A researcher studying the nutritional value of a new candy places a 4.30-gram sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.77 °C. If the heat capacity of the calorimeter is 28.90 kJ·K–1, how many nutritional Calories are there per gram of the candy?
Please help, I don't know how to start!
q = Ccal x delta T
(Ccal is heat capacity of the calorimeter 28.90 kJ/K and delta T = 2.77 C).
Solve for q = heat produced by 4.30 g of the candy in kJ.
Convert that J (multiply by 1000).
Convert that to calories (divide by 4.184).
Convert that to nutritional calories (divide by 1000) which gives you calories for the 4.30 g piece of candy.
Divide by 4.30 to convert to nutritional calories/grams candy.
Thank you so much!
Is K kalvin? If so, why isn't celcius converted?
Kelvin*
To determine the number of nutritional Calories per gram of the candy, we need to calculate the heat released during combustion using the observed temperature increase and the heat capacity of the calorimeter.
First, let's convert the observed temperature increase from Celsius to Kelvin. The temperature in Kelvin is obtained by adding 273.15 to the temperature in Celsius.
Temperature in Kelvin = 2.77 + 273.15 = 275.92 K
Next, we can calculate the heat released during combustion using the formula:
Heat released (in Joules) = heat capacity (in Joules per Kelvin) * temperature increase (in Kelvin)
Heat released = 28.90 kJ·K^(-1) * 275.92 K
Next, convert the heat released back to kilocalories (kcal) because the nutritional calorie is often referred to as a kilocalorie.
1 kcal = 1000 cal
So:
Heat released (in kilocalories) = (heat released in Joules) / 1000
Finally, to determine the number of nutritional Calories per gram of candy, divide the heat released by the mass of the sample:
Calories per gram = Heat released (in kilocalories) / mass of the sample (in grams)
Now you can substitute the values into the equation and calculate the answer.