A researcher studying the nutritional value of a new candy places a 3.50-gram sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.23 °C. If the heat capacity of the calorimeter is 31.30 kJ·K–1, how many nutritional Calories are there per gram of the candy?
q = Ccal x delta T gives you kJ/3.5 g. Convert to kJ/g. Then remember there are 4.184 kcal/kJ. I have an answer of approx 5 kcal but that's just a close estimate.
To determine the number of nutritional Calories per gram of the candy, we need to calculate the heat released during combustion.
The heat released (ΔH) can be calculated using the equation:
ΔH = C × ΔT
where ΔH is the heat released, C is the heat capacity of the calorimeter, and ΔT is the observed temperature increase.
Plugging in the given values:
C = 31.30 kJ·K–1
ΔT = 2.23 °C
However, since the heat capacity is given in kilojoules (kJ) and the temperature is given in Celsius, we need to convert the units to match.
ΔH = (31.30 kJ·K–1) × (2.23 °C)
Now, we need to convert the units of ΔH from kilojoules to nutritional Calories. 1 nutritional Calorie is equal to 1 kilocalorie (kcal), which is equal to 1000 calories (cal).
1 kJ = 0.239006 kcal
1 kcal = 1000 cal
To convert kJ to nutritional Calories per gram, we perform the following calculations:
ΔH (cal) = (31.30 kJ·K–1) × (2.23 °C) × (0.239006 kcal/kJ) × (1000 cal/kcal)
Finally, we need to divide ΔH (cal) by the mass of the candy sample (3.50 grams) to determine the number of nutritional Calories per gram of the candy.
Nutritional Calories per gram = ΔH (cal) / 3.50 g
By plugging in the calculated values, we can find the answer.