A researcher studying the nutritional value of a new candy places a 5.80-gram sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.93 °C. If the heat capacity of the calorimeter is 38.50 kJ·K–1, how many nutritional Calories are there per gram of the candy?

q = heat released = heat cap x delta T

q = 38.5 kJ/K x 2.93 = approx 113 kJ but you need a better answer than my estimate.
That's approx 113 kJ/5.80 g candy bar = approx 19 kJ/gram.
I would then convert 19 kJ/g to J/g, then to calories (that's with a small c) using 4.184 J/cal then convert to kcal/g (nutritional calorie).

To determine the number of nutritional calories per gram of the candy, we need to calculate the heat released during the combustion of the candy sample in the bomb calorimeter.

First, we need to calculate the heat absorbed by the bomb calorimeter (Q_calorimeter) using the formula:

Q_calorimeter = heat capacity of calorimeter (C_calorimeter) * temperature change (ΔT)

Q_calorimeter = 38.50 kJ·K^(-1) * 2.93 °C

Note: It's important to convert the temperature change to Kelvin by adding 273.15 to the observed temperature change:

Q_calorimeter = 38.50 kJ·K^(-1) * (2.93 + 273.15) K

Next, we'll convert the mass of the candy sample to grams, since we want to determine the calories per gram. The sample weighs 5.80 grams.

Now, we can calculate the heat released during the combustion of the candy sample (Q_sample):

Q_sample = -Q_calorimeter

Since the heat released during the combustion of the candy sample is equal in magnitude but opposite in sign to the heat absorbed by the calorimeter.

Finally, we can calculate the nutritional calories per gram of the candy:

Nutritional Calories per gram = Q_sample / mass of the candy sample

Substituting the values we have:

Nutritional Calories per gram = (-Q_calorimeter) / 5.80 g

Evaluate (-Q_calorimeter) and divide by 5.80 grams to obtain the answer.

Please note that nutrition calories (Calories) in food are typically expressed in kilocalories (kcal), where 1 kilocalorie is equal to 1000 calories (cal).