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Hi

Enthalpy is defined as

H = U + PV where U is internal energy of system and PV are pressure and volume of system

You can define the difference between H and U like so according to a book i'm reading:

H(initial) = U(initial) + PV(initial)

H(initial) = U(initial) + n(initial)RT <==replace PV with nRT

H(final) = U(final) + PV(final)

H(final) = U(final) + n(final) RT<==replace PV with nRT

D(H) = H(final) - H(initial)

D(H) = D(U) + (n(final) - n(initial))RT

When working out PV or nRT in the initial conditions I understand that you can use the initial temperature

But when you calculate PV for the final conditions, how can you use the initial temperature? The result for PV, at constant pressure, will depend on how many moles of gas have been produced or consumed and also the temperature of the system which will have changed during the reaction. In other words, the temperature of the system will be changing as the gas is expanding due to energy released/absorbed by the reaction. Is the use of the initial temperature is a necessary simplification or am I missing a key point?

Thanks

Enthalpy is defined as

H = U + PV where U is internal energy of system and PV are pressure and volume of system

You can define the difference between H and U like so according to a book i'm reading:

H(initial) = U(initial) + PV(initial)

H(initial) = U(initial) + n(initial)RT <==replace PV with nRT

H(final) = U(final) + PV(final)

H(final) = U(final) + n(final) RT<==replace PV with nRT

D(H) = H(final) - H(initial)

D(H) = D(U) + (n(final) - n(initial))RT

When working out PV or nRT in the initial conditions I understand that you can use the initial temperature

But when you calculate PV for the final conditions, how can you use the initial temperature? The result for PV, at constant pressure, will depend on how many moles of gas have been produced or consumed and also the temperature of the system which will have changed during the reaction. In other words, the temperature of the system will be changing as the gas is expanding due to energy released/absorbed by the reaction. Is the use of the initial temperature is a necessary simplification or am I missing a key point?

Thanks

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That's a great and thorough answer but I don't quite see how it answers what i asked in my question about this relationship between U and H

D(H) = D(U) + (n(final) - n(initial))RT

In the book i am reading you can convert between DU and DH by the final term (n(final) - n(initial))RT. The temperature used is the initial temperature. I don't understand how you can use the initial temperature unless it is a simplification

Can the end temperature be different from the beginning temperature? You bet.. but then not only is U changed (more thermal energy added) but the change in PV will no longer be

Delta(PV) = (n(final) - n(initial) )RT but (Delta(PV) = R(n(final)T(final)-n(initi

It would seem your book is simplifying for an example

It should be clear that in the isothermal reaction, as extra gas is added from the chemical reaction, PV will increase and internal energy will decrease (loss of chemical energy).

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Start your 7-day free trialD(U) for the combustion of 1 mol of glucose is -2559 kj at 298 K

What is the change in enthalpy?

D(H) = D(U) + (n(final) - n(initial))RT

n final - n initial = 12 - 6 = 6 moles of gas

D(H) = -2559 + (6 * 8.314 * 298)

D(H) = -2544 kj/mol

D(H) = D(U) + PD(V) at constant pressure

calculate PD(V) at constant pressure

V(1) = n(1) RT / P

V(2) = n(2) RT/P

D(V) = V2 - V1

= (n2 - n1) RT/P

PD(V) = P * (n2 - n1) RT/P

P(DV) = (n2 - n1) RT

This is assuming constant temperature like you said.

But the book definitely doesn't mention constant temperature. Is this something i should know and it is taken as read? For example, are enthalpies generally determined in such a way that the system stays at constant temperature?

In any problem starting and ending conditions have to be known to calculate results. In a textbook problem you are normally safe to assume that unless specifically stated a starting condition will be an ending condition. It simplifies things.

One can keep going in circles here. You throw in more variables, you have to make more assumptions or tie down more degrees of freedom to be able to calculate answers. In a textbook question, such things as speed of reaction, internal friction of gases, heat transfer to container, etc... are not considered.

I think its saying the temperature is constant as any heat generated/lost is immediately removed/replaced and the final term calculates the energy needed to expand the gas at that temperature. I dont think its any more complicated than that. Like you say its a book

Math / Science

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OK... now

Short answer: use of initial temperature is only necessary if you need to calculate PV from the mass of the gas and its temperature as part of initial conditions. Calculation of final PV depends on how much energy is put into or taken from the system thru chemical reactions or work, how much mass is added or taken out.

Long answer (Oh... forget it... it's too long to read any way)

In physics, very often one of the easiest ways of keeping track of what is going on in a series of formulas is to keep track of the units. Your enthalpy H represents joules of energy. U or your internal energy also represents joules of energy It can also be considerd here to be the thermal energy of the system. . p and V represent pressure (pascals) and volume (cubic meters) and heat energy in a perfect gas (in joules) equals pV. The conversion of nHT with pV is merely a different way of representing the same thing. nHT = pV... is a relationship. Increase pressure without increasing volume, temperature goes up... etc. Ok.. it's all a matter of energy. How? Enthalpy H is equal to Internal Energy plus the energy represented by the "springiness" or compressibility of the gas [PV or nRT]. You compress a gas you put energy into the "spring" . If no energy is added or subtracted, then an equilibrium exists. Temperature increase only occurs with a volume decrease.

Now to your question. Calculating a PV for final conditions. You start with an initial condition. Initial temperature, initial pressure, initial volume, initial moles of gas. You change the system by changing pressure, volume, moles of gas, or a combination. You can also add energy (heat the system) or remove energy (cool the system). That is where your consuming or creating moles of gas comes in and the heat in the system. I assume no chemical reactions here. Now. Given an H and a U How do you calculate the end PV? You can not. Sorry....

In the end, if you have defined the total internal energy (U) and enthalpy (H) than to calculate P you must know V and to calculate V you must know P. You can not solve for both simultaneously. Temperature is immaterial. In fact, once n is known and the internal energy and entropy are known, you can calculate the final temperature without calculating P or V In fact to solve for any variable in the initial equation for enthalpy, you only need to know the other variables.

That is how they are related.

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