[salocime]

I'm trying to work through some chemistry on my own over the summer and doing okay--until now.

Here's the question:

Predict the final temperature of a 500 g iron ring that is initially at 25.0 degreesC and is heated by combusting 4.95 g of ethanol, [delta]_cH=-1234.8 kJ/mol C₂H₅OH (_l) in an open system.

The sample problem right before it is a CLOSED system with the heat capacity of the calorimeter given. This isn't anything like it. I thought it was like earlier reaction questions I'd done, but apparently not. In any case, here's my latest attempt at solving. I'd really appreciate knowing where I'm going wrong:


REQUIRED
final temperature of the iron ring

EQUATIONS that could be used
Q=mc[delta]t; n=m/M, <[delta]H=n[delta]_cH

GIVEN INFO
mass of iron: 500 g
mass of ethanol: 4.95 g
initial temperature (t_i)=25.0 degreesC
[delta]_cH=-1234.8 kJ/mol C₂H₅OH (l)
assumed: specific heat capacity of ethanol is similar to water: 4.19 J/g degreesC

attempted SOLUTION
first, find the moles of ethanol:
n=m/M
=4.95/(2 * 12.01 g/mol + 6 * 1.01 g/mol + 16.00 g/mol)
=0.137195 mol

Then, use moles to solve for [delta]H=n[delta]_cH:
[delta]H= 0.137195 mol * -1234.8 kJ/mol = -169.408 kJ

which means Q = 169.408 kJ or 169 408 J

For Q = mc[delta]t, m is total mass of the system.
Q = mc(t_f - t_i)
t_f= (Q/mc) + t_i
=(169 408 J/(504.95 g * 4.19 J/g*degreesC)) + 25.0 degreesC
=105.07 degreesC
=105 degreesC (when done to correct significant digits)

The ACTUAL answer in the text is 616 degreesC.

[salocime]

CORRECTION!!! Need to find FINAL temperature. Woops. Sorry.

[enahs]

First, your assumption that ethanol has the same specific heat if water is just flat wrong. That is one of the amazing properties of water. Only water has the specific solutions of water, and dilute solutions in water as well can be assumed to be.

But, the specific heat of ethanol is irrelevant.
You need the specific heat of the iron. It is in the back of your book most likely, or in a table in the chapter dealing with this material. Or online.

How much energy is released by the combustion of the ethanol?
That energy goes into the iron.
Q_{(ethanol combustion)} = m_(iron)C_(iron)ΔT_(iron)

You know everything but T_final.
Try again!

[salocime]

Okay, heat capacity of iron makes sense since I'm trying to find the heat change of the iron. I think all of the other questions were dealing with the change in temperature of the solution (reaction equations; as I said, they only gave on combustion equation and it was a closed system), and they all had you make the assumption that the heat capacity was close enough to water to use water's heat capacity.

Shoot, I just checked some of my values and I must have made a mistake with putting in the numbers into my calculator in addition to using the wrong information. Fixing that and using the correct mass, I think I've got it now.

Let me start with the moles of ethanol:

n=m/M
=4.95 g/(2*12.01 g/mol + 6*1.01 g/mol + 16.00 g/mol)
=0.107422 mol

ΔH= nΔ_cH
=0.107422 mol * -1234.8 kJ/mol
=-132.645 kJ
Q=132.645 kJ or 132 645 J

Q=mcΔt
t_f=(Q/mc) + t_i
=(132 645 J/(500 g * .449 J/(g*degreesC)) + 25 degreesC
=615.8 degreesC
=616 degreesC

Thanks!!!