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Thermochemistry Example Problems

Recognizing Endothermic & Exothermic Processes

On a sunny winter day, the snow on a rooftop begins to melt. As the melted water drips from the roof, it refreezes into icicles. Describe

the direction of heat flow as the water freezes. Is this process endothermic or exothermic?

1) Analyze – Identify the relevant concepts. Heat flows from a warmer object to a cooler object. An endothermic process absorbs

heat from the surroundings. An exothermic process releases heat to the surroundings.

2) Solve – Apply concepts to this problem.

a. Identify the system & the surroundings.

b. Determine the direction of heat flow.

c. Determine if the process is endothermic or exothermic.

System = water Surroundings = air

For the water to freeze, the temperature must go down so heat flows out of the water and into the air. Since heat is released, this

process is exothermic.

Now you try…

When barium hydroxide octahydrate, Ba(OH)2•8H2O, is mixed in a beaker with ammonium thiocyanate, NH4SCN, a reaction occurs.

The beaker becomes very cold. Is the reaction endothermic or exothermic?

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Calculating the Specific Heat of a Substance

The temperature of a 95.4 g piece of copper increases from 25.0⁰C to 48.0⁰C when the copper absorbs 849 J of heat. What is the

specific heat of the copper?

1) Analyze – List the knowns & the unknown. Use the known values and the definition of specific heat.

2) Calculate – Solve for the unknown.

a. Start with the equation for specific heat.

b. Substitute the known quantities into the equation to calculate c.

q = 849 J

m = 95.4 g

c = ?

ΔT = 48.0⁰C – 25.0⁰C = 23.0⁰C

Now you try…

When 435 J of heat is added to 3.4 g of olive oil at 21⁰C, the temperature increases to 85⁰C. What is the specific heat of the olive oil?

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Enthalpy Change in a Calorimetry Experiment

When 25.0 mL of water containing 0.025 mol HCl at 25.0⁰C is added to 25.0 mL of water containing 0.025 mol of NaOH at 25.0⁰C in

a foam cup calorimeter, a reaction occurs. Calculate the enthalpy change (in kJ) during this reaction if the highest temperature observed

is 32.0⁰C. Assume the densities of the solutions are 1.00 g/mL and that the volume of the final solution is equal to the sum of the volumes

of the reacting solutions.

1) Analyze – List the knowns & the unknown. Use dimensional analysis to determine the mass of the water. You must also calculate

ΔT. Use ΔH= -qsurr = - mcΔT to solve for ΔH.

2) Calculate – Solve for the unknown.

c = 4.184 J/g⁰C

Vfinal = VHCl + VNaOH = 25.0 mL + 25.0 mL = 50.0 mL

Ti = 25.0⁰C

Tf = 32.0⁰C

Densitysolution = 1.00 g/mL

Now you try…

When 50.0 mL of water containing 0.50 mol HCl at 22.5⁰C is mixed with 50.0 mL of water containing 0.50 mol NaOH at 22.5⁰C in a

calorimeter, the temperature of the solution increases to 26.0⁰C. How much heat (in kJ) is released by this reaction?

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Using the Heat of Reaction to Calculate Enthalpy Change

Calculate the amount of heat (in kJ) required to decompose 2.24 mol of NaHCO3(s).

2 NaHCO3(s) + 85 kJ Na2CO3(s) + H2O(l) + CO2(g)

1) Analyze – List the knowns & unknowns. Use the thermochemical equation above to write a conversion factor relating kilojoules

of heat and moles of NaHCO3. Then use the conversion factor to determine ΔH for 2.24 mol NaHCO3.

2) Calculate – Solve for the unknown.

2.24 mol NaHCO3

ΔH = 85 kJ for 2 mol NaHCO3

Now you try…

The production of iron and carbon dioxide from iron III oxide and carbon monoxide is an exothermic reaction. How many kilojoules of

heat are produced when 3.40 mol Fe2O3 reacts with an excess of CO?

Fe2O3(s) + 3 CO(g) 2 Fe(s) + 3 CO2(g) + 26.3 kJ

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Using the Heat of Fusion in Phase Change Calculations

How many grams of ice at 0⁰C will melt if 2.25 kJ of heat are added?

1) Analyze – List the knowns & the unknown. Find the number of moles of ice that can be melted by the addition of 2.25 kJ of heat.

