[Big-Daddy]

Why is your volume changing?

Because the numbers of moles of each gas are changing (for example), and a certain number of moles of one gas takes up more volume than the same number of moles of another gas. How should I express the volume then? Perhaps as the sum of the number of moles of each species multiplied by the molar volume of that species, this seems completely general to me (and then express the molar volumes in terms of pressure and temperature, if they are changing too).

[curiouscat]

Why is your volume changing?

Because the numbers of moles of each gas are changing (for example), and a certain number of moles of one gas takes up more volume than the same number of moles of another gas. How should I express the volume then? Perhaps as the sum of the number of moles of each species multiplied by the molar volume of that species, this seems completely general to me (and then express the molar volumes in terms of pressure and temperature, if they are changing too).

Sounds good. Do it that way. Use your gas laws.

[Big-Daddy]

Do it that way. Use your gas laws.

OK, so V can always be defined as the number of moles of each species, multiplied by V_m, summed. So we can write it as such, assuming the change in volume is referring to the effects of the reaction itself (no. of moles changing) rather than, say, the container volume being externally changed.

Then the question is what is V_m: if it's constant, then I just write it in as such; otherwise, using the gas laws, it will be a function of pressure, temperature and nothing else (and then gas constants, depending on which gas law is used). If pressure is non-constant (as a result of changing number of moles of gas), anything I can do to model it?

[curiouscat]

OK, so V can always be defined as the number of moles of each species, multiplied by V_m, summed.

For gases, yes.

So we can write it as such, assuming the change in volume is referring to the effects of the reaction itself (no. of moles changing) rather than, say, the container volume being externally changed.

Then the question is what is V_m: if it's constant, then I just write it in as such; otherwise, using the gas laws, it will be a function of pressure, temperature and nothing else (and then gas constants, depending on which gas law is used). If pressure is non-constant (as a result of changing number of moles of gas), anything I can do to model it?

Please define your system carefully first. Is it isothermal? Isobaric? Isochoric? etc.

Think physically. Is it a fixed volume container? If not, what?

[Big-Daddy]

Please define your system carefully first. Is it isothermal? Isobaric? Isochoric? etc.

For the time being, we could model it as isothermal, with both pressure and volume non-constant.

Think physically. Is it a fixed volume container? If not, what?

Well I imagine for example adding acid to a solution of a soluble carbonate (e.g. sodium). CO₂ gas gets released, increasing both the volume of the system (because CO₂ gas takes up more volume per mole than the carbonate anion in solution) and the pressure. The temperature would also change but I am happy for now to consider the system as isothermal.

If it is little additional difficulty to consider it "really", i.e. temperature, pressure and volume can all change, then I would want to learn to do that. Otherwise - isothermal.

[curiouscat]

Please define your system carefully first. Is it isothermal? Isobaric? Isochoric? etc.

For the time being, we could model it as isothermal, with both pressure and volume non-constant.

So how'd you construct such a system? Practically. Please describe it.

[Big-Daddy]

So how'd you construct such a system? Practically. Please describe it.

I don't know. In the case of adding acid to carbonate solution (i.e. pressure, volume and temperature are all non-constant) there doesn't seem to be anything to describe, it's clear why all 3 will change. I don't know how you might keep it isothermal though.

[curiouscat]

So how'd you construct such a system? Practically. Please describe it.

I don't know. In the case of adding acid to carbonate solution (i.e. pressure, volume and temperature are all non-constant) there doesn't seem to be anything to describe, it's clear why all 3 will change. I don't know how you might keep it isothermal though.

If you take a strong closed container why would volume change? Doesn't seem "clear" to me.

You assume too much.

[Big-Daddy]

If you take a strong closed container why would volume change?

Well, because not all the volume is being taken up by reacting species at the beginning (it's a solution, to which acid is added - a gas is then released, which thereby adds to the volume).

In any case that probably isn't very relevant to think about. OK, how do we deal with a constant volume ("isochoric"?) system with changing pressure and temperature?

[curiouscat]

If you take a strong closed container why would volume change?

Well, because not all the volume is being taken up by reacting species at the beginning (it's a solution, to which acid is added - a gas is then released, which thereby adds to the volume).

In any case that probably isn't very relevant to think about. OK, how do we deal with a constant volume ("isochoric"?) system with changing pressure and temperature?

Same as before. If V doesn't change, where's your problem?

[Big-Daddy]

Same as before. If V doesn't change, where's your problem?

Pressure and temperature are both changing. Beyond affecting the rate constants, this shouldn't make a difference to the ODEs for concentration, right? But let's say that I want to be able to calculate the total pressure in terms of time, or the temperature at a certain point in time - how do I do that? (I imagine pressure will rely on temperature and number of moles, but I'm unclear how to model it for inclusion into our ODE system; temperature will probably rely on Gibbs' energy changes and number of moles, but I'm still unclear how to include this into the ODE system)

[curiouscat]

Same as before. If V doesn't change, where's your problem?

Pressure and temperature are both changing. Beyond affecting the rate constants, this shouldn't make a difference to the ODEs for concentration, right? But let's say that I want to be able to calculate the total pressure in terms of time, or the temperature at a certain point in time - how do I do that? (I imagine pressure will rely on temperature and number of moles, but I'm unclear how to model it for inclusion into our ODE system; temperature will probably rely on Gibbs' energy changes and number of moles, but I'm still unclear how to include this into the ODE system)

Do an energy balance. Equate heat of reaction to specific heat capacity. Assuming adiabatic conditions.

[Big-Daddy]

Do an energy balance. Equate heat of reaction to specific heat capacity. Assuming adiabatic conditions.

OK, this definitely seems beyond my current thermodynamics knowledge. I'll have to read up a bit more on thermo before we can tackle this.

Let's say the temperature is constant as well as volume, or maybe the temperature is varied at a controlled rate externally. How do we deal with just calculating the (total) pressure (which should be a function of temperature as well, mind) at any point in time?

What I'm trying to do here, across the last few posts, is understand how to include volume into the calculations, as well as pressure (which would probably affect the volume, and vice versa) as well as temperature, by understanding how to write the volume function in terms of number of moles, pressure and temperature (already been explained), then how to write the pressure function in terms of number of moles and temperature. Then I would consider how to think about temperature being varied.

[curiouscat]

Let's say the temperature is constant as well as volume, or maybe the temperature is varied at a controlled rate externally. How do we deal with just calculating the (total) pressure (which should be a function of temperature as well, mind) at any point in time?

So long as V is constant previous ODE applies.

[tex]
\frac{dc_A}{dt}= R_A \\

n = c \cdot V \\

P=\frac{nRT}{V} \\

[/tex]

If  T varies as an input you already know T=fn(t).

[Big-Daddy]

[tex]
\frac{dc_A}{dt}= R_A \\

n = c \cdot V \\

P=\frac{nRT}{V} \\
[/tex]

Ah of course ... if V is constant, then we just find the number of moles of each gas, sum them and this is n, which we can then use in a gas law. As you wrote below we can write T as a function of time if necessary.

I really want to find out what to do if pressure and volume are both changing as a result of number of moles of gas changing. Temperature is either constant, or can be written as a function of time. In principle we need to write V_m as a function of pressure (and temperature), but then pressure cannot be a function of V (because V_m is itself being used to find V) ...

Every question comes down to this: is there any way to express P without V (when P is changing due to changing number of moles of gas)?

If  T varies as an input you already know T=fn(t).

Got that one, thanks. Makes sense.