A researcher studying the nutritional value of a new candy places a 5.90g
sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.53 degrees Celsius. If the heat capacity of the calorimeter is 34.40 kJ⋅K^-1, how many nutritional calories are there per gram of the candy?
just a guess - the real chemists can answer with certainty, but the numbes and units suggest
2.53°C * 34.4 kJ/°C = 87.032 kJ
because °C = °K in this context.
Now, don't you have a conversion factor for kJ to calories?
To follow up on oobleck.
You have 87.032 kJ. That converts to 87.032 kJ x (1000 J/kJ) x (1 cal/4.184 J) = what the nutritionists call a "small calorie". Divide by 1000 to convert to what the nutritionists call "big or large calorie). You can see that the calories we think we are eating actually are big calories; i.e., a cup of milk is listed on all of the charts as about 160 calories but that actually is 160 kcal.
To determine the nutritional calories per gram of the candy, we need to calculate the heat generated during the combustion. We can use the equation:
q = m * C * ΔT
where:
q = heat generated during combustion
m = mass of the candy (5.90 g in this case)
C = heat capacity of the calorimeter (34.40 kJ⋅K^-1 or 34.40 * 10^3 J⋅K^-1 in SI units)
ΔT = temperature increase (2.53 °C or 2.53 K in SI units)
First, we need to convert the temperature increase from Celsius to Kelvin by adding 273.15:
ΔT = 2.53 + 273.15 = 275.68 K
Then, plug the values into the formula:
q = 5.90 g * 34.40 * 10^3 J⋅K^-1 * 275.68 K
Calculate the value of q:
q = 5.90 * 34.40 * 10^3 * 275.68 = 5.016 * 10^6 J
Next, we need to convert the energy from joules to nutritional calories. One nutritional calorie is equal to 4.184 joules:
q (in nutritional calories) = (5.016 * 10^6 J) / (4.184 J/cal)
Calculate the value of q in nutritional calories:
q (in nutritional calories) = 5.016 * 10^6 J / 4.184 J/cal ≈ 1197446 cal
Finally, to find the nutritional calories per gram of the candy, we divide the obtained value by the mass:
Nutritional calories per gram = 1197446 cal / 5.90 g
Calculate the value:
Nutritional calories per gram = 1197446 cal / 5.90 g ≈ 202688 cal/g
Therefore, there are approximately 202688 nutritional calories per gram of the candy.