Problem: A quantity of CO gas occupies a volume of 0.51 L at 1.5 atm and 312 K . The pressure of the gas is lowered and its temperature is raised until its volume is 3.1 L .Find the density of the CO under the new conditions.

FREE Expert Solution

We will calculate the density using the ideal gas law equation:

PV=nRT

PVV=nRTVP=nRTV

n=mass (m)molar mass (M)

P=mRTMV

mV=gL=density (d)

P (M)=dRTM(M)PMRT=dRTRTd=PMRT


For the new conditions, the only given value is the final volume of the CO gas. We’ll have to determine the final pressure and temperature.

PV=nRT

Assuming the amount of gas in moles (n) remains constant and R is also a constant:

PV=nRTPVT=TTPVT=1

Relate initial and final conditions:

P1V1T1=P2V2T2

Given:

V1 = 0.51 L                V2 = 3.1 L
P1 = 1.5 atm              P2 = ?
T1 = 312 K                 T= ?


(1.5 atm)(0.51 L)(312 K)=P2 (3.1 L)T22.4519×10-3atm·LK3.1 L=P2 (3.1 L)T2 (3.1 L)P2T2=7.9094×10-3 atmK


We can now calculate the density of CO gas in the new conditions:

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Problem Details

A quantity of CO gas occupies a volume of 0.51 L at 1.5 atm and 312 K . The pressure of the gas is lowered and its temperature is raised until its volume is 3.1 L .

Find the density of the CO under the new conditions.

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