Question 10.6: A Famous Amos bite-sized chocolate chip cookie weighing 7.25...
A Famous Amos bite-sized chocolate chip cookie weighing 7.25 \text{g} is burned in a bomb calorimeter to determine its energy content. The heat capacity of the calorimeter is 39.97 \text{kJ/°C}. During the combustion, the temperature of the water in the calorimeter increases by 3.90°\text{C}. Calculate the energy content (in \text{kJ/g}) of the cookie.
Strategy Use Equation 10.16 (q_\text{rxn} = –C_\text{cal}∆T) to calculate the heat released by the combustion of the cookie. Divide the heat released by the mass of the cookie to determine its energy content per gram.
Setup C_\text{cal} = 39.97 \text{kJ/°C} and ∆T = 3.90°\text{C}.
From Equation 10.16 we have
q_\text{rxn} = –C_\text{cal}∆T = –(39.97 \text{kJ/°C})(3.90°\text{C}) = –1.559 × 10^2 \text{kJ} ^*
Because energy content is a positive quantity, we write
\text{energy content per gram} = \frac{1.559 × 10^2 \text{kJ}}{7.25 \text{g}} = 21.5 \text{kJ/g}
^* Student Annotation: The negative sign in the result indicates that heat is released by the combustion.