How Can I Find the Partial Pressure of SO2 in a Gas Mixture?

[physgirl]

so there's a mixture of CO2, SO2, and H2O gases in a 21L tank. Pressure inside is 850Torr at 45*C. if SO2 concentration in mixture is 7.95x10^3 ppmv (where ppmv=[V component/V total mixture]x10^6), find its partial pressure.

so i found the volume of SO2 to be 0.16695L using the ppmv (where V total mixture was 21L and V component/SO2 was what I solved for).

but i can't simply use P1V1=P2V2 (where 1=given condition, 2=SO2 conditions) because "n" isn't constant in both cases...

so how can I find the partial pressure of SO2?

 

[chemhelper]

Ignore P1V1=P2V2 because nothing is changing.

You found the volume of SO2. In this instance, it is safe to assume that this is an ideal gas. Do you know how to convert a volume of an ideal gas into moles?

 

[physgirl]

would you use the formula for molar concentration, n/V=P/(RT)? since molar concentration is same for all ideal gas under given conditions... so when I try n[SO2]/V[SO2]=n[mixture]/V[mixture]

n[SO2]/0.167=0.9/21
n[SO2)]=0.0072 mol

so... P=nRT/V = 0.0072R(318)/0.167 = 1.1175 atm

but P for the whole mixture is 850torr, which is 1.1184 atm... so it didn't really make sense to me that the partial P of SO2 would be so large...

 

[Gokul43201]

would you use the formula for molar concentration, n/V=P/(RT)? since molar concentration is same for all ideal gas under given conditions... so when I try n[SO2]/V[SO2]=n[mixture]/V[mixture]

When you write this, aren't you implicitly assuming P(SO2)=P(mixture)? That's where the error is.

What do you know about Dalton's Law (for partial pressures)?

 

[physgirl]

oh... hm, i see.

well, here's another method i tried although i have no idea if it's correct.

I set up:
P[SO2]V[SO2]/n[SO2]=P[tot]V[tot]/n[tot]
along with: P[SO2] + n[x]P[tot] = P[tot] ----> where x represents CO2+H2O
and also: n[x] + n[SO2] = n[tot]

and hoping my algebra is right, I solved for n[SO2] this way by eliminating other unknown variables... and I got 7.2x10^-4 to be the # of moles for SO2... I plugged this value back in the original equation I set up here, which was: P[SO2]V[SO2]/n[SO2]=P[tot]V[tot]/n[tot]

and then I got the pressure of SO2 to be 0.1126 atm (out of 1.118 atm total)... does that method possibly sound correct assuming my algebra in the middle was right?

 

[Gokul43201]

No, you can't actually do this:

P[SO2]V[SO2]/n[SO2]=P[tot]V[tot]/n[tot]

This equation will not work. Remember, the partial pressure is nothing but the mathematical "contribution" to the total pressure from a particular species (in this case, SO2). This does not mean the SO2 molecules feel only this pressure. They will, in fact, feel the same average pressure as all the rest of the molecules - the total pressure P[tot]. So, the only correct way to apply the ideal gas equation would be as:

P[tot]V[SO2]/n[SO2] = P[tot]V[tot]/n[tot], which reduces to n[SO2]/n[tot] = V[SO2]/V[tot]

In other words the mole fraction is equal to the given volume fraction. So, knowing the mole fraction, you can directly apply Dalton's Law to find the partial pressure.

along with: P[SO2] + n[x]P[tot] = P[tot] ----> where x represents CO2+H2O

There's a tiny error here. It should be:
P[SO2] + (n[x]/n[tot])*P[tot] = P[tot]
but you don't need to use this now, since you have the above approach instead.

 

[physgirl]

Ohh, I see, thank you so much!

So whenever a question asks for partial pressure, the only way I can find it really is by using mole fraction multiplied by total pressure?