Convert moles of ice to grams of ice.

2) Calculate – Solve for the unknown.

Initial & Final temperature = 0⁰C

ΔHfus = 6.01 kJ/mol

ΔH = 2.25 kJ

mice = ?? g

Now you try…

How many kilojoules of heat are required to melt a 50.0 g popsicle at 0⁰C. Assume the popsicle has the same molar mass and heat of

fusion as water.

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Using the Heat of Vaporization in Phase Change Calculations

How much heat (in kJ) is absorbed when 24.8 g H2O(l) at 100⁰C and 101.3 kPa is converted to H2O(g) at 100⁰C?

1) Analyze – List the knowns & the unknown. Convert grams of water into moles of water. Then find the amount of heat that is

absorbed when the liquid is converted to steam.

2) Calculate – Solve for the unknown.

Initial & final conditions = 100⁰C and 101.3 kPa

m = 24.8 g

ΔHvap = 40.7 kJ/mol

ΔH = ?? kJ

Now you try…

How much heat is absorbed when 63.7 g H2O(l) at 100⁰C and 101.3 kPa is converted to H2O(g) at 100⁰C? Express your answer in kJ.

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Calculating the Enthalpy Change in Solution Formation

How much heat (in kJ) is released when 2.50 mol NaOH(s) is dissolved in water?

1) Analyze – List the knowns & the unknown. Use the heat of solution for the dissolution of NaOH(s) in water to solve for the

amount of heat released (ΔH).

2) Calculate – Solve for the unknown.

ΔHsoln = -44.5 kJ/mol

amount of NaOH(s) dissolved = 2.50 mol

ΔH = ?? kJ

Now you try…

How many moles of NH4NO3(s) must be dissolved in water so that 88.0 kJ of heat is absorbed from the water? ΔHsoln for the

dissolution of NH4NO3(s) in water is 25.7 kJ/mol.

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Using Hess’s Law to Calculate the Heat of Reaction

Diamond is converted to graphite by the following reaction:

C(s,diamond) C(s, graphite)

Calculate the enthalpy change for this reaction given the following combustion reactions.

C(s,diamond) + O2(g) CO2(g) ΔH = -395.4 kJ

C(s,graphite) + O2(g) CO2(g) ΔH = -393.5 kJ

1) Write the overall equation for the reaction if not given.

2) Manipulate the given equations for the steps of the reaction so they add up to the overall equation. If you flip the equation, the

sign for ΔH changes!

3) Add up the equations cancelling common substances in reactant & product.

4) Add up the heats of the steps to get the heat of the overall reaction.

C(s,diamond) + O2(g) CO2(g) ΔH = -395.4 kJ

CO2(g) C(s,graphite) + O2(g) ΔH = 393.5 kJ

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C(s,diamond) C(s,graphite) ΔH = -1.9 kJ

Now you try…

Calculate the enthalpy change for the formation of lead (IV) chloride by the reaction of lead (II) chloride with chlorine.

PbCl2(s) + Cl2(g) PbCl4(l) ΔH = ??

Use the following thermochemical equations:

Pb(s) + 2 Cl2(g) PbCl4(l) ΔH = -329.2 kJ

Pb(s) + Cl2(g) PbCl2(s) ΔH = -359.4 kJ

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Calculating the Standard Heat of Reaction

What is the standard heat of reaction (ΔH⁰) for the reaction of CO(g) with O2(g) to form CO2(g)?

1) Analyze – List the knowns & the unknown. Balance the equation of the reaction of CO(g) with O2(g) to form CO2(g). Then

determine ΔH⁰ using the standard heats of formation for the reactants and products.

2) Calculate – Solve for the unknown.

ΔHf⁰ CO(g) = -110.5 kJ/mol ΔHf⁰ O2(g) = 0 kJ/mol (free element) ΔHf⁰ CO2(g) = -393.5 kJ/mol

2 CO(g) + O2(g) 2 CO2(g)

Now you try…

What is the standard heat of reaction (ΔH⁰) for the formation of NO2(g) form NO(g) and O2(g)?

ΔHf⁰ NO2(g) = 33.85 kJ/mol ΔHf⁰ NO(g) = 90.37 kJ/mol ΔHf⁰ O2(g) = 0 kJ/mol