Solving Dissociation Reaction Homework

[krootox217]

Homework Statement

Hi, I tried the following task:

I tried to solve it, but apparently it's not correct:

Can someone show me the right way to do this?

Homework Equations

See above

The Attempt at a Solution

see above[/B]

 

[SteamKing]

Please post HW threads in the appropriate HW forum by subject.

 

[krootox217]

Sorry, we had this task in thermodynamics, so I posted it into the physics forum instead of the chemistry forum.

Can someone help me to get the correct values?

 

[epenguin]

Can you justify your 3× factor ?

 

[krootox217]

In the task it says, that the pressure is 3 bar, so i used this value for the partial pressure

is this wrong?

 

[epenguin]

OK got that - I was reading rapidly and imagined it was some mixup deriving from the 3 in PCl₃.

Also I had to check back because I had a queasy moment of wondering whether I had ever understood right. But I was reassured by the Wikipedia article https://en.m.wikipedia.org/wiki/Equilibrium_constant#Pressure_dependence

You see I am coming from biochemistry/biophysics where it is usual to give units when stating equilibrium constants. This is very convenient for visualisation (whether a 'binding constant' is mM, μM, or nM speaks to you immediately of how tight a binding is. If talking of binding of oxygen to respiratory proteins mm Hg or atm is also suggestive.) And you always know what you are talking about if you use such units. So it was only here that I realized that a lot of people use K's without any units, and officially when no units are quoted, molarities (to an appropriate power) are intended. I hate this convention.

But I guess that is the convention being used here, so I suggest convert your atm into molarities, assume the quoted K is for molarities, and see if you get the right answer.

(About half the time this is not an issue, for equilibria like A ⇔ B or A + B ⇔ C + D the equilibrium constant would be dimensionless.)

Second opinions welcome.

 

[krootox217]

When I try it that way, I get 0.019M for PCl5 at the end and 0.05M for each of the resulting substances. Therefore the dissociation degree of PCl5 would be 73% since the start amount was 0.069M. Do these values make sence?

 

[epenguin]

I will understand the question to be that the pressure was 3 bar at the end of the reaction. I guess it doesn't matter what it was at the beginning. That is the simplest thing but I don't know how you get your start molarity. The way I do it at STP I remember one mole gas occupies 22.4 L, therefore 1 L at STP contains 1/22.4 moles ≈ 0.0446 M. so if it is 3 bar that is about 0.14 M. (though that is not very far from your final total molarity). So maybe you are in the right ball park but unless you set it out a bit more it is not very clear.

 

[krootox217]

Oh i thought that the 3 bar were at the beginning, so I converted everything in SI units and used p*V=n*R*T to get the volume. Then i converted the volume in liters, and divided the starting amount of moles to get the mol/l which I used to calculate the values

 

[Chestermiller]

You got the mole fractions wrong also.

OK got that - I was reading rapidly and imagined it was some mixup deriving from the 3 in PCl₃.

Also I had to check back because I had a queasy moment of wondering whether I had ever understood right. But I was reassured by the Wikipedia article https://en.m.wikipedia.org/wiki/Equilibrium_constant#Pressure_dependence

You see I am coming from biochemistry/biophysics where it is usual to give units when stating equilibrium constants. This is very convenient for visualisation (whether a 'binding constant' is mM, μM, or nM speaks to you immediately of how tight a binding is. If talking of binding of oxygen to respiratory proteins mm Hg or atm is also suggestive.) And you always know what you are talking about if you use such units. So it was only here that I realized that a lot of people use K's without any units, and officially when no units are quoted, molarities (to an appropriate power) are intended. I hate this convention.

But I guess that is the convention being used here, so I suggest convert your atm into molarities, assume the quoted K is for molarities, and see if you get the right answer.

(About half the time this is not an issue, for equilibria like A ⇔ B or A + B ⇔ C + D the equilibrium constant would be dimensionless.)

Second opinions welcome.

The quoted K is based on partial pressures expressed in bars. The equilibrium constant is dimensionless because the standard state of each species is 1 bar.

 

[Chestermiller]

Oh i thought that the 3 bar were at the beginning, so I converted everything in SI units and used p*V=n*R*T to get the volume. Then i converted the volume in liters, and divided the starting amount of moles to get the mol/l which I used to calculate the values

If x is the number of moles that dissociate, the total number of moles increase to 1+x, so the final mole fractions are x/(1+x), x/(1+x), and (1-x)/(1+x). If the pressure is held constant at 3 bars, then the final partial pressures are 3x/(1+x), 3x/(1+x), and 3(1-x)/(1+x). Try the problem again with these substitutions and see what you get.

Chet

 

[krootox217]

It worked, thank you :)