A candy bar has a total mass of 75.0 grams. In a calorimetry experiment, a 1.0-g sample of this candy bar was burned in a calorimeter surrounded by 1000g of water. The temperature of the water in contact with the burning candy bar was measured and found to increase from an initial temperature of 21.2C to a final temperature of 24.3C.
a. Calculate the amount of heat in calories release when the 1.0-g sample burned.
b. Convert the heat in calories to nutritional Calories and then calculate the energy content (fuel value) in Cal/g.
c. Calculate the total caloric content of the candy bar in Calories.
In a calorimetry experiment, the heat released when a 1.0-g sample of a candy bar burned can be calculated using the formula q = mcΔT. The heat released is 3100 calories. Converting this to nutritional Calories and calculating the energy content (fuel value) in Cal/g gives an energy of 3.1 Cal/g. The total caloric content of the candy bar is calculated by multiplying the energy content by the mass of the candy bar.
Explanation:a. Calculate the amount of heat in calories released when the 1.0-g sample burned.
The heat released can be calculated by using the formula:
q = mcΔT
Where:
q is the heat released in caloriesm is the mass of the water (1000g)c is the specific heat capacity of water (1 cal/g°C)ΔT is the change in temperature (24.3 - 21.2 = 3.1°C)Plugging in the values into the formula:
q = (1000g)(1 cal/g°C)(3.1°C) = 3100 calories
b. Convert the heat in calories to nutritional Calories and then calculate the energy content (fuel value) in Cal/g.
Nutritional Calories are equivalent to 1000 calories. To convert from calories to nutritional Calories:
Energy in nutritional Calories = heat released in calories / 1000
Energy in nutritional Calories = 3100 calories / 1000 = 3.1 nutritional Calories
Energy content (fuel value) in Cal/g = energy in nutritional Calories / mass of the sample (1.0g)
Energy content in Cal/g = 3.1 nutritional Calories / 1.0g = 3.1 Cal/g
c. Calculate the total caloric content of the candy bar in Calories.
To calculate the total caloric content of the candy bar in Calories, we can use the formula:
Total caloric content = energy content (fuel value) in Cal/g * mass of the candy bar (75.0g)
Total caloric content = 3.1 Cal/g * 75.0g = 232.5 Calories
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