

M = 1.01 * 10^(-5) *  8.314 * 287 / ( 1.01 * 10^(-2) )
M = 2.386 kg / mole
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