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A container with a volume of 5 L holds 1...

A container with a volume of 5 L holds 100 g of `CO_(2)` at `40^(@)C`. For `CO_(2)` gas, a `=3.59L^(2)*atm*mol^(-2)` and `b=4.27xx10^(-2)L*mol^(-1)`. Determine the pressure of `CO_(2)` gas. How much does this value differ from that calculated by using ideal gas equation?

Text Solution

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van der waals equation for 'n' mol of a real gas:
`(P+(n^(2)a)/(V^(2)))(V-nb)=nRT`
Given, `V=5L,T=(273+40)=313K,n=(100)/(33)=2.27mol`,
`a=3.59L^(2)*atm*mol^(-2)&b=4.27xx10^(-2)L*mol^(-1)`.
`therefore P=(nRT)/(V-nb)-(n^(2)a)/(V^(2))`
`=(2.27xx0.0821xx313)/((5-2.27xx4.27xx10^(-2)))-((2.27)^(2)xx3.59)/((5)^(2))`
`=(11.9-0.74)atm=11.16atm`
Substituting the given values of V, T and n in the ideal gas equation PV=nRT we get,
`P=(nRT)/(V)=(2.27xx0.0821xx313)/(5)=11.66atm`
`therefore ` pressure of `CO_(2)` obtaied from van der waals equation is less than calculated from ideal gas equation by `(11.66-11.16)=0.50` atm.
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