A researcher studying the nutritional value of a new candy places a 4.10-gram sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.47 °C. If the heat capacity of the calorimeter is 33.90 kJ·K–1, how many nutritional Calories are there per gram of the candy?
I've answered enough of these. You've shown no work, no thought, no nothing. I'll be glad to help but no more freebies with me doing all of the thinking.
To calculate the nutritional Calories per gram of the candy, we need to determine the heat released by the combustion of the candy sample.
To find the heat released, we can use the formula:
q = CΔT
Where:
q is the heat released or absorbed
C is the heat capacity of the calorimeter
ΔT is the temperature change observed
First, let's convert the temperature change from Celsius to Kelvin:
ΔT = 2.47 °C = 2.47 K
Now we can substitute the given values into the formula:
q = (33.90 kJ·K–1) * (2.47 K)
Calculate the heat released:
q = 83.973 kJ
Now that we have the heat released, we need to convert it to nutritional Calories. 1 nutritional Calorie is equal to 1 kilocalorie (kcal), which is equal to 1000 calories (cal).
83.973 kJ = 83.973 kcal
Finally, we need to determine the nutritional Calories per gram. Since we started with a 4.10-gram sample of the candy, we divide the total nutritional Calories by the mass:
Calories per gram = (83.973 kcal) / (4.10 g)
Calculate the nutritional Calories per gram:
Calories per gram ≈ 20.48 kcal/g
Therefore, the candy has approximately 20.48 nutritional Calories per gram.