Question

A 0.100-g sample of your favorite candy is burned in a calorimeter that contains 1.00 kg of water initially at 21.0 ∘C. After the candy is burned, the water temperature is 34.5 ∘C. How many Calories are there per gram of your candy?

Answer 1

When the candy is burned, the heat transferred to the water is 13500 small calories. Consequently, there are 135 dietary Calories (Cal) per gram of the candy, calculated from the temperature change and the mass of the water and candy.

Step-by-step explanation:

To calculate the number of Calories per gram of candy based on a calorimetry experiment, we use the concept of specific heat capacity. The specific heat capacity of water is typically 4.184 J/g°C (or 1 cal/g°C). Given that 1,000 small calories are equivalent to one large calorie (also known as the dietary Calorie), we can determine the amount of heat transferred to the water in Calories and then divide by the mass of the candy.

We'll apply the formula: Heat (q) = mass (m) × specific heat capacity (c) × temperature change (ΔT), then convert joules to Calories and determine the Calories per gram of candy.

Let's calculate: mass of water = 1.00 kg = 1000 g, specific heat capacity of water = 1 cal/g°C, initial temperature = 21.0 °C, final temperature = 34.5 °C. Heat (q) = (1000 g) × (1 cal/g°C) × (34.5 °C - 21.0 °C) = 1000 g × 1 cal/g°C × 13.5 °C = 13500 cal. This is the heat absorbed by the water, which is the heat released by burning the candy. To find the Calories per gram of candy, we then divide this value by the mass of the candy: Calories/g = 13500 cal / 0.100 g = 135000 cal/g = 135 Cal/g.

Answer 2

Answer: 565.245kJ
To answer this question, you need to know how much water heat capacity which was 4.187 kJ/kg K. First, we need to find the calorie absorbed by water. Since the sample is 1kg, initial temperature is 21 ∘C and final temperature is 34.5 ∘C then the calculation would be:

Energy= (Final temp - initial temp) * heat capacity * mass
Energy = (34.5-21) ∘C * 4.187 * kJ/kg K * 1kg= 56.5245 kJ

The energy is made from 0.1 gram, then for 1 gram of energy it should be:
1 gram/ 0.1gram x 56.5245 kJ= 565.245kJ