# Autoignition

https://isaacphysics.org/questions/autoignition?stage=a_level

I managed to get the right answer but I dont think my working makes sense?

For eg, in part b, I calculated the mean weighted pressure, (which I totally made up - is mean weighted pressure real?) but it happened to work and I dont really know why/was it luck?
Either way Id like to know the proper method.

Working:
Original post by mosaurlodon
https://isaacphysics.org/questions/autoignition?stage=a_level

I managed to get the right answer but I dont think my working makes sense?

For eg, in part b, I calculated the mean weighted pressure, (which I totally made up - is mean weighted pressure real?) but it happened to work and I dont really know why/was it luck?
Either way Id like to know the proper method.

I am unsure what your issue is as you are told
"By considering the average gas density, find the root mean square speed of the molecules in the mixture."
in Hint 2.
My bad I really should have clarified better.

I havent come across average gas density before, is it literally just the weighted average of the density according to the number of moles of the gas so

average gas density = (n_g1 * p_g1 + n_g2 * p_g2)/(n_g1+n_g2)?
where n_g1 = number of moles of gas 1, and p_g1 = density of gas 1.
and n_g2 = number of moles of gas 2, and p_g2 = density of gas 2.
Original post by mosaurlodon
My bad I really should have clarified better.

I havent come across average gas density before, is it literally just the weighted average of the density according to the number of moles of the gas so

average gas density = (n_g1 * p_g1 + n_g2 * p_g2)/(n_g1+n_g2)?
where n_g1 = number of moles of gas 1, and p_g1 = density of gas 1.
and n_g2 = number of moles of gas 2, and p_g2 = density of gas 2.

If you have “made up” the average gas density as the weighted average of the density, it seems that you have good intuition.
If you are studying A-level physics, I doubt you have not come across average density.
average density = total mass / total volume
It applies to all situations including gas.
Using the above “definition” of average density, you should be able to derive what you have made up.
(edited 2 weeks ago)
lucky guess is a better swap for "good intuition" but here goes my method:

average density = total mass / total volume = M_t/V_t = (M_a + M_h)/(V_a+V_h) where _a is for air and _h for hydrogen.
Then im assuming you have to use ideal gas law? Since stuff like p and RT cancels so
pV_a = n_a RT
pV_h= n_h RT
V_a/V_h = n_a/n_h

and (M_a + M_h)/(V_a+V_h) = (p_a*V_a+p_h*V_h)/(V_a+V_h) and divide by V_h so
(p_a*V_a/V_h+p_h)/(V_a/V_h+1) =
(p_a*n_a/n_h+p_h)/(n_a/n_h+1)
so then finally

average density = (p_a*n_a+p_h*n_h)/(n_a+n_h)

Thank you
Original post by mosaurlodon
lucky guess is a better swap for "good intuition" but here goes my method:

average density = total mass / total volume = M_t/V_t = (M_a + M_h)/(V_a+V_h) where _a is for air and _h for hydrogen.
Then im assuming you have to use ideal gas law? Since stuff like p and RT cancels so
pV_a = n_a RT
pV_h= n_h RT
V_a/V_h = n_a/n_h

and (M_a + M_h)/(V_a+V_h) = (p_a*V_a+p_h*V_h)/(V_a+V_h) and divide by V_h so
(p_a*V_a/V_h+p_h)/(V_a/V_h+1) =
(p_a*n_a/n_h+p_h)/(n_a/n_h+1)
so then finally

average density = (p_a*n_a+p_h*n_h)/(n_a+n_h)

Thank you

I don’t really understand your work.
As I don’t understand the following statements:
pV_a = n_a RT
pV_h= n_h RT

I don’t know how you came to the conclusion that the two gases are the same pressure when the different gases occupy different volumes and have different moles.
You better check with your teacher what misconceptions you have.

I also don’t really know why you are using Ideal Gas law to do the proof.
Err wait so I basically used the wrong method to get the right answer? So was my method just lucky to stumble across the right equation?

I thought the 2 gases would be the same pressure since theyre in the same container - and if gases are contained in the same container they must exert the same pressure? The reason their volumes are different, is because each gas takes up a different volume inside the container?

I used ideal gas law since its only equation I know that adds moles into the mix, which is needed for the average density equation. The only other way I know is Moles = Mass/Mr but thats from gcse chemistry?
I dont really know how else you would do the proof.
Original post by mosaurlodon
Err wait so I basically used the wrong method to get the right answer? So was my method just lucky to stumble across the right equation?

I thought the 2 gases would be the same pressure since theyre in the same container - and if gases are contained in the same container they must exert the same pressure? The reason their volumes are different, is because each gas takes up a different volume inside the container?

I used ideal gas law since its only equation I know that adds moles into the mix, which is needed for the average density equation. The only other way I know is Moles = Mass/Mr but thats from gcse chemistry?
I dont really know how else you would do the proof.

Again, I don’t know why you have this thinking “I thought the 2 gases would be the same pressure since theyre in the same container - and if gases are contained in the same container they must exert the same pressure? The reason their volumes are different, is because each gas takes up a different volume inside the container?”.
Have you checked this?
You are self-contradicting especially with the reason. You can plug values into the ideal gas law to show it is wrong.
It is also quite difficult to understand whether you are making statements, explaining, or asking questions.

