There are two main units used to describe heat, the calorie and the Joule. The conversion between them is 1 calorie = 4.184 J. A food calorie is equal to 1000 calories of heat or 1 kcal. So if you have a strip of bacon containing 22.0 g of fat and it takes 9 kcal/g of energy( heat) to digest fat, how many kJ of energy have you used? Express your answer to 3 significant figures.
22.0 g fat x 9 kcal/g x (4.184 kJ/kcal) = ? kJ
To find the amount of energy used in kilojoules (kJ), we need to first calculate the total amount of energy used to digest the fat in the strip of bacon.
Given:
Mass of fat = 22.0 g
Energy required to digest fat = 9 kcal/g
First, we need to calculate the total energy required:
Total energy = Energy per gram * Mass of fat
Total energy = 9 kcal/g * 22.0 g
Total energy = 198 kcal
Since 1 kcal = 1000 cal, we can convert kcal to cal by multiplying by 1000:
Total energy = 198 kcal * 1000 cal/kcal
Total energy = 198,000 cal
Next, we can convert calories to joules using the conversion factor:
Total energy = 198,000 cal * 4.184 J/cal
Total energy = 827,832 J
Finally, to convert joules to kilojoules, divide by 1000:
Total energy = 827,832 J / 1000
Total energy = 827.832 kJ
Therefore, you have used approximately 828 kJ of energy to digest the fat in the strip of bacon.
To calculate the amount of energy used in kilojoules (kJ), we need to convert the given information into the appropriate units and apply the appropriate conversions.
Given:
- Amount of fat in the strip of bacon: 22.0 g
- Energy required to digest fat: 9 kcal/g
To find the energy used, we need to multiply the amount of fat by the energy required to digest it.
1. Convert 22.0 grams to kilograms:
We know that 1 kg = 1000 grams, so:
22.0 g = 22.0/1000 kg = 0.022 kg
2. Convert kilocalories to calories:
Since 1 kcal = 1000 calories, we can calculate the energy in calories by multiplying the amount of fat in kilograms by the energy required per gram:
Energy (in calories) = 0.022 kg * 9 kcal/g * 1000 calories/kcal
3. Convert calories to joules:
Using the conversion factor of 1 calorie = 4.184 Joules, we can convert the energy in calories to joules:
Energy (in joules) = Energy (in calories) * 4.184 J/calorie
4. Convert joules to kilojoules:
Since 1 kJ = 1000 J, we divide the energy in joules by 1000 to get the energy in kilojoules:
Energy (in kilojoules) = Energy (in joules) / 1000
Now we can calculate it step by step:
Energy (in calories) = 0.022 kg * 9 kcal/g * 1000 calories/kcal
= 198 calories
Energy (in joules) = 198 calories * 4.184 J/calorie
≈ 828.432 Joules
Energy (in kilojoules) = 828.432 J / 1000
≈ 0.828 kJ
Therefore, you have used approximately 0.828 kJ of energy to digest the strip of bacon containing 22.0 g of fat.