The initial temperature of a bomb calorimeter is [tex]$28.50^{\circ} C$[/tex]. When a chemist carries out a reaction in this calorimeter, its temperature decreases to [tex]$27.45^{\circ} C$[/tex]. If the calorimeter has a mass of 1.400 kg and a specific heat of [tex]$3.52 J /\left( g \cdot{ }^{\circ} C \right)$[/tex], how much heat is absorbed by the reaction?
Use [tex]$q=m C_p \Delta T$[/tex].
A. 140 J
B. 418 J
C. [tex]$1,470 J$[/tex]
D. [tex]$5,170 J$[/tex]
Answer (2)
Convert the mass from kg to g: m = 1.400 × 1000 = 1400 g.
Calculate the change in temperature: Δ T = 27.45 − 28.50 = − 1.0 5 ∘ C .
Calculate the heat absorbed: q = m C p Δ T = 1400 × 3.52 × − 1.05 = − 5174.4 J.
The heat absorbed by the reaction is approximately 5 , 170 J .
Explanation
Problem Analysis We are given the initial and final temperatures of a calorimeter, its mass, and its specific heat. We need to find the amount of heat absorbed by the reaction using the formula q = m C p Δ T .
Mass Conversion First, we need to convert the mass of the calorimeter from kilograms to grams. Since 1 kg = 1000 g, we have: m = 1.400 kg = 1.400 × 1000 g = 1400 g
Temperature Change Next, we calculate the change in temperature, Δ T , which is the final temperature minus the initial temperature: Δ T = T f ina l − T ini t ia l = 27.4 5 ∘ C − 28.5 0 ∘ C = − 1.0 5 ∘ C
Heat Calculation Now we can calculate the heat absorbed, q , using the formula q = m C p Δ T :
q = (1400 \text{ g}) \times (3.52 \frac{\text{J}}{\text{g} \,^{\circ} C}) \times (-1.05^{\circ} C) = -5174.4 \text{ J} Since the temperature decreased, the reaction released heat, meaning the heat absorbed by the reaction is negative. The question asks for the amount of heat absorbed, so we take the absolute value.
Final Answer The amount of heat absorbed by the reaction is approximately 5174.4 J. Rounding to the closest option, we get 5170 J.
Examples
Bomb calorimeters are often used to measure the caloric content of food. For example, if you wanted to determine how many calories are in a gram of sugar, you could combust a known mass of sugar inside a bomb calorimeter and measure the temperature change of the water surrounding the bomb. Knowing the mass of the water and its specific heat capacity, you can calculate the heat released by the sugar, which is directly related to its caloric content. This principle helps nutritionists and food scientists determine the energy content of different foods.
The heat absorbed by the reaction in the bomb calorimeter is approximately 5170 J, calculated by using the mass, specific heat, and temperature change. Since the temperature dropped, the reaction released heat, but we consider the absolute value for absorption. The correct answer is option D.
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