Rearranging equation for heat capacity

[FLgirl]

1. To determine whether a shiny gold rock is actually gold, a student decides to measure its heat capacity. She first weighs the rock and finds it has a mass of 4.7g. She then finds that upon absorbtion of 57.2 J of heat, the temperature of the rock rises from 25 degree Celsius to 57 degree Celsius. Find the specific heat capacity of the substance composing the rock and determine whether the value is consistent with the rock being pure gold.
2. q = m X Cs X temperature change
Cs of gold = 0.128 J/g x Celsius
3. 4.7g X 0.128 J/g x C X 32 C = 19.25
c = 9/temperature change = J/C = 57.2/32 C
4.7g X 32 C / 57.2 J


Actual solution: 57.2 J / 4.7g X 32 CSo my question is; why is 57.2 divided by the others, when if you had brought it over from the other side, wouldn't you divide it BY 57.2?

 

[Borek]

3. 4.7g X 0.128 J/g x C X 32 C = 19.25
c = 9/temperature change = J/C = 57.2/32 C
4.7g X 32 C / 57.2 J

No idea what you are doing here.

$$q = mc_s\Delta T$$

Solve for c_s. Don't put numbers into the equation yet, just solve symbolically.

 

[FLgirl]

How do you do that... why are chemists so cryptic

 

[Borek]

Solve symbolically means rearrange so that c_s will be on the left hand side of the equation and everything else will be on the right hand side.

There is nothing cryptic here, this is basic algebra that you should learn long ago. And if you have read forum rules you know we don't give final answers, we rather help you solve the problem guiding you in the right direction.

 

[DeeNos]

I would like to clarify that the equation for heat capacity is actually q = m x c x delta T, where q is the amount of heat absorbed, m is the mass of the substance, c is the specific heat capacity, and delta T is the change in temperature. Therefore, the rearranged equation should be c = q / (m x delta T).

To answer your question, in this specific scenario, we are trying to find the specific heat capacity of the substance composing the rock, which is represented by c. The value of 57.2 J is given as the amount of heat absorbed by the rock, and we divide it by the other values (mass and temperature change) to find the specific heat capacity. This is because we are trying to isolate the value of c in the equation.

I hope this helps clarify any confusion. It is important to always use the correct equation and rearrange it properly to get accurate results in scientific experiments.