Question

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

Answer 1

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

Answer 2

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)

Answer 3

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

Answer 4

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..

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

so isnt it irrelevant?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

okay

Answer 13

so ummmm hold on let me plug in the equation

Answer 14

what is the mass of the equation? :/

Answer 15

the mass of the solution, the density is assumed to be the same as water's

so \(\sf mass=density*volume=1~g/mL*60~mL=60~g\)

Answer 16

im confused right now....

Answer 17

What are you confused about?

Answer 18

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

Answer 19

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

so i just rearranged

Answer 20

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

Answer 21

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

Answer 22

oh, you added the two volumes?

Answer 23

yeah

Answer 24

Thats the volume of the solution

Answer 25

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

Answer 26

right?

Answer 27

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

Answer 28

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

Answer 29

where do those come in?

Answer 30

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

Answer 31

okay, so hold on

Answer 32

The answer would be -627?

Answer 33

yep, just tack on some units to that

Answer 34

okay, thnx so much!!!!

Answer 35

no problem !