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A rigid container holds 2.0molof gas at a pressure of 1.0atmand a temperature of 30°C.

a. What is the container’s volume?

b. What is the pressure if the temperature is raised to 130°C?

Short Answer

Expert verified

a. The container’s volume is 0.050m3.

b. The pressure if the temperature is raised to130°Cis1.33atm

Step by step solution

01

Defining the Ideal Gas Law

Theideal gas law shows the relationship between the four state variables for an ideal gas, namely the volume Vof the container, the pressure pexerted on the gas, the temperature Tof the gas, and the number of moles nof the gas in the container.

The ideal gas law is given by PV=nRT
Where Ris the universal gas constant and in units of SI its value is 8.31J/mol.K
Solve this for Vwe get : V=nRTP

Temperature must be expressed in Kelvin and pressure in Pascals, so we must convert the units from Celsius. The conversion between the Celsius scale and the Kelvin scale is given by TK=TC+273

02

Finding the container’s volume .

(a) Substitute the value forTC=30°C to get
TC=TC+273=30°C+273=303K
To calculate the pressure in Pa, we use the following formula p=(1atm)1.01325x105Pa1atm5Pa)=1.01325x105Pa
Now we substitute the values for n,R,Tandpinto the equationV=nRTP to get:

V=nRTP=(2mol)(8.314J/mol-K)(303K)1.01325×105Pa=0.050m3
03

Finding the pressure if the temperature is raised to 130°C

(b) As can be seen from the ideal gas law, pressure pis directly proportional to temperatureT. Thus, if the volume is constant for the same gas, we can obtain the relationship for two points in time as follows.
p2p1=T2T1p2=(T2T1)p1
With T=130°+273=403K,T=303K,andp=1atm. It follows that :
p2=(403K303K)(1atm)=1.33atm

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