Substituting the mathematical relationship for q gives:
−(csolid×msolid×ΔTsolid) =cwater×mwater×ΔTwater
This equation can then be solved for the specific heat capacity of the solid.
The constant-volume bomb calorimeter is used to measure the energy changes that
occur during combustion reactions. A weighed sample of the substance being investigated
is placed in the calorimeter, and compressed oxygen is added. The sample is ignited by a
hot wire, and the temperature change of the calorimeter and a known mass of water is
measured. The heat capacity of the calorimeter/water system is sometimes known.
For example, a 1.5886 g sample of glucose (C 6 H 12 O 6 ) was ignited in a bomb calorime-
ter. The temperature increased by 3.682°C. The heat capacity of the calorimeter was
3.562 kJ/°C, and the calorimeter contained 1.000 kg of water. Find the molar heat of reac-
tion (i.e., kJ/mole) for:
C 6 H 12 O 6 (s) +6 O 2 (g) →6 CO 2 (g) +6 H 2 O(l)
Answer:
total heat =13.12 kJ +15.40 kJ = 28.52 kJ
Note: The temperature increased so the reaction was exothermic (−)
→−28.52 kJ
(.
.
1 000
1000
1
4 184 1
1000
kg)
g
kg
J
gC
kJ
J
⎛
⎝
⎜
⎞
⎠
⎟
°
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝⎝
⎜
⎞
⎠
⎟(.3 682 C) = 15.40 kJ°
(.
(
(.
3 562
3 682
kJ)
C)
C)=13.12 kJ
°
°
Thermodynamics 125
Electrical
source
+
Stirrer
Thermometer
Water bath
Ignition coil
Stirrer Thermometer
Polystrene cups
Water
Sample
(a) Coffee-cup calorimeter
(constant pressure) (b) Bomb calorimeter (constant volume)
Figure 9.1 Two types of calorimeters.