Question

In this problem you will be calculating enthalpy changesforN2 . Do not assume constant values of heat capacity. Use a reference state o fT = 25 ̊C and 1 atm pressureto set H = 0 kJ/mol.

a.What is the change in enthalpy thereference state to400 ̊C?

b.What is the change in enthalpy from 800 ̊C to 400 ̊C? In addition, what is the value for enthalpyat 800 ̊C?

c.If the reference state for N2was changed to 100 ̊C, would your answer for part (b) change? If so, what would the change be?

Answer 1

Enthalpy change over a given temperature is given by,

dH = C_pdT

where, H = Enthalpy , J/mol

C_p = Specific heat, J/mol K

T = Temperature, K

Specific heat equation for Nitrogen is given as ( From Introduction to Chemical Engineering Thermodynamics, Appendix C) :

C_p /R = 3.280 + 0.593*10^-3T + 0.040*10⁵/T²

substituting this in,

dH = C_pdT , gives

dH = R*(3.280 + 0.593*10^-3T + 0.040*10⁵/T² ) dT

On integrating we get,

H = R * (3.280 T + 0.593*10^-3 * (T²/2) - 0.040*10⁵/T) ------------------------------ 1

Applying limits :

at T1 = 298 K(25 C) , H = H1 = 0 ;

at T2 = 673 K ( 400 C), H = H2

and R= 8.314 J/mol K

H2 - H1 = 8.314* [3.280 * (673 - 298 ) + 0.593*10^-3 * ( 673² - 298²)/2 - 0.040*10⁵ * ( 1/673 - 1/298)]

H2 = 8.314*[1230 + 268.587 + 7.479 ] = 12521.432 J/mol = 12.521 KL/mol

b) Enthalpy change from 800 C to 400 C can be directly calculated from equation 1 using different limits.

at T1 = 1073 K (800 C) , H = H1 and T2 = 673 K ( 400 C) , H = H2

H2 - H1 = 8.314* [3.280 * (673 - 1073 ) + 0.593*10^-3 * ( 673² - 1073²)/2 - 0.040*10⁵ * ( 1/673 - 1/1073)] -------------- (2)

H2 - H1 = -14369.64 J/mol = - 14.369 KJ/mol

Enthalpy change from 800 C to 400 C = -14.369 KJ/mol

Now enthalpy at 800 C , i.e to calculate H1,

H2 - H1 = - 14.369 KJ/mol

H2 = 12.521 KJ/mol

H1 = 26.89 KJ/mol

Enthalpy at 800 C = 26.89 KJ/mol

C) Equation 2 gives the enthalpy change from 800 C to 400 C , and we can see that the reference temperature does not play any role in its calculation. Thus there is no difference in change of enthalpy from 800 to 400 C.

But to calculate enthalpy at 800 C , we have used enthalpy at 400 C, which is calculated from reference temperature of 25 C. So once the reference temperature is increased to 100 C, this value will change.

We can calculate enthalpy at 800 C using equation 1 with reference temperature 100 C. So we have,

T1 = 373 K (100 C), H = H1 =0, and at T2 = 1073 K (800 C) H = H2

H2 - H1 = 8.314* [3.280 * (1073 - 373 ) + 0.593*10^-3 * ( 1073² - 373²)/2 - 0.040*10⁵ * ( 1/1073 - 1/373)]

H2 = 24137.45 J/mol = 24.137 KJ/mol

Enthalpy of N₂ at 800 C with Tf at 100 C = 24.137 KJ/mol