Next, Moles = Mass/Mr, what is Mr? If Mr is relative molecular mass, and you are using this to compute moles without knowing that it is incorrect conceptually at A level, it seems that you are using equations or formulas without much thought. At GCSE level, students can be pardon for using this to compute mole and indeed, we can use this to compute mole at any level (univ, A level, etc) and get the correct result. But it is incorrect fumadentally!

Indeed, to prove the average density, you just need GCSE level chemistry (concepts in mole calculations) and GCSE level physics (density definition) and no ideal gas law is needed.
I tried to do some research because I was quite confused - why is the Moles = Mass/Mr equation "incorrect conceptually"?
I watched this video: https://www.youtube.com/watch?v=v5bHIA5xeMM&t=309s and around 5;00 they come up with an equation that works, but you said to not use the ideal gas law so now im really stuck.

But anyway let me try again
average density = total mass / total volume = M_t/V_t = (M_a + M_h)/(V_a+V_h) where _a is for air and _h for hydrogen.
(M_a + M_h)/(V_a+V_h) = (M_a*p_a*p_h + M_h*p_a*p_h)/(M_a*p_h+M_h*p_a)

and we want to get the moles in there so Mass = Mr*Moles
(n_a*mr_a*p_a*p_h + n_h*mr_h*p_a*p_h)/(n_a*mr_a*p_h+n_h*mr_h*p_a) -> mr_ is the molar mass of _
but now I cant really see a way forward
(edited 1 week ago)
Original post by mosaurlodon
I tried to do some research because I was quite confused - why is the Moles = Mass/Mr equation "incorrect conceptually"?
I watched this video: https://www.youtube.com/watch?v=v5bHIA5xeMM&t=309s and around 5;00 they come up with an equation that works, but you said to not use the ideal gas law so now im really stuck.

But anyway let me try again
average density = total mass / total volume = M_t/V_t = (M_a + M_h)/(V_a+V_h) where _a is for air and _h for hydrogen.
(M_a + M_h)/(V_a+V_h) = (M_a*p_a*p_h + M_h*p_a*p_h)/(M_a*p_h+M_h*p_a)

and we want to get the moles in there so Mass = Mr*Moles
(n_a*mr_a*p_a*p_h + n_h*mr_h*p_a*p_h)/(n_a*mr_a*p_h+n_h*mr_h*p_a) -> mr_ is the molar mass of _
but now I cant really see a way forward

I would "address" 2 issues first:
- What is Mr?
- I said "no ideal gas law is needed" NOT "not to use ideal gas law".
If you do not understand the difference, I would use an analogy: Let's say we want to connect the points on a graph paper to plot a curve. Assume I am good at connecting the points using free hand. I would tell others that a curve ruler is not needed/required NOT don't use a curve ruler.

All the underscore _ are driving me nuts. It would be better if you hand-write your work or write them in latex.
Well Mr is just mass relative to 1/12 of some carbon atom but I dont see how that helps but I dont do a level chem and my gcse knowledge might be a bit hazy

I rewrote my work (not including the other stuff I tried because it didnt get me anywhere) and dont know where to go from here:

Can you tell me roughly how many lines this proof should be? I dont if its short like less than 5 lines or long >10 lines, and I dont really know if im complicating the proof too much.
Original post by mosaurlodon
Well Mr is just mass relative to 1/12 of some carbon atom but I dont see how that helps but I dont do a level chem and my gcse knowledge might be a bit hazy

I rewrote my work (not including the other stuff I tried because it didnt get me anywhere) and dont know where to go from here:

Can you tell me roughly how many lines this proof should be? I dont if its short like less than 5 lines or long >10 lines, and I dont really know if im complicating the proof too much.

Original post by mosaurlodon
and we want to get the moles in there so Mass = Mr*Moles
(n_a*mr_a*p_a*p_h + n_h*mr_h*p_a*p_h)/(n_a*mr_a*p_h+n_h*mr_h*p_a) -> mr_ is the molar mass of _
but now I cant really see a way forward

Note how you mention the same notation Mr differently: in post #12, you said Mr is relative mass and in post earlier #10, you denote Mr as molar mass. This kind of inconsistency have nothing to do with whether you take chemistry at A level or being hazy at GCSE chemistry.

Original post by mosaurlodon
I tried to do some research because I was quite confused - why is the Moles = Mass/Mr equation "incorrect conceptually"?

Why is the Moles = Mass/Mr equation incorrect conceptually?

In physics or science, the equation or formula should have a consistent unit(s) or dimension(s) on both sides.
In chemistry or physics, as far as I know, we denote Mr as relative molecular mass or formula unit mass and it has no unit. This implies that the left-hand side has a unit of mole while the right-hand side has a unit of kilogram which is inconsistent.

As for deriving the average density of a mixture of gases in terms of the weighted density of the individual gas, one would need 2 or more concepts.
namely
- density = mass / volume
- Avogadro's Law states that equal volumes of gases under the same conditions of temperature and pressure contain the same number of molecules (irrespective of the nature of the gaseous particles). This implies that we can calculate the amount of gas (in moles) from the volume of gas.
- Assume the volumes of gases are additives meaning V1 + V2 = total volume.
- mole = mass / molar mass

Although Avogadro’s law can be argued to stem from ideal gas law, in deriving the average density the equation pV = nRT does not appear in my derivation.

“Can you tell me roughly how many lines this proof should be?” IMO, this is a very ambiguous question and is most likely to have ambiguous answers.
If you want an ambiguous answer, I “see” the derivation in “2 steps”.