Science Buddies: "Ask an Expert"

This question is regarding the Cold Pack Chemistry project: https://www.sciencebuddies.org/science- ... background

After completing my experiment, I now want to analyse the data to be put into my report.
I used 25g of ammonium nitrate into 25g of water.
My starting temperature was 19C, and finished up as 0C.
After using 'equation 1' on the project page, I found the ammonium nitrate has absorbed 3971J of energy.
However, let's say I started my experiment like before with the water temperature at 19C.
Is there any way I could work out the end temperature if all I knew was that the starting water temp was 19C and I was dissolving 25g of ammonium nitrate into 25g of water? (This is for a piece of analysis to be put into the report.)

Thanks for your help.

Hello,

Good observation! Yes, you can work out the end temperature of the water by doing some algebra. Using the same equation and variables from the Cold Pack Chemistry link you sent me, you can derive an equation that lets you find the end temperature of the water.

q = c m (T1-T2)

If we divide both sides of this equation by c m
q/ (c m) = [c m (T1-T2)]/ ( c m)

we get...
q/ (c m) = T1-T2

Subtracting T1 from both sides
[q/ (cm)]- T1= T1-T2-T1

we get...
[q/ (cm)]- T1= -T2

Dividing both sides by -1
{[q/ (cm)]- T1}/ (-1) = -T2/ (-1)

we get...
T2= T1- [q/(c m)]

If you know what T1, q, c, and m are; you can calculate what T2 should be theoretically. In your case, you wouldn't be able to calculate the end temperature as you don't know how much energy the ammonium nitrate released into the water unless you use the data from your first experiment.

What you've described is what Algebra is all about. Normally algebra is not taught until High School, which may make the above explanation difficult to understand.

Briefly, algebra is used to answer questions about what you don't know, from things you do know. You've done a little of this just with arithmetic and multiplication, but algebra does some new concepts. To try to illustrate this, you know what "2+2" equals. 2+2=4.

In algebra, you'd express the problem as

2+2=X, solve for X

the above is the same as

2-x=2

or

-x = -2-2

You've managed to use a formula successfully, so what boydrew did was rearrange the formula like I did with the above arithmetic to show you how to use it to solve something different, when what you know is different.

Or to put it another way, you just asked "If I know the answer is 4, can I calculate what I add to 2 to get 4"
the formula 2+2=X

was changed to

2+Y=4, solve for Y
and then perhaps changed to
Y=4-2

and you know what 4-2 equals...because you know arithmetic. 4-2 = 2, so Y is 2.