Test your skills on the following problems.

**Example:** An unknown gas expands in a container increasing the volume from 8.7 L to 18.9 L at a constant pressure of 1380 mmHg.

(a) Calculate the work done (in J) by the gas as it expands. (1 L· atm = 101.3 J).

(b) Calculate the internal energy of the system if the system absorbs 235.5 J of energy.

(c) Calculate the internal energy of the system if work was done against a vacuum. (1 L · atm = 101.3 J).

5m **Example:** Calculate the amount of heat absorbed when 12.0 g of water is heated from 20^{o}C to 100^{o}C. (c = 4.184 J/g· ^{o}C).

**Example:** 101.3 g of an unknown metal has an initial temperature of 25^{o}C. If it absorbs 639.1 J of energy to obtain a final temperature of 32.01^{o}C identify the unknown metal.

**Example:** Which substance has the highest molar heat capacity?

a) Copper (specific heat Cu (s): 0.39 J/g · ^{o}C)

b) Silver (specific heat Ag (s): 0.23 J/g · ^{o}C)

c) Iron (specific heat Fe(s): 0.46 J/g · ^{o}C)

d) Lead (specific heat Pb (s): 0.13 J/g · ^{o}C)

**Example:** 25.00 g of heated metal ore is placed into an insulated beaker containing 615.5 g of water at 42.18^{o}C. If the metal gains 19.11 kJ of energy, what is the final temperature of the water? (cwater = 4.184 J/g · ^{o}C).

**Example:** If 53.2 g Al at 25.0 ^{o}C is placed in 110.0 g H_{2}O at 90 ^{o}C, what is the final temperature of the mixture? The specific heat capacities of water and aluminum are 4.184 J/g · ^{o}C and 0.897 J/g · ^{o}C, respectively.

**Example:** A 20.0 g sample of iron, specific heat Fe (s) = 0.46 J/g⋅^{o}C, has an initial temperature of 30.2 ^{o}C. If 0.310 kJ are applied to the iron sample, calculate its final temperature.

**Example:** A sample of H_{2}O (l) containing 2.50 moles has a final temperature of 45.0 ^{o}C. If the sample absorbs 3.00 kJ of heat, what is the initial temperature of the H_{2}O (l)? The specific heat of H_{2}O (l) is 4.184 J/g⋅ ^{o}C .

**Example:** Determine the heat released when 80.0 g H_{2}O (l) at 90 ^{o}C is cooled to ice at – 10.0 ^{o}C. Specific Heat of H2O (l) = 4.184 J / g⋅^{o}C. Specific Heat of H_{2}O (s) = 2.09 J / g⋅^{o}C. Heat of Fusion of water = 333 J/g .

**Example:** If 1050 g of aluminum metal with a specific heat capacity of 0.902 J/g⋅^{o}C at – 20 ^{o}C is placed in liquid water at 0.00 ^{o}C, how many grams of liquid water are frozen by the time that the aluminum metal has warmed to – 10 ^{o}C? Heat of Fusion of water = 333 J/g.

**Problem:** How much heat (in kilojoules) is evolved when 255.0 g of aluminum (MW: 26.98 g/mol) reacts with excess Fe_{2}O_{3}?

2 Al (s) + Fe_{2}O_{3} (s) → 2 Fe (s) + Al_{2}O_{3} (s) ∆H_{rxn} = **-** 852.0 kJ

**Problem:** Solve the following question based on the given chemical equation:

NO_{2}Cl (g) + NO (g) → NOCl (g) + 3 NO_{2} (g)

Calculate the ∆H_{rxn} if the standard enthalpies of NO_{2}Cl_{, }NO, NOCl and NO_{2 }are – 724.2 kJ/mol , – 83.5 kJ/mol , 119.3 kJ/mol and – 393.5 kJ/mol.

**Problem:** Choose the thermochemical equation that illustrates ΔH_{f}^{°}for Li_{2}SO_{4}.

a) 2 Li^{+} (aq) + SO_{4}^{2-} (aq) → Li_{2}SO_{4} (aq)

b) 2 Li (s) + 1/8 S_{8} (s, rhombic) + 2 O_{2} (g) → Li_{2}SO_{4} (s)

c) Li_{2}SO_{4} (aq) → 2 Li^{+} (aq) + SO_{4}^{2-} (aq)

d) 8 Li_{2}SO_{4} (s) → 16 Li (s) + S_{8} (s, rhombic) + 16 O_{2} (g)

e) 16 Li (s) + S_{8}(s, rhombic) + 16 O_{2} (g) → 8 Li_{2}SO_{4} (s)

**Problem:** Calculate the enthalpy, **∆****H _{rxn}, ** for

CH_{4} (g) + 2 O_{2} (g) → CO_{2} (g) + 2 H_{2}O (l)

Given the following reactions:

CH_{2}O (g) + H_{2}O (g) → CH_{4} (g) + O_{2} (g) ∆H^{o} = 284 kJ

CH_{2}O (g) + O_{2} (g) → CO_{2} (g) + H_{2}O (g) ∆H^{o} = -518 kJ

H_{2}O (l) → H_{2}O (g) ∆H^{o} = 44.0 kJ