Complete combustion of a 0.350 g sample of a compound in a bomb calorimeter releases 14.0 kJ of heat. The bomb calorimeter has a mass of 1.20 kg and a specific heat of [tex]$3.55 J /\left( g _{ i }{ }^{\circ} C \right)$[/tex].
If the initial temperature of the calorimeter is [tex]$22.5^{\circ} C$[/tex], what is its final temperature?
Use [tex]$q=m C_p \Delta T$[/tex].
A. [tex]$19.2^{\circ} C$[/tex]
B. [tex]$25.8^{\circ} C$[/tex]
C. [tex]$34.2^{\circ} C$[/tex]
D. [tex]$72.3^{\circ} C$[/tex]
Answer (1)
Convert the mass of the calorimeter from kg to g and the heat released from kJ to J.
Calculate the change in temperature, Δ T , using the formula q = m c a l or im e t er C p Δ T .
Calculate the final temperature, T f , using the formula T f = T i + Δ T .
The final temperature of the calorimeter is 25. 8 ∘ C .
Explanation
Understanding the Problem We are given a problem involving the complete combustion of a compound in a bomb calorimeter. We are given the mass of the compound, the heat released during combustion, the mass and specific heat of the calorimeter, and the initial temperature of the calorimeter. We are asked to find the final temperature of the calorimeter using the formula q = m C p Δ T .
Unit Conversions First, we need to convert the mass of the calorimeter from kilograms (kg) to grams (g). Since 1 kg = 1000 g, we have: m c a l or im e t er = 1.20 kg × 1000 kg g = 1200 g Next, we need to convert the heat released from kilojoules (kJ) to joules (J). Since 1 kJ = 1000 J, we have: q = 14.0 kJ × 1000 kJ J = 14000 J
Calculating the Temperature Change Now, we can use the formula q = m C p Δ T to calculate the change in temperature, Δ T . We have: q = m c a l or im e t er C p Δ T Δ T = m c a l or im e t er C p q Substituting the values we have: Δ T = 1200 g × 3.55 g ⋅ ∘ C J 14000 J = 1200 × 3.55 14000 ∘ C = 4260 14000 ∘ C ≈ 3.286 ∘ C
Calculating the Final Temperature Finally, we can calculate the final temperature, T f , using the formula Δ T = T f − T i , so T f = T i + Δ T . We have: T f = T i + Δ T = 22.5 ∘ C + 3.286 ∘ C = 25.786 ∘ C Rounding to one decimal place, we get T f = 25.8 ∘ C .
Final Answer The final temperature of the calorimeter is approximately 25. 8 ∘ C .
Examples
Bomb calorimeters are used to measure the heat released during chemical reactions, such as the combustion of fuels or the metabolism of food. For example, if we wanted to determine the caloric content of a new snack food, we could combust a known mass of the food in a bomb calorimeter and measure the heat released. This information is then used to calculate the number of calories per serving, which is displayed on the nutrition label. The principles of calorimetry are also used in industrial processes to optimize reaction conditions and ensure efficient energy usage.
