AP Chemistry · Lesson 1

Heat and calorimetry

Know Know it

Heat flows from a warmer object to a cooler one until they reach the same temperature, thermal equilibrium. The system is the process you study; the surroundings are everything else. Energy is conserved, so the heat the system loses equals the heat the surroundings gain.

With no phase change, the heat a substance gains or loses is q=mcΔTq = mc\Delta T: mass (g) times specific heat (J/(g·°C)) times the temperature change, final minus initial. Water's specific heat is 4.18 J/(g·°C).

In a coffee-cup calorimeter, a reaction happens in water. If the water warms, the reaction released heat: it is exothermic and its q is negative. If the water cools, the reaction absorbed heat: it is endothermic and its q is positive. In symbols, qreaction=−qwaterq_{\text{reaction}} = -q_{\text{water}}.

During a phase change the temperature stays constant while heat goes into or out of the substance: q = n × ΔH of the change, such as the enthalpy of fusion for melting.

Calculator On the exam

You may use a scientific or graphing calculator on both sections of the exam; a four-function calculator is allowed but not recommended, and a reference booklet of equations and constants is provided. Calorimetry answers come out in joules from q=mcΔTq = mc\Delta T; divide by 1000 for kilojoules before you divide by moles, and give the sign and the unit (kJ/mol) with a molar enthalpy.

Worked example Easy

How much heat does 125 g of water absorb when it warms from 22.0 °C to 48.0 °C? (Water: c = 4.18 J/(g·°C).)

  1. 25.1 kJ
  2. 11.5 kJ
  3. 13.6 kJAnswer
  4. 0.109 kJ

How to solve it

  1. ΔT = 48.0 − 22.0 = 26.0 °C.
  2. q = 125 × 4.18 × 26.0 = 13,585 J.
  3. Rounded to 3 significant figures: 13.6 kJ, absorbed by the water.

Why each choice is right or wrong

  • A. Incorrect. 25.1 kJ uses the final temperature, 48.0 °C, as ΔT; the change is 48.0 − 22.0 = 26.0 °C.
  • B. Incorrect. 11.5 kJ uses the starting temperature, 22.0 °C, as ΔT instead of the change of 26.0 °C.
  • C. Correct. q = mcΔT = 125 g × 4.18 J/(g·°C) × 26.0 °C = 13,585 J, or 13.6 kJ.
  • D. Incorrect. 0.109 kJ leaves out the 125 g mass, giving the heat for just 1 g of water.

Trap Warm water means a negative q for the reaction

When the water in a calorimeter warms up, the water gained heat, so the reaction lost it. Do not give the reaction the water's positive sign: an exothermic reaction has a negative q and a negative ΔH.

Explain Explain it

Task verbs: calculate, explain

To find a specific heat or a final temperature, set heat lost equal to heat gained: −m1c1ΔT1=m2c2ΔT2-m_1c_1\Delta T_1 = m_2c_2\Delta T_2. Each ΔT is that object's own final minus initial temperature, and both objects share the same final temperature.

To find a molar enthalpy, compute the heat the water gained, flip the sign for the reaction, and divide by the moles of the substance named in the question.

Worked example Medium

A 150.0 g block of an unknown metal is heated to 100.0 °C and dropped into 80.0 g of water at 20.0 °C in an insulated cup. The water and metal reach a final temperature of 31.5 °C. Assume no heat is lost to the cup or the air.

What is the specific heat of the metal? (Water: c = 4.18 J/(g·°C).)

  1. 0.374 J/(g·°C)Answer
  2. 0.814 J/(g·°C)
  3. 1.32 J/(g·°C)
  4. 0.256 J/(g·°C)

How to solve it

  1. Heat gained by water: 80.0 g × 4.18 × (31.5 − 20.0) = 3846 J.
  2. The metal lost 3846 J while cooling from 100.0 °C to 31.5 °C, a change of 68.5 °C.
  3. c = 3846 J ÷ (150.0 g × 68.5 °C) = 0.374 J/(g·°C).

Why each choice is right or wrong

  • A. Correct. The water gains 80.0 × 4.18 × 11.5 = 3846 J, the metal loses that heat over a 68.5 °C drop, and 3846 ÷ (150.0 × 68.5) = 0.374 J/(g·°C).
  • B. Incorrect. 0.814 uses 31.5 °C, the final temperature, as the metal's ΔT; the metal cooled by 100.0 − 31.5 = 68.5 °C.
  • C. Incorrect. 1.32 swaps the two masses, putting 150.0 g with the water and 80.0 g with the metal.
  • D. Incorrect. 0.256 uses 100.0 °C as the metal's temperature change, as if it cooled all the way to 0 °C.

Explain Your turn

A student dissolves a salt in water in a coffee-cup calorimeter, and the temperature of the water falls from 24.0 °C to 19.5 °C. Say whether dissolving this salt is endothermic or exothermic, explain your answer using the direction of heat flow, and give the sign of ΔH for the dissolving.

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Compare with a model answer

A full answer does this

  • Says the dissolving is endothermic
  • Explains that heat flows from the water into the dissolving salt (the system), so the water cools
  • Gives ΔH a positive sign

Model answer

Dissolving this salt is endothermic. As the salt dissolves, it absorbs heat from the water around it, so heat flows from the water (the surroundings) into the dissolving salt (the system), and the water's temperature falls from 24.0 °C to 19.5 °C. Because the process absorbs heat, ΔH for the dissolving is positive.

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