A researcher studying the nutritional value of a new candy places a 4.20 g sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.91 ∘ C. If the heat capacity of the calorimeter is 46.80 kJ ⋅ K - 1, how many nutritional Calories are there per gram of the candy?

7.75 Calories per gram of candy

Explanation:

The equation of a calorimeter is:

Q = C*ΔT

Where Q is heat involved in the reaction, C is heat capacity of the calorimeter (46.80kJ K⁻¹) and ΔT is change in temperature (2.91°C). Replacing:

Q = 46.80kJ K⁻¹ ₓ 2.91K

Q = 136.2 kJ are produced. If 4.184 kJ = 1kCal:

136.2 kJ ₓ (1kCal / 4.184 kJ) = 32.55 kCal per 4.20g of candy. Thus, Calories / g of candy are:

32.55 kCal / 4.20g = 7.75 Calories per gram of candy