Aresearcher studying the nutritional value of a new candy places a 4.10 g sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. the observed temperature increase is 2.10 ∘c. if the heat capacity of the calorimeter is 41.50 kj⋅k−1, how many nutritional calories are there per gram of the candy?

5.078 Cal/g

We are given;

Mass of the sample of candy as 4.10 g

Change in temperature, °C = 2.1 °C

Heat capacity of the calorimeter, C = 41.50 kJ/K

We are required to calculate the nutritional Calories per gram of candy

Since the Candy sample was burnt

Then the heat lost by the candy is equivalent to the heat absorbed by the calorimeter.

Therefore, we need to calculate the heat energy absorbed by the calorimeter.

Quantity of heat = Heat capacity × Change in temperature

Q = C×Δt

Q = 41.50 kJ/K × 2.1 K

  = 87.15 kJ

Therefore;

The heat released by 4.10 g of candy is  87.15 kJ

Calories per gram = Heat energy ÷  mass of candy

But; 1 kJ = 4.186  Calories

Therefore;

Number of calories =  87.15 kJ ÷ 4.186 Claories/kJ

                                = 20.82 Calories

Hence, calories per gram = 20.83 Cal ÷ 4.10 g

                                          = 5.078 Cal per g

                                          = 5.078 Cal/g

Thus, the nutritional Calories per gram of candy is  5.078 Cal/g