Question

A researcher studying the nutritional value of a new candy places a 3.00-gram sample of the candy inside a bomb calorimeter and combusts it in excess oxygen. The observed temperature increase is 2.09 °C. If the heat capacity of the calorimeter is 46.30 kJ·K–1, how many nutritional Calories are there per gram of the candy?

Answer 1

Change the temperature from celsius to kelvins so you can use the specific heat capacity equation
\(\Large Q=c*\Delta T\)

So, \(\Large \Delta T_{celsius}=\Delta T_{kelvins}\)

Answer 2

because this involves specific heat capacity

Answer 3

When calculating Q=m*c*deltaT, the only thing that matters with temperature is the difference or temperature change. The size of the temperature change is the same as the temperature change in kelvins.

Answer 4

2.09 °C this is just a temperature change in celsius
so, changed into kelvins
2.09 k

Answer 5

@carlos1291996

Answer 6

yes

Answer 7

\(Q = c\Delta T \)

c is kj
delta t is the delta K
Q will be in kJ
plug everything and tell me what you get for kJ

Answer 8

dont forget, nutritional Calories are in kcal. So after you get kJ, you convert it to kcal

Answer 9

So it would be (46.30X10^3)/(2.09) then devide that by 3?

Answer 10

i am sorry i am really confuse :/

Answer 11

Q=c * delta T
Q= (46.30 kJ K^-1)*(2.09 K)
Q=96.77 kJ

Then convert from kj to kcal. How many kJ are there for kcal?

Answer 12

Then reason i said you should convert kj to kcal, because the question is asking "how many \(\color{red}{nutritional~Calories}\) are there per gram of the candy?"
The question wants the answer in kcal per grams.

Normally, the calories we see on food labels (aka. nutritional calories) is usually in 1000 calories, which is kilocalories (kcal).

Answer 13

Here's a hint:

\(\LARGE 1~~kcal=4.184 ~~kJ\)

Answer 14

Use this as a conversion factor to convert from kJ to kcal

Answer 15

makes sense? @carlos1291996

Answer 16

so 96.77/4.184=23.12kcal

Answer 17

Yep :)

Answer 18

We are not done yet, we only got the first part of the answer, getting kcal's but the question wants nutritional calories per \(\color{red}{grams}\)

Answer 19

How are you going to get the kcal into kcal per grams (aka. \(\LARGE \frac{kcal}{grams}\))

Answer 20

@carlos1291996

Answer 21

I got it ! it's (46.30 kj*C) X ( 2.09 C ) / 3.00 g X 0.239 kcal/kj

Answer 22

just want to make sure is it correct?

Answer 23

The answer i got was 7.71 Cal/g

Answer 24

Yes, to get kcal per grams
You have 23.15 for kcal and 3.00 for grams

\(\LARGE \frac{kcal}{grams}=\frac{23.15~kcal}{3.00~grams}=\large 7.71~ kcal ~~per ~~grams\)

Answer 25

Good job ^_^ @carlos1291996

Answer 26

typo, i meant 23.12 not 23.15

Answer 27

oh okay thank you!

Answer 28

You're welcome! :)