[leve]

The solubility of oxygen in water is 4.00ppm at 25ºC. What is Henry's Law constant for water at this temperature? The mole fraction of oxygen in air with a total pressure of 1atm is about 0.21 and the density is water is 1.00g/mL

This is what my professor showed us as the solution

S = kPgas
[(1,000g*4/1,000,000)/32]/L = k(.21atm)
k = 5.95x10^-4

My question is why is it 1,000g*4/1,000,000?

From what I read, ppm is the same as 1g solute per 1x10⁶g solution. The solubility is 4.00ppm so wouldn't it be [(4/1,000,000)/32g]/L = k(.21)? Where did the 1,000g come from?

[pfnm]

Okay, I'll try and explain this one.

The short answer is, your Professor is converting to molarity, which is where the [1000g*4/1,000,000/32] comes from.

His solution's answer to the molarity equation will be 1.25*10^-4, divided by 0.21 atm for k, which will equal, as listed, 5.95x10^-4.

Think of it this way: when you are given 4 ppm, you can 'presume' any amount of oxygen to any amount of water, as long as the ratio stays at 4 parts of oxygen per 1 million parts of solvent.

So for example you could have 4g oxygen to 1 million grams of water.

But Henry's Law, Sg=kPg (Sg meaning solubility of the gas, Pg meaning partial pressure of the gas over solution), usually asks for Sg to be expressed as molarity, that is, moles per litre.

To find molarity, you can use n=CV (where C stands for molarity).

But since you aren't given grams of solute and you aren't given grams of solution, you must realise you have been given a ratio of solute to solution (4:1,000,000). So solute can weigh anything and solution can weigh anything AS LONG AS there is 4 parts of one, to 1 million parts of the other.

So your professor has for the sake of convenience, calculated molarity by presuming you have 4,000 g:

moles = mass/molar mass, so 4,000g/32g per mole O2 = 125 moles.

125 moles

But as I said, if you adjust one number, you need to adjust the other. 4ppm can be 4g/1,000,000 g or 4,000g/1,000,000,000g.

So your professor has changed 4ppm to mean 4000g/4*10^9mL or 4,000g/1,000,000 L.

Then, dividing 4,000/1,000,000L by 32g molar mass of O2, we have 1.25*10^-4, which, divided by Pg, is k (5.95*10^-4).

So your professor hasn't noted it, but he's just tinkered with units. He hasn't changed the relationship between units, he's just changed amounts. 4ppm is a ratio.

In this case he's using 4,000g to 4*10^9mL, for purposes of calculating molarity.

It might be easier if your Professor showed you units (mL, L, etc) when he showed you your solutions. Could be less confusing.

The way I'd explain how to do the problem is like this:

In Henry's Law, Sg = kPg, where Sg = solubility of the gas in solution (expressed as molarity, that is, moles/L), where Pg = the partial pressure of the gas over the solution.

So you can rearrange the equation to solve for k, or Henry's constant.

k= Sg/Pg