Worksheet 2 – Energy, Enthalpy, Work, and Heat Capacity
Energy, Work, Enthalpy and Heat Capacity
Introduction
Thermochemistry is a branch of chemistry that describes the energy changes that occur during
chemical reactions. In some situations, the energy produced by chemical reactions is actually of
greater interest to chemists than the material products of the reaction. For example, the controlled
combustion of organic molecules, primarily sugars and fats, within our cells provides the energy
for physical activity, thought, and other complex chemical transformations that occur in our
bodies. Similarly, our energy-intensive society extracts energy from the combustion of fossil
fuels, such as coal, petroleum, and natural gas, to manufacture clothing and furniture, heat your
home in winter and cool it in summer, and power the car or bus that gets you to class and to the
movies.
Learning Objectives
●
●
●
●
Distinguish between systems and surroundings
Distinguish between exothermic and endothermic processes
Relate internal energy, E, to heat flows and work
Calculate energies gained or lost during changes in temperature and physical state
Resources
Gilbert, Section 10.1 - 10.4
ChemTours
All Chemtours
Videos
Internal energy
Heat capacity and specific heat (with example problems)
Prerequisites
Heat, properties of gasses,
1
Vocabulary
System, surroundings, internal energy, endothermic, exothermic
Focus Information
Thermodynamics - The study of energy and its transformations.
Thermochemistry - The part of thermodynamics dealing with chemical reactions.
First Law of Thermodynamics - Conservation of energy. Energy cannot be created or
destroyed, but it can be moved between the system and the surroundings.
System - the part of the universe we are interested in
Surroundings - everything else
Universe = system + surroundings
∆Euniv = ∆Esys + ∆Esurr
Energy - the capacity to do work or transfer heat
work = force × distance
Heat - (kinetic) energy transferred from a hot body to a cold body (from high T to low T). Once
the temperature becomes uniform, we say it has reached thermal equilibrium.
Internal energy is related to q and w and is expressed as
∆E = q + w
Where E is the internal energy of the system, q is the heat flow into the system, and w is the
work done on the system.
If q is positive, heat flows into the system. If q is negative, heat flows out of the system
If w is positive, work is done on the system, if w is negative, work is done by the system (to the
surroundings).
Thermal energy is the kinetic energy associated with the random motion of atoms or molecules.
The thermal energy is proportional to the temperature.
2
State function - depends only upon the current state of the system, not upon the path used to
arrive at the state. Changes in state functions depend only upon the initial and final states, not on
the path. Energy is a state function.
ΔE = ΔE f
­ ΔE
i
Other examples of state functions: T, P, V, n
Heat and work are not state functions
Exothermic process - heat flows out of)the system
Endothermic process - heat flows into the system
Energy Units and Pressure-Volume Work
The units of energy, work, and heat must be the same (Joules, J) when doing calculations.
When a system expands (against a constant pressure) it does work. The amount of work is given
by -PΔV. (Note: pressure = force/area, so P V = f orce distance . Also, when a system
expands, it expends energy and so w is negative).
×
Therefore, substituting -PΔV for work, ΔE = q
×
­ P ΔV
Enthalpy and Enthalpy Changes
ΔH = qp − the heat flow under constant pressure conditions.
ΔH = Hf – Hi = Hproducts - Hreactants
If ΔH > 0, heat flows into the system - Endothermic process
If ΔH < 0, heat flows out of the system - Exothermic process
Heating Curves, Molar Heat Capacity, and Specific Heat
When heat flows, the temperature changes by some amount (ΔT).
- More heat → larger ΔT.
- ΔT is positive for heat flow into the system, negative for heat flow out of the system.
- The composition of the system affects ΔT. This is expressed in terms of the heat
capacity C - the amount of energy required to raise the temperature of an object by 1°C
(or 1 K).
→ q = CΔT (where ΔT = Tf – Ti)
3
-
-
The size of the system affects ΔT. A larger system requires more heat to flow to get the
same ΔT → larger heat capacity. So, C = mcs , where cs is the specific heat - the amount
of energy required to raise the temperature of 1 gram of a substance by 1°C.
Since it is common to express the amounts of chemicals in terms of moles, the molar heat
capacity, cp, is usually used.
→ q = ncpΔT
For phase changes, instead of using the heat capacity, we simply look up the molar heat
of transition. For melting it is the molar heat of fusion (Hfus) and for boiling it is the molar
heat of vaporization (Hvap).
Useful conversions
1 L.atm = 101.325 J
4
Worksheet 2 – Energy, Enthalpy, Work, and Heat Capacity
Questions to be graded - 3 and 11
Homework related to
Key Questions
1. Explain what is meant by a state function.
2. The figure represents a chemical reaction between
CH4 and H2O taking place at constant temperature
and pressure.
a. Write a balanced chemical equation for the
reaction.
b. Is w positive, negative, or zero for this
reaction?
3. Assuming the kernels of unpopped popcorn in the figure
constitute a thermodynamic system, what are the signs of q,
w, and ΔE during the popping process?
4. Which of the following processes are exothermic, and which are endothermic?
a. Molten aluminum solidifies.
b. Rubbing alcohol evaporates from the skin.
c. Fog forms over San Francisco Bay.
5
5. Calculate ΔE when
a. q = 100.0 J, w = 50.0 J
b. q = 6.2 kJ, w = 0.70 L.atm
c. q = -615 kJ, w = -3.25 kilowatt.hours (1 kWh = 3600 kJ)
6. Calculate ΔE for the combustion of a gas that releases 210.0 kJ of heat to its surroundings
and does 65.5 kJ of work on its surroundings.
7. Calculate ΔE for a chemical reaction that releases 90.7 kJ of heat but does no work on its
surroundings.
8. Breaking the small pouch of water inside a chemical cold pack containing ammonium nitrate
activates the pack, which is used by sports trainers for injured athletes. What is the sign of
ΔH for the process taking place in the cold pack?
9. The stable forms of hydrogen and oxygen at room temperature and pressure are the gas-phase
diatomic molecules H2 and O2. What is the sign of ∆H for the following processes?
a. A solid with metallic properties is formed when hydrogen gas is compressed under
extremely high pressure: H2(g) ➝ H2(s)
b. High-energy light shines on oxygen gas in the upper reaches of the atmosphere,
converting oxygen gas to oxygen atoms: O2(g) ➝ 2 O(g)
10. Gypsum is the common name of calcium sulfate dihydrate, which has the formula CaSO4 • 2
H2O. When gypsum is heated to 150°C, it loses most of the water in its formula and forms
plaster of Paris (CaSO4 • 0.5 H2O):
2 CaSO4 • 2 H2O(s) ➝ 2 CaSO4 • 0.5 H2O(s) + 3 H2O(g)
What is the sign of ΔH for making plaster of Paris from gypsum?
11. Why is the heat of vaporization of water so much larger than its heat of fusion?
6
12. 100.0 grams of water is initially kept at 30oC.
a. Convert 100.0 g of water to moles of water.
b. If the molar heat capacity of water is 75.3 J/mol.oC, how much energy must be absorbed
by the water to raise its temperature from to 100.0°C?
13. During a strenuous workout, an athlete generates 233 kJ of thermal energy.
a. If the ∆Hvap for water is 40.7 kJ/mol, how many moles of water have to evaporate from
the athlete’s skin to dissipate this energy?
b. What mass of water would have to evaporate from the athlete’s skin to dissipate this
energy?
7