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D2.3 · Calculate reaction heat with Q = mcΔT

Learn to calculate reaction heat with q = mcδt through clear examples and targeted practice.

Ontario Grade 12 Chemistry

Energy Changes and Rates of Reaction

Use measured temperature change without losing the sign

A calorimeter lets us estimate heat transferred during a process by measuring a temperature change in a surrounding substance, often water. The basic SCH4U calculation begins with the mass being warmed or cooled, its specific heat capacity, and its temperature change. Keep the system boundary explicit: the water and the chemical reaction exchange energy in opposite directions.

What you will learn

  • Calculate the heat gained or lost by water.
  • Relate the sign of the water heat to the sign of reaction heat.
  • Convert heat from one sample to an amount per mole when enough data are given.

Set up the heat equation

Use the mass of the substance whose temperature you measured, not automatically the mass of the reactant. In a simple water calorimeter, the measured substance is water. Its specific heat capacity is approximately 4.18 joules per gram per degree Celsius near room temperature. Calculate final temperature minus initial temperature before substituting.
The heat value is positive when that measured substance warms and negative when it cools. Include units so grams and degrees Celsius cancel properly.
q=mc\Delta T, \Delta T=T_{final\mathrm{final}}-T_{initial\mathrm{initial}}

Connect water to the reaction

If we neglect heat absorbed by the container and heat lost to the room, energy conservation gives the reaction heat as the opposite of the water heat. An exothermic reaction releases energy while the surrounding water warms. That does not mean the reaction heat is positive: for the reaction system it is negative.
A real calorimeter can absorb some heat, so this simple relation is an approximation. Report that assumption rather than presenting a measured value as exact. To express heat per mole of reaction, divide by the amount of reactant corresponding to the balanced equation and state which reactant amount you used.
q_{reaction\mathrm{reaction}}\approx -q_{water\mathrm{water}}

Worked example

Water warms during a reaction

A reaction warms 100.0 g of water from 20.0 °C to 25.0 °C. Estimate the heat absorbed by the water and the heat released by the reaction, assuming negligible heat loss and calorimeter heat capacity.
  1. Find the temperature change
    Subtract the initial temperature from the final temperature.
    ΔT=25.0−20.0=5.0 °C\Delta T=25.0-20.0=5.0\ °\mathrm C
  2. Calculate water heat
    Substitute the water mass and specific heat capacity.
    q_{water\mathrm{water}}=(100.0\ \mathrm g)(4.18\ Jg−1°C−1\mathrm{J g^{-1} {}° C^{-1}})(5.0\ °\mathrm C)=2.09\times10^3\ \mathrm J
  3. Apply the energy balance
    The reaction releases approximately the heat that the water absorbs.
    q_{reaction\mathrm{reaction}}\approx-2.09\times10^3\ \mathrm J
Answer: The water absorbs about 2.1 kJ; the reaction releases about 2.1 kJ, so its heat is about −2.1 kJ for this sample.
Check: The water temperature rose, so its heat is positive and the exothermic reaction heat is negative.

Common mistakes and how to avoid them

Assigning the same positive sign to both water and reaction heat.
Correction: State which system your heat value describes. Under the stated approximation, the two heat values have opposite signs.
Calling the result a molar enthalpy without the reacted mole amount.
Correction: The sample heat is not an energy-per-mole value. Divide by moles only when the amount and balanced reaction are known.

Lesson summary

  • Calculate temperature change as final minus initial.
  • For the measured substance, use its mass and heat capacity in q=mcDeltaTq=mcDelta T.
  • Use the opposite sign for the reaction only under the stated energy-balance approximation.

Check your understanding

Question 1

Water cools during a process. Under the simple energy balance, what is the sign of the reaction heat?
  1. Positive
  2. Negative
  3. Always zero
Show answer and explanation
Positive
Cooling water loses heat, so water heat is negative. The reaction absorbs that heat and is endothermic, so reaction heat is positive.

Key terms

Specific heat capacity
Heat needed to raise one unit mass of a substance by one degree of temperature.
Calorimeter
An apparatus used to estimate heat transfer from measured temperature changes.

Continue through SCH4U

View the complete SCH4U Ontario Grade 12 Chemistry curriculum and lessons

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Chemistry (SCH4U), expectation D2.3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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