Question

Calorimetry can also be used to determine nutritional Calories, which are actually kilocalories. One (1) nutritional Calorie = 1000 calories, and 1 calorie = 4.184 J. When 1.0 g of a snack cake is combusted in a constant-volume bomb calorimeter with a heat capacity (including its water) of 10.0 kJ/°C, the temperature of the calorimeter rises by 1.42°C. How many nutritional calories (Calories) are in one serving (28 g) of this snack cake? Enter your answer to three significant figures in units of Calories.

Answer 1

95.0 nutritional calories

Step-by-step explanation:

Given that:

One (1) nutritional Calorie = 1000 calories,

1 calorie = 4.184 J

Energy released when 1.0 g of a snack cake is combusted = Heat capacity(q) × temperature rise of the calorimeter ( ΔT)

= 10.0 kJ/°C × 1.42 °C

= 14.2 kJ

Energy released when 28 g snack cakes are used = 14.2 kJ × 28

= 397.6 kJ

In calories, the energy released =
`(397.6*10^3J)/(4.184J)` (since; 1 calorie = 4.184 J)

= 95028.68069

≅ 95.029 × 10³ calories

∴ the nutritional calories in one serving (28 g) of this snack cake can be calculated as:

=
`(95.029*10^3calories)/(1000 calories)`

= 95.029 nutritional calories

= 95.0 nutritional calories (to 3 significant figures)

∴ there are 95.0 nutritional calories in one serving (28 g) of this snack cake.