Interesting Analytical Chem Problem

[ghelman]

Hi all,

I need to solve this problem for my environmental chemistry class. It is supposed to be a "review" problem of concepts from analytical and gen. chem. but I certainly do not know how to do it.

Homework Statement

If you work at the wastewater treatment plant, you are exposed to 1,4-dichlorobenzene, which is used in urinal deodorant cakes.

a. If you work in a 500 m³ space with an exposed body of wastewater and can still smell the DCB (smell threshold 500 ppbv) what is the concentration of DCB in the water?

b. In the winter the temperature of the water falls to 5C and you can no longer smell the DCB; what is the maximum concentration of DCB in the water at the new temperature?

The Attempt at a Solution

V=500 m³
C_DCB=500 parts per billion by volume
P=1 atm (assumably)
I assume that the wastewater plant operates at a temperature of 25^o C. I am not sure if that is a good assumption or not. Anyone have any insight to that?

I also assumed that the system is in equilibrium. I am not sure if I am allowed to assume that, but it seems reasonable. Doing so gives:

Vapor pressure of DCB = 1.76 mm Hg

At this point I do not know what to do. I have a concentration for DCB in air, but how do I relate that to the concentration of DCB in water at equilibrium?

I know that the fugacities will be equal at equilibrium, but I am not sure whether that will be useful or if it is just a wild goose chase.

Help!

Thanks in advance!

 

[AGNuke]

1.) Assumption is justified. 25°C is totally justified. It is a standard Temperature.

2.) Henry's Law for conc. of DCB in water?

 

[ghelman]

Hmmmm...but how would using Henry's Law make use of the given concentration in the air?

 

[Borek]

Unless I am missing something, there is not enough data to solve the problem.

And no idea how you got 1.76 mmHg.

 

[ghelman]

I got the vapor pressure from a research article. We are allowed to look up any values we think we may need. Given that, what will we need to know in order to solve the problem?

 

[Borek]

It is probably vapor pressure over a solid DCB at STP - so of no use here (unless it can be somehow related to solubility/pressure over solution). You need either a Henry's constant, or some kind of information that will let you calculate it.

 

[ghelman]

I can probably find an article with a Henry's law constant, but if I solved it that way, how would that make use of the given concentration? Also, how would I solve part b?

 

[Borek]

I can probably find an article with a Henry's law constant, but if I solved it that way, how would that make use of the given concentration?

Huh? Simple plug and chug. Or is your problem conversion between concentration and partial pressure?

Also, how would I solve part b?

Assuming Henry's constant is not temperature dependent. Or using value for 5°C. It is almost exactly the same problem.

 

[ghelman]

So would I assume that the system is in equilibrium and use the vapor pressure as the partial pressure in Henry's Law? If I did that then how would I use the given concentration of 500 ppbv?

Or am I supposed to plug in the given concentration and solve for the partial pressure? But then what would I do with that?

 

[AGNuke]

Convert 500ppbv into partial pressure. That's the amount of DCB in atmosphere, by volume, and by ideality (which we generally consider to make our life at least not miserable) 500ppb(pressure).

This "should" solve your answer.

 

[JohnRC]

(1) I suspect that the "given" 500 cubic metre of workspace is irrelevant except insofar as it suggests an environment where the vapour phase DCB will be in equilibrium with the liquid phase DCB -- that is, that the volume is fairly small, and suggests an enclosed, draught free workspace.

(2) I also think that it is important to remember that you are dealing with inequalities here -- the conc of DCB is not = 500 ppbv but >= 500 ppbv

(3) The equilibrium vapour pressure of the solid is relevant if you combine it with the (low) solubility of the solid in water, because the PCB activity in the solid is 1, and so the PCB concentration in the solution will therefore be equal to the same proportion of the saturation concentration as that of the vapour is to the saturated vapour in equilibrium with the solid (as expressed in the saturation vapour pressure).

(4) Wastewater facilities are usually kept to around 5-10°C if the outdoor temperature is below freezing, but they are usually places where no other heating or cooling is applied. If a temperature is not specified, an assumption of 15°, 20° or 25 °C would be reasonable.

 

[Borek]

If you have air at 1 atm, and 21% of the air by volume is oxygen (in other words: concentration of oxygen is 21% v/v), what is the partial pressure of oxygen?

This is an application of Avogadro's principle.

 

[JohnRC]

If you have air at 1 atm, and 21% of the air by volume is oxygen (in other words: concentration of oxygen is 21% v/v), what is the partial pressure of oxygen?

This is an application of Avogadro's principle.

I do not believe that an answer like this is really grasping the difficult part of this problem, which hinges on how to relate a concentration in air to a concentration in aqueous solution

(Borek again):

It is probably vapor pressure over a solid DCB at STP - so of no use here (unless it can be somehow related to solubility/pressure over solution). You need either a Henry's constant, or some kind of information that will let you calculate it.

A datum like this can be brought into the solution of the problem, since the saturation vapour pressure is effectively the "solubility" of the solid in air, which can be matched to the actual solubility of the solid in water, and provide the information needed to match other airborne and aqueous concentrations.

 

[Borek]

I do not believe that an answer like this is really grasping the difficult part of this problem, which hinges on how to relate a concentration in air to a concentration in aqueous solution

My understanding of the situation is that OP has no idea how to convert 500 ppb to partial pressure (at least that's what I read between lines in earlier posts). Without doing this (simple) step, you can't proceed with the more difficult part.

the saturation vapour pressure is effectively the "solubility" of the solid in air, which can be matched to the actual solubility of the solid in water

If I understand you correctly you want to assume activity of the DCP to be the same in the air and in the solution? Perhaps it will work, I have never seen it done this way (but I am far from claiming I have seen everything, quite the opposite).

 

[JohnRC]

If I understand you correctly you want to assume activity of the DCP to be the same in the air and in the solution? Perhaps it will work, I have never seen it done this way (but I am far from claiming I have seen everything, quite the opposite).

Not the activity, but the chemical potential -- the chemical potential must be equal in the solid, the saturated vapour, and the saturated solution. The last two can therefore be equated and scaled down to lower concentrations. This is really just the fugacity or Henry's law approach in another guise, and an accurate solubility figure for DCB can be fairly easily obtained.