A researcher studying the nutritional value of a new candy places a 3.10-gram sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.34 °C. If the heat capacity of the calorimeter is 33.50 kJ·K–1, how many nutritional Calories are there per gram of the candy?
q = Ccal x delta T.
q = 33500 J x 2.34 = about 79,000 J (but you need to do it more accurately).
That's 79000 J/3.10 g = 25,000 J/g.
25,000 J/g x (1 cal/4.184 J) = about 6,000 cal/g or 6 kcal/g = 6 nutritional calories/g.
To calculate the number of nutritional Calories per gram of the candy, we will use the heat capacity of the calorimeter and the observed temperature increase.
First, let's convert the observed temperature increase from Celsius to Kelvin. We add 273.15 to the temperature increase in Celsius.
Temperature increase in Kelvin = 2.34 °C + 273.15 = 275.49 K
Next, we need to calculate the heat transferred during the combustion of the candy sample using the heat capacity of the calorimeter.
Heat transferred = Heat capacity of the calorimeter × Temperature increase in Kelvin
Heat transferred = 33.50 kJ·K–1 × 275.49 K
Now, we convert the heat transferred from kilojoules to joules.
Heat transferred = 33500 J·K–1 × 275.49 K
The result of this calculation will give us the total heat transferred during the combustion process.
Next, we need to convert the heat transferred to nutritional Calories. One nutritional Calorie is equivalent to 4.18 kJ.
Number of Calories = (Heat transferred in joules) / (4.18 kJ)
Finally, to determine the nutritional Calories per gram of the candy, we divide the number of Calories by the mass of the candy sample.
Nutritional Calories per gram = (Number of Calories) / (3.10 g)
By following these steps, you can calculate the nutritional Calories per gram of the candy sample.