Exam 1 Solutions – 100 points

5.) (14 points) The temperature dependence of the molar constant pressure heat capacity of CO 2 gas may berepresented by the function8C p,m = α + β T + γ T 2 ,€€where α , β , and γ are constants. For CO 2 , these constants have the values α = 18.86 J K −1 mol −1 ,β = −0.01452 J K −2 mol −1 , and € γ = 3.142 ×10 −5 J K −3 mol −1 .In € this case, € 2.5 mol of CO 2 gas is heated reversibly from 300 to 1200 € K at a constant pressure of 1.0 bar.Calculate ΔH for the € process, assuming ideal gas behavior.In this problem, we know that the heat at constant pressure is the enthalpy,differential € of enthalpy isdq p = dH . For an ideal gas, thedH = C p dT .€On a molar basis, this equation becomes€dH = nC p,m dT .Integrating,€H 2T∫ dH = ∫2nC p,m dTT1H 1Substituting the values of the parameters, we have€TΔH = n ∫2( α + β T + γ T 2) dTT1ΔH = nα ( T 2 −T 1 ) + nβ 2 T 2 2 2( −T 1 ) + nγ 3 T 2 3 3( −T 1 ).ΔH = nα ( T 2 −T 1 ) + nβ 2 T 2 2 2( −T 1 ) + nγ 3 T 2 3 3( −T 1 )ΔH = ( 2.5 mol) ( 18.86 J mol −1 K −1)( 1200 K − 300 K)( 2.5 mol) ( −0.01452 J mol −1 K −2) 1200 K+ 1 ( ) 2 − ( 300 K) 22( )( )( 3.142 ×10 −5 J mol −1 K −3)(( 1200 K) 3 − ( 300 K) 3)( )( 16974 J/mol − 9801 J/mol + 17815J/mol)+ 1 2.5 mol3= 2.5 molΔH = 62470 J .Thus, at constant pressure,€q p = ΔH = 62470 J .€