A researcher studying the nutritional value of a new candy places a 4.90 gram sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.75 Celsius. If the heat capacity of the calorimeter is 29.50 kJ K^-1, how many nutritional calories are there per gram of the candy? Answer in cal/g

Wouldn't you have to convert the temperature to K in order to cancel out the units and obtain a value in joules. For the very first step of the solution

29,500 J/K x 2.75 K = about 81,000 J(approximate) from the combustion.

81,000 J/4.90 = about 16,000 J/g.
16,000 J/g x (1 cal/4.184 J) = about 4,000 cal.
4,000 cal = 4 kcal = about 4 nutritional calories.

that's amazing... thank you so much Dr Bob!

Thank you so much!!! That helped me too!

Grub!

Well, let's see if I can cook up an answer for you! To figure out the nutritional calories per gram of the candy, we need to calculate the energy released during combustion.

First, we need to convert the observed temperature increase from Celsius to Kelvin. So, 2.75 Celsius + 273.15 = 275.90 Kelvin.

Now, we can calculate the heat released using the equation Q = m * c * ΔT, where Q is the heat released, m is the mass of the sample, c is the heat capacity of the calorimeter, and ΔT is the temperature change.

Q = (4.90 g) * (29.50 kJ K^-1) * (275.90 K)

Now, we need to convert Q from kilojoules (kJ) to calories (cal). Since 1 calorie is equal to 4.184 joules and 1 kilojoule is equal to 1000 joules, we can convert like this: (4.90 g) * (29.50 kJ K^-1) * (275.90 K) * (1000 cal/kcal) / (4.184 J/cal)

After doing the math, we get the amount of calories released during combustion. Since we're looking for nutritional calories per gram of the candy, we'll divide the energy released by the mass of the sample (4.90 g).

The final answer is the amount of nutritional calories per gram of the candy.

But hey, instead of calories, maybe we should measure it in "big smiles per gram". I wager that candy would get quite a high score!

To find the nutritional calories per gram (cal/g) of the candy, we need to calculate the heat released during combustion. Let's follow these steps:

Step 1: Convert the observed temperature increase from Celsius to Kelvin.
ΔT(K) = ΔT(°C) + 273.15
ΔT(K) = 2.75 + 273.15 = 275.9 K

Step 2: Calculate the heat released (q) using the equation:
q = CΔT
where
q is the heat released
C is the heat capacity of the calorimeter
ΔT is the temperature change in Kelvin

q = 29.50 kJ K^(-1) * 275.9 K
q = 8130.45 kJ

Step 3: Convert the heat released from kilojoules to calories:
1 kJ = 0.239 kcal
8130.45 kJ * 0.239 kcal/kJ = 1949.66 kcal

Step 4: Calculate the nutritional calories per gram:
Nutritional calories per gram = (heat released in calories) / (mass of the sample in grams)
Nutritional calories per gram = 1949.66 kcal / 4.90 g
Nutritional calories per gram ≈ 398.52 cal/g

Therefore, there are approximately 398.52 nutritional calories per gram of the candy.