Answer to Question #148299 in General Chemistry for liam donohue

Question

A sample of high quality dog food was analysed for its energy content. Using calorimetry, a 25.8g sample of food was combusted and the surrounding water bath (92.0g) starting at 20.2 degrees raised to 26,7 degrees.

How many calories are in the dog food per gram? S(H2O)= 4.181 J g^-1 degrees^-1

Answer 1

Q148299

A sample of high quality dog food was analysed for its energy content. Using calorimetry, a 25.8g sample of food was combusted and the surrounding water bath (92.0g) starting at 20.2 degrees raised to 26,7 degrees.

How many calories are in the dog food per gram? S(H2O)= 4.181 J g^-1 degrees^-1

Solution :

25.8g of food was combusted and the energy released was used in increasing the temperature of 92.0 g of water.

We can find the energy gained by the water in the form of heat and then by using energy and mass of food, we can find the calories per gram in the dog feed.

The relation between heat and specific heat capacity is given as.

$$Q = m * s * ∆T ;$$

where Q is the heat gained by water in Joules.

‘s’ is the specific heat capacity of water in J/g ⁰ C.

‘m’ is the mass of water in grams

∆T = change in temperature of the water.

m = 92.0 g,

s = 4.181 J/ g ⁰ C.

T_initial = 20.2 ⁰C.

T_final = 26.7 ⁰ C.

∆T = T_initial - T_final = 26.7 ⁰ C - 20.2 ⁰C = 6.5 ⁰C.

Plug all this information in the formula, we have

Q = 92.0 g * 4.181 J/ g ⁰ C * 6.5 ⁰C.

Q = 2500.24 Joules.

This is the energy released by burning 25.8 g of food.

To find the energy released per gram, we divide the calculated energy by the mass of the food.

Energy released per gram = 2500.24 J / 25.8 g = 96.908 J/g .

In question, we are asked ‘calories in the feed per gram’ , so we convert J/g to calories/g

by using, 1 calorie = 4.184 J.

Calories in the dog feed per gram = $\frac{96.908J}{1g}*\frac{1 calorie}{4.184 J } = 23.16 calorie/g .$

= 23.16 calories per gram.

In question, we are given all the quantities in 3 significant figures, so our final answer must also be in 3 significant figures.

Hence calories in the dog feed per gram is 23.2 calories per gram.