5.E: First Law of Thermodynamics (Exercises)

Q3.1

In the attempt to measure the heat equivalent of mechanical work (as Joule did in his famous experiment) a student uses an apparatus similar to that shown below:

The 1.50 kg weight is lifted 30.0 cm against the force due to gravity (9.8 N). If the specific heat of water is 4.184 J/(g °C), what is the expected temperature increase of the 1.5 kg of water in the canister?

Q3.2

1.00 mol of an ideal gas, initially occupying 12.2 L at 298 K, expands isothermally against a constant external pressure of 1.00 atm until the pressure of the gas is equal to the external pressure. Calculate $$\Delta p$$, $$q$$, $$w$$, $$\Delta U$$, and $$\Delta H$$ for the expansion.

Q3.3

Consider 1.00 mol of an ideal gas expanding isothermally at 298 K from an initial volume of 12.2 L to a final volume of 22.4 L. Calculate $$\Delta p$$, $$q$$, $$w$$, $$\Delta U$$, and $$\Delta H$$ for the expansion.

Q3.4

Consider 1.00 mol of an ideal gas (CV = 3/2 R) Occupying 22.4 L that undergoes an isochoric (constant volume) temperature increase from 298 K to 342 K. Calculate $$\Delta p$$, $$q$$, $$w$$, $$\Delta U$$, and $$\Delta H$$ for the change.

Q3.5

Consider 1.00 mol of an ideal gas (Cp = 5/2 R) initially at 1.00 atm that undergoes an isobaric expansion from 12.2 L to 22.4 L. Calculate $$\Delta T$$, $$q$$, $$w$$, $$\Delta U$$, and $$\Delta H$$ for the change.

Q3.6

Consider 1.00 mol of an ideal gas (CV = 3/2 R) initially at 12.2 L that undergoes an adiabatic expansion to 22.4 L. Calculate $$\Delta T$$, $$q$$, $$w$$, $$\Delta U$$, and $$\Delta H$$ for the change.

Q3.7

Derive an expression for the work of an isothermal, reversible expansion of a gas that follows the equation of state (in which $$a$$ is a parameter of the gas)

$pV = nRT -\dfrac{an^2}{V}$

from $$V_1$$ to $$V_2$$.

Q3.8

Use the following data [Huff, Squitieri, and Snyder, J. Am. Chem. Soc., 70, 3380 (1948)] to calculate the standard enthalpy of formation of tungsten carbide, $$WC(s)$$.

Reaction $$\Delta H^o$$ (kJ)
$$C(gr) + O_2(g) \rightarrow CO_2(g)$$ -393.51
$$WC(s) + 5/2 O_2(g) \rightarrow WO_3(s) + CO_2(g)$$ -1195.79
$$W(s) + 3/2 O_2(g) \rightarrow WO_3(s)$$ -837.42

Q3.9

The standard molar enthalpy of combustion ($$\Delta H_c$$) of propane gas is given by

$C_3H_8(g) + 5 O_2(g) \rightarrow 3 CO_2(g) + 4 H_2O(l)$

with $$\Delta H_c = -2220 \,kJ/mol$$

The standard molar enthalpy of vaporization ($$\Delta H_{vap}$$) for liquid propane

$C_3H_8(l) \rightarrow C_3H_8(g)$

with $$\Delta H_{vap} = 15\, kJ/mol$$

1. Calculate the standard enthalpy of combustion of liquid propane.
2. Calculate the standard internal energy change of vaporization ($$\Delta U_{vap}$$) for liquid propane.
3. Calculate the standard internal energy change of combustion ($$\Delta H_c$$) for liquid propane.

Q3.10

The enthalpy of combustion ($$\Delta H_c$$) of aluminum borohydride, $$Al(BH_4)_3(l)$$, was measured to be -4138.4 kJ/mol [Rulon and Mason, J. Am. Chem. Soc., 73, 5491 (1951)]. The combustion reaction for this compound is given by

$Al(BH_4)_3(l) + 6 O_2(g) \rightarrow ½ Al_2O_3(s) + 3/2 B_2O_3(s) + 6 H_2O(l)$

Given the following additional data, calculate the enthalpy of formation of $$Al(BH_4)_3(g)$$.

• $$Al_2O_3(s)$$: $$\Delta H_f = -1669.8 \, kJ/mol$$
• $$B_2O_3(s)$$: $$\Delta H_f = -1267.8 \, kJ/mol$$
• $$H_2O(l)$$: $$\Delta H_f = -285.84 \, kJ/mol$$
• $$Al(BH_4)_3(l)$$: $$\Delta H_{vap} = 30.125 \, kJ/mol$$

Q3.11

The standard enthalpy of formation ($$\Delta H_f^o$$) for water vapor is -241.82 kJ/mol at 25 °C. Use the data in the following table to calculate the value at 100 °C.

Substance $$C_p$$ (J mol-1 K-1)
H2(g) 28.84
O2(g) 29.37
H2O(g) 33.58

Q3.12

$$\Delta C_p = (1.00 + 2.00 \times 10^{-3} T)\, J/K$$ and $$\Delta H_{298} = -5.00\, kJ$$ for a dimerization reaction

$2 A \rightarrow A_2$

Find the temperature at which $$\Delta H = 0$$.

Q3.13

From the following data, determine the lattice energy of $$BaBr_2$$.

$Ca(s) \rightarrow Ca(g)$

with $$\Delta H_{sub} = 129\, kJ/mol$$

$Br_2(l) \rightarrow Br_2(g)$

with $$\Delta H_{vap} = 31\, kJ/mol$$

$Br_2(g) \rightarrow 2 Br(g)$

with $$D(Br-Br) = 193 \, kJ/mol$$

$Ca(g) \rightarrow Ca^+(g) + e^-$

with $$1^{st} \, IP(K) = 589.8 \, kJ/mol$$

$Ca^+(g) \rightarrow Ca^{2+}(g) + e^-$

with $$2^{nd} IP(K) = 1145.4 \,kJ/mol$$

$Br(g) + e^- \rightarrow Br-(g)$

with $$1^{st} EA(Br) = 194 \, kJ/mol$$

$Ca(s) + Br_2^-(l) \rightarrow CaBr_2(s)$

with $$\Delta H_f = -675 \, kJ/mol$$

Q3.15

Using average bond energies (Table T3) estimate the reaction enthalpy for the reaction

$C_2H_4 + HBr \rightarrow C_2H_5Br$