There are only a few main types of thermochemistry problems to deal with, and keeping track of the types of problems will help when developing strategies to solve a particular problem. This guide is not meant to be a comprehensive explanation of how to solve problems, but rather a supplement that assumes familiarity with the language of thermochemistry. Reading the book and the Intro To Thermo prior to using this guide is essential.

Calorimetry problems. (just one of two subcategories; the 2nd category will be in the next module).

Calorimetry problems involve measuring temperature changes due to either combining substances with different temperatures or conducting chemical reactions inside of a calorimeter. The energy changes occurring can be calculated with the formula q = mass × ΔT × C_s. ΔT is defined as T_final – T_initial and it is important to keep track of the + or – sign of ΔT. Be aware of the sign of q, as it will help determine if the reaction or process is endo or exothermic.

Here's an example of a coffee cup calorimeter used to measure heat energy changes when a hot piece of metal is placed in cool water. Because the object is a metal and not soluble in water, we treat the heat energy changes separately.

The metal will get cooler as heat energy from the metal is transferred to the cool water. The value of ΔT (and q) for the metal will be negative since T_final is less than T_initial .

The water will get warmer as heat energy from the metal is transferred to the cool water. The value of ΔT (and q) for the water will be positive since T_final is greater than T_initial.

Substances with different temperatures, no chemical reactions: This is applicable for situations where two substances, each, each at different temperatures, are combined in a calorimeter and the substances come to thermal equilibrium without dissolving or reacting. This could be a block of metal in a liquid or two liquids mixing together. Thermal equilibrium means that the temperature of the two substances will eventually equalize to a common value. It is possible to determine the amount of heat energy that the cooler substance (q_cool) requires to warm up separately from the amount of heat energy that the warmer substance (q_warm) releases as it cools.

The values of q_warm and q_cool are theoretically equal but with opposite signs, due to the 1^st law of thermo. Whatever heat energy the warm object releases will be absorbed by the cool object, so q_warm = – q_cool. The formula q = mass × ΔT × C_s can be used to calculate both q_warm and q_cool separately, using the specific heat, mass, and ΔT specific to what is warming up, or what is cooling off.

Here are some things to watch out for when solving these kinds of problems.

ΔT: There are probably two values of ΔT for this type of problem, as the temperature changes (up and down) are not likely to be the same.
Mass: There are probably two values of ΔT for this type of problem, as each substance can have a mass independent of the other.
C_s: There are probably two values of C_s for this type of problem, as each substance can have a mass independent of the other.

Example:

Calculate the specific heat of a metal if adding 100.0 g of the metal at 50.00 °C is added to 50.0 g of water at 20.00 °C results in a final temperature of 23.10 °C. The C_s of water is 4.18 J/g∙°C.

Solution: q_metal = – q_water and q_metal = m_metal × $\Delta$ $Δ$ T_metal × C_s(metal) and q_water = m_water × $\Delta$ $Δ$ T_water × C_s(water)

100.0 g × 26.90 °C × C_s(metal₎ = 50.0 g × 3.10 °C × 4.18 J/g∙°C or C_s(metal) = 0.241 J/g∙°C

Review Questions:

What is the mathematical formula that relates heat energy changes to mass and temperature? ? q = mass × ΔT × Cs. ΔT
How is ΔT determined? ? T_final – T_initial
Can ΔT be negative? ? sure, if the final temp is less than the initial temp (gets cooler)
If a piece of cold metal is placed in hot water, what is the sign of q for the metal (q_m)? ? positive, since ΔT is positive, and the metal is warming up
If a piece of cold metal is placed in hot water, what is the sign of q for the water (q_w)? ? negative, since ΔT is negative as the water cools off
A substance needs 625 J of energy to heat 211 g by 2.30 °C. What is it's specific heat capacity? ? Cs = 1.29 J/g∙°C
A 5.00 g mass of a the new metal aquarium (Aq) was heated to 100.0 ^oC and then plunged into 100.0 g of water at 24.0 ^oC. The temperature of the resulting mixture became 28.0 ^oC.

1. What is the value of q for the water? ? 1.7x10³ J
2. What is the value of q for the sample of Aq? ? –1.7x10³ J
3. What is the specific heat capacity of this sample of Aq? ? 4.52 J/g∙°C

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positive, since ΔT is positive