A sample of propane [tex]$\left( C _3 H _8\right)$[/tex] has a mass of 0.47 g. The sample is burned in a bomb calorimeter that has a mass of 1.350 kg and a specific heat of [tex]$5.82 J /\left( g \cdot{ }^{\circ} C \right)$[/tex]. How much energy is released by the reaction if the temperature of the calorimeter rises by [tex]$2.87^{\circ} C$[/tex]? Use [tex]$q=m C_p \Delta T$[/tex].
Answer (1)
Convert the mass of the calorimeter from kg to g: 1.350 k g × 1000 = 1350 g .
Calculate the heat absorbed by the calorimeter: q = 1350 g × 5.82 J / ( g ⋅ ∘ C ) × 2.87 ∘ C = 22549.59 J .
Convert the energy from Joules to kJ: q ( k J ) = 22549.59 J /1000 = 22.54959 k J .
The energy released by the reaction is approximately 22.5 k J .
Explanation
Problem Analysis We are given the mass of a calorimeter, its specific heat, and the temperature rise when a sample of propane is burned. We need to find the amount of energy released by the reaction using the formula q = m C p Δ T .
Convert mass to grams First, we need to convert the mass of the calorimeter from kilograms to grams since the specific heat is given in J / ( g ⋅ ∘ C ) .
m c a l ( g ) = m c a l ( k g ) × 1000 m c a l = 1.350 × 1000 = 1350 g
Calculate heat absorbed by calorimeter Next, we calculate the heat absorbed by the calorimeter using the formula q = m c a l C p Δ T , where m c a l is the mass of the calorimeter in grams, C p is the specific heat of the calorimeter, and Δ T is the temperature rise. q = 1350 g × 5.82 J / ( g ⋅ ∘ C ) × 2.87 ∘ C q = 22549.59 J
Convert to kJ and round The energy released by the reaction is equal to the heat absorbed by the calorimeter. Since we want the energy released, we can take the absolute value of q. Finally, we convert the energy from Joules to kJ: q ( k J ) = q ( J ) /1000 q ( k J ) = 22549.59 J /1000 = 22.54959 k J Rounding to one decimal place, we get 22.5 kJ.
Final Answer Therefore, the amount of energy released by the reaction is approximately 22.5 kJ.
Examples
Bomb calorimeters are used to measure the heat released during combustion reactions, such as burning fuel. For example, knowing the energy released by burning a specific amount of propane helps engineers design efficient heating systems. If a home heating system burns 10 kg of propane, we can calculate the total energy released to estimate how well it will heat the house. This calculation is crucial for optimizing energy consumption and reducing costs.
