NORTH CAROLINA STATE UNIVERSITY

Department of Chemistry

CH 431 Take-home Quiz 3

Physical Chemistry I

  1. Use standard enthalpies of formation to calculate the standard enthalpies of the following reactions at 298 K:
  1. 2NO2 (g) à N2O4 (g)

    2. DfHo(N2O4) = 9.66 kJ/mol

    DfHo(NO2) = 33.55 kJ/mol

    DrHo = DfHo(N2O4) - 2DfHo(NO2) = 9.66 - 2(33.55) = -58.04

  2. NH3 (g) + HCl (g) à NH4Cl (s)

DfHo(NH3) = -46.11 kJ/mol

DfHo(HCl) = -92.31 kJ/mol

DfHo(NH4Cl) = -315.4 kJ/mol

DrHo = DfHo(NH4Cl) - DfHo(NH3) - DfHo(HCl) = -315.4 - (-46.11 - 92.31) = -177.0

  1. Given the reaction (a) and (b) below determine DrHo and DrUo for reaction (c).

    2. (a) H2 (g) + I2 (s) à 2 HI (g) DrHo = + 52.96 kJ/mol

    (b) 2 H2 (g) + O2 (g) à 2 H2O (g) DrHo = -483.96 kJ/mol

    (c) 4 HI (g) + O2 (g) à 2 I2 (s) + 2 H2O (g)

    DrHo (c) = DrHo (b) - 2DrHo (a) = -483.96 - 2(52.96) = - 589.88 kJ/mol

    DrHo = DrUo + DnRT Dn = -3

    DrUo = DrHo - DnRT = - 589.88 kJ/mol + (3)(8.31 J/mol-K)(298 K)

    = - 589.88 kJ/mol + 7.43 kJ/mol = 582.45 kJ/mol

  2. Evaluate a for an ideal gas.

    3. Solution:

  3. For an ideal gas the internal pressure is pT = (U/V)T = 0. In a future lecture we will show that:

    4. Using the above relation calculate (U/V)T for an van der Waal’s. gas. It is easiest to use the following form of the van der Waal’s equation of state.

    Solution:

  4. Using the definition of the enthalpy H = U +PV derive the corresponding expression for enthalpy:

Solution:

Substitute: U = H - PV

 

Using

We obtain

or

6. Using the definition derived in problem 5 calculate the isothermal Joules-Thompson coefficient mT for a van der Waal’s gas.

Solution: Beginning with the above expression for the isothermal J-T coefficient

we must find the derivative dV/dT. To do this we can use the chain relation to obtain derivatives with respect to P and T that are tractable for the van der Waal's equation of state.

Putting the two partial derivatives together we obtain:

or

7. The isothermal compressibility of lead at 293 K is 2.21x 10-6 atm-1. Calculate the pressure that must be applied in order to increase its density of 0.08 per cent.

Solution:

Assuming that the initial pressure is 1 atm, we have that
  1. The expansion coefficient of lead is 0.861 x 10-4 K-1. Calculate the volume change of 100 cm3 of lead if the temperature is raised from 298 K to 2000 K.

    2. Solution:

     

  2. Calculate the volume change of lead if the pressure is increased from 1 atm to 10,000 atm and the temperature is increased from 298 K to 2000 K.

Solution: