But calculating Δn for this reaction is not something I've understood yet.
Go back to your original chemical equation. You are reacting 14.40 g of oxygen - how many moles is that? How many moles of ammonia will it react with? How many moles of products will be produced? In the ideal gas law, it doesn't matter what the identity of the gas molecules is, only how many total moles of gas molecules are present, so you are looking for the change in number of moles of your total gas mixture.
OK, but this approach does not seem to yield the right answer:
Moles of O2 (g) in Reactants=14.40/32=0.45mol
Moles of Gas in Reactants: ((4/3)+1)*0.45=1.05mol
Moles of Gas in Products: (2/3)*0.45=0.30mol
Δn
g=0.30-1.05=-0.75mol
Whereas according to the answer this should be Δn
g=n
g=-1.25mol.
Also, leaving the calculations themselves aside for a second to focus on the definitions: ΔE is the change in internal energy of the system, ΔU, which =q+w, right? So why does this sum say q
v=ΔE? Particularly when it is evident that w does not equal 0 since there is a decrease in the total volume of gases (decrease because this is at constant pressure and temperature and the number of moles is decreasing).
If we take ΔE=q+w, w here =-pΔV=-Δn
g*R*T (which makes sense, because if the number of moles of gas drops and the gas thus contracts, Δn
g will be negative so -Δn
g will be positive and represent a positive work done by the system, adding to its total energy, which is what we want and expect), so why does q now equal ΔH? They are fundamentally different I thought - q refers to the quantity of heat taken in, ΔH to the increase in heat per mole.
At the end, qv and ΔE seem to revert back to their meanings as we know them - amounts, i.e. previously they referred to the energy increase for 1 mole and now they are being multiplied out by the number of moles used. I don't understand any of this. Does it mean ΔE=ΔH-Δn
g*R*T applies only for 1 mole of the reaction? Then how is Δn
g found? And how can ΔE be defined to describe just 1 mole of a reaction? Please help me with this.