If 30.0 mL of 0.150 M aqueous sodium hydroxide is mixed with 30.0 mL of 0.150 M aqueous hydrochloric acid in a calorimeter at an initial temperature of 25.0 degrees Celsius, what is the enthalpy change of this reaction if the final temperature reached in the calorimeter is 27.5 degrees Celsius?
NaOH + HCl yields NaCl + H2O

- Theloshua

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- aaronq

For calorimetry reactions, use the equation: \(q=m_{water}*C_p*\Delta T\)
where m is the mass of water (or solution in this case)
Cp is the specific heat capacity for the system (i would assume it to be the same as water here)
\(\Delta T\) is change in temperature the system underwent

- aaronq

oh yea and q is the heat evolved (which is equal to the change in enthalpy under constant pressure, which I assume it's valid here)

- Theloshua

okayy.....
so.....
wait

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- aaronq

lol so \(C_p=4.18 ~J/~ ^oC*g\)
So we have \(\sf q=m*(4.18 ~J/~ ^oC*g)*(T_{final}-T_{initial})\)
we need the mass and the temperatures..

- Theloshua

ummm.... but water isnt involved in the reaction...

- aaronq

I know, but we're measuring the temperature of the water (solution), and that is how (indirectly) we're getting the change in enthalpy

- Theloshua

but the solution isnt water XD so you dont know its heat capacity....

- Theloshua

so isnt it irrelevant?

- aaronq

It's common in these problems to make the simplification that the specific heat capacity is equal to that of water, unless you're told otherwise... same with the density of the solution, it's equal to that of water

- Theloshua

okayy.... I hope your right... :p

- aaronq

Unless you're told (in the question) otherwise, i'm right lol

- Theloshua

okay

- Theloshua

so ummmm hold on let me plug in the equation

- Theloshua

what is the mass of the equation? :/

- aaronq

the mass of the solution, the density is assumed to be the same as water's
so \(\sf mass=density*volume=1~g/mL*60~mL=60~g\)

- Theloshua

im confused right now....

- aaronq

What are you confused about?

- Theloshua

you took the density and volume of water to find the mass right?

- aaronq

yep, the definition for density is: \(\sf density=\dfrac{mass}{volume}\)
so i just rearranged

- Theloshua

but doesnt the density and volume of water depend on the amount? or no?

- aaronq

the density depends on a lot of things, most importantly temperature. Again, these problems make the simplification that the density of the solution is the same as that of water .. which is further simplified and rounded to 1 g/mL.
The volume is given in the question

- Theloshua

oh, you added the two volumes?

- aaronq

yeah

- aaronq

Thats the volume of the solution

- Theloshua

okayyyy so
\[Q = 60 \times 4.18 \times (27.5 - 25)\]

- Theloshua

right?

- aaronq

yep. theres one final thing, because this is the energy absorbed by the water it is an endothermic process, but the reaction is exothermic as energy was released.
\(\sf q_{absorbed}=-q_{released}\)
you need to change the sign

- Theloshua

oh okay, but what about the values given (0.250 M)?

- Theloshua

where do those come in?

- aaronq

they don't, unless they want the molar enthalpy of the reaction. You'll come across questions that include more info than you need and you have to know what to use and what is irrelevant

- Theloshua

okay, so hold on

- Theloshua

The answer would be -627?

- aaronq

yep, just tack on some units to that

- Theloshua

okay, thnx so much!!!!

- aaronq

no problem !

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