Calorimetry: Measuring Heat Changes in Chemical Reactions

5.5 Calorimetry

Learning Objectives

• Understand the concept and application of calorimetry.

• Define heat capacity and specific heat.

• Calculate specific heat and heat of reaction using calorimetric data.

Calorimetry

Definition and Purpose

Calorimetry is the experimental technique used to measure the heat exchanged during chemical or physical processes. It is especially important for determining the change in enthalpy ($\Delta H$) of a reaction.

• A calorimeter is a device used to measure the heat flow from a system to its surroundings.

• Common calorimeters include simple coffee-cup calorimeters (for reactions at constant pressure) and bomb calorimeters (for reactions at constant volume).

Example apparatus: A typical coffee-cup calorimeter consists of two nested Styrofoam cups, a thermometer, a glass stirrer, and a cork stopper to minimize heat exchange with the environment.

Heat Capacity (C)

Definition and Formula

Heat capacity ($C$) is the amount of energy required to raise the temperature of a substance by 1 Kelvin (K) or 1 degree Celsius (°C).

• Measured in units of Joules per Kelvin (J/K).

• Heat capacity depends on both the type and amount of substance.

Formula:

$C = \frac{q}{\Delta T}$

• $q$ = heat transferred (Joules)

• $\Delta T$ = temperature change (K or °C)

Note: Heat capacity is an extensive property (depends on the amount of substance).

Specific Heat Capacity ($C_s$)

Definition and Formula

Specific heat capacity ($C_s$), also called specific heat, is the amount of energy required to raise the temperature of 1 gram of a substance by 1 K (or 1 °C).

• Measured in Joules per gram per degree Celsius (J/g·°C).

• Specific heat is an intensive property (independent of the amount of substance).

Formula:

$C_s = \frac{q}{m \Delta T}$

• $q$ = heat transferred (Joules)

• $m$ = mass of substance (grams)

• $\Delta T$ = temperature change (K or °C)

Example: It takes 4.184 J of heat to raise the temperature of 1.00 g of liquid water by 1 °C.

Conversion: $1 \text{ cal} = 4.184 \text{ J}$

Calculating Heat of Reaction Using Calorimetry

Example 5.7: Combustion of Methylhydrazine

The combustion of methylhydrazine ($\mathrm{CH_6N_2}$), a liquid rocket fuel, produces nitrogen gas, carbon dioxide, and water:

$2\ \mathrm{CH_6N_2}(l) + 5\ \mathrm{O_2}(g) \rightarrow 2\ \mathrm{N_2}(g) + 2\ \mathrm{CO_2}(g) + 6\ \mathrm{H_2O}(l)$

• 4.00 g of methylhydrazine is combusted in a bomb calorimeter.

• The temperature of the calorimeter increases from 25.00 °C to 39.50 °C.

• The heat capacity of the calorimeter is 7.794 kJ/°C.

Step 1: Calculate Temperature Change

$\Delta T = T_f - T_i = 39.50\ ^\circ\mathrm{C} - 25.00\ ^\circ\mathrm{C} = 14.50\ ^\circ\mathrm{C}$

Step 2: Calculate Heat Absorbed by Calorimeter

$q = C \Delta T = (7.794\ \mathrm{kJ}/^\circ\mathrm{C})(14.50\ ^\circ\mathrm{C}) = 113.013\ \mathrm{kJ}$

Step 3: Relate Heat to System

In a bomb calorimeter, the heat released by the reaction ($q_{system}$) is absorbed by the calorimeter ($q_{surroundings}$):

$q_{surroundings} = -q_{system}$

So, $q_{system} = -113.013\ \mathrm{kJ}$

Step 4: Calculate Moles of Methylhydrazine

Molar mass of $\mathrm{CH_6N_2}$ = 46.1 g/mol

$\text{Moles} = \frac{4.00\ \mathrm{g}}{46.1\ \mathrm{g/mol}} = 0.08677\ \mathrm{mol}$

Step 5: Calculate Heat of Reaction per Mole

$\text{Heat of reaction} = \frac{-113.013\ \mathrm{kJ}}{0.08677\ \mathrm{mol}} = -1302\ \mathrm{kJ/mol} \approx -1.30 \times 10^3\ \mathrm{kJ/mol}$

Summary Table: Key Calorimetry Quantities

Quantity	Symbol	Definition	Units	Formula
Heat Capacity	C	Energy required to raise temperature of a substance by 1 K (or 1 °C)	J/K	$C = \frac{q}{\Delta T}$
Specific Heat Capacity	$C_s$	Energy required to raise temperature of 1 g of a substance by 1 K (or 1 °C)	J/g·°C	$C_s = \frac{q}{m \Delta T}$
Heat Transferred	q	Amount of heat absorbed or released	J or kJ	$q = C \Delta T$ or $q = m C_s \Delta T$

Additional info: In bomb calorimetry, the reaction occurs at constant volume, so the measured heat corresponds to the change in internal energy ($\Delta U$), which is approximately equal to $\Delta H$ for reactions involving only solids and liquids, or when the change in moles of gas is small.