One tablespoon of peanut butter has a mass of 16 g. It is combusted in a calorimeter whose heat capacity is 120.0 kJ/°C. The temperature of the calorimeter rises from 22.2 °C to 25.4 °C. Find the food caloric content of peanut butter.

Verified step by step guidance

1. Identify the temperature change (\( \Delta T \)) of the calorimeter by subtracting the initial temperature from the final temperature: \( \Delta T = T_{\text{final}} - T_{\text{initial}} \).
2. Use the formula for heat absorbed or released: \( q = C \times \Delta T \), where \( q \) is the heat absorbed or released, \( C \) is the heat capacity of the calorimeter, and \( \Delta T \) is the temperature change.
3. Calculate the total heat absorbed by the calorimeter using the heat capacity and the temperature change.
4. Convert the heat absorbed (in kJ) to food calories (Cal), knowing that 1 Cal = 1 kcal = 4.184 kJ.
5. Determine the caloric content per gram of peanut butter by dividing the total caloric content by the mass of the peanut butter sample (16 g).

Key Concepts

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this context, it involves using a calorimeter to determine the heat released during the combustion of peanut butter. The temperature change in the calorimeter, along with its heat capacity, allows us to calculate the energy produced by the reaction.

Heat Capacity

Heat capacity is the amount of heat energy required to change the temperature of a substance by one degree Celsius. In this problem, the calorimeter has a specific heat capacity of 120.0 kJ/°C, which means it absorbs this amount of energy for each degree of temperature increase. This property is crucial for calculating the total heat absorbed by the calorimeter during the combustion process.

Food Caloric Content

The food caloric content refers to the amount of energy provided by food when consumed, typically measured in kilocalories (kcal). To find this value for peanut butter, we calculate the total heat released during combustion and convert it to kilocalories, as food energy is commonly expressed in this unit. Understanding this concept helps in evaluating the energy contribution of different foods in a diet.