[Wienerbroed]

I need help solving a question about finding the change in internal energy.
The question is:

When it explodes, nitroglycerin splits into nitrogen gas, carbon dioxide, oxygen and water vapor. The enthalpy of formation is -365,0 kJ/mol for nitroglycerin, -393,5 kJ/mol for carbon dioxide and -241,8 kJ/mol for water vapor.
Calculate the enthalpy of reaction (ΔH) as well as the change in internal energy (ΔU) when nitroglycerin completely decomposes with a constant pressure of one bar. Assume an ideal gas is formed, that performs volume change work.

I've been able to calculate the ΔH, but I do not know how to calculate the ΔU. I know that I'm supposed to use
ΔU = q + w and PV = nRT, but I don't know how.

[Borek]

Reaction equation would probably help.

[Orcio_87]

@Wienerbroed

Did you read about enthalpy definition ?

ΔH = ΔU + pΔV

Here pressure is constant so the second term (pΔV) relies only on the gaseous products (water is also included as a gas).

[Wienerbroed]

@Orcio_Dojek

Yes, I am aware of that, however I do not know how to get a measurement for the change in volume.

[Borek]

Yes, I am aware of that, however I do not know how to get a measurement for the change in volume.

And that's where the reaction equation comes to the rescue.

How many moles of gas before? After? Can you use this information to calculate ΔV?

[Wienerbroed]

@Borek

We don't know the amount of moles for any given substance. I only know what each of the substances moles are relative to each other thanks to the reaction formula:

4C₃H₉N₃O₉  6N₂ + 12CO₂ + 10H₂O + O₂

I assume the amount of moles of gas before the reaction is 0, since all products were part of the nitroglycerin in liquid form?
Can I use the enthalpy of formation to somehow calculate each products amount of moles?

[Orcio_87]

Can I use the enthalpy of formation to somehow calculate each products amount of moles?

No, as enthalpy of formation relates on formation of compound from pure elements.

[Wienerbroed]

@Orcio_Dojek

Any idea to how I can find the amount of moles in that case?

[Orcio_87]

I see that there are 29 moles of gas for every 4 moles of nitro-glycerine.

[Borek]

We don't know the amount of moles for any given substance.

I've been able to calculate the ΔH

These two statements contradict each other - unless you did calculations per 1 mole of nitroglycerine. If so, do the same for ΔU.

[Wienerbroed]

These two statements contradict each other - unless you did calculations per 1 mole of nitroglycerine. If so, do the same for ΔU.

Don't I need the concentration of each substance? To find ΔU, i need to find ΔV, and to do that I should need the concentration (since V = n/c). How should I find the concentration in that case?
@Borek

[Orcio_87]

Don't I need the concentration of each substance? To find ΔU, i need to find ΔV, and to do that I should need the concentration (since V = n/c). How should I find the concentration in that case?

Equation tells us that N₂ constitutes about 21 % of products (quantitative), CO₂ about 41 % and so on...

 

[Wienerbroed]

How could we find the concentration of nitroglycerin?

[Orcio_87]

Hard to say, it can be 100 or 99 % pure or - mixed with something. But - if not stated otherwise - it can be assumed that it is 100 % pure.

[Borek]

Show how you did calculations of ΔH.

You don't need concentration of anything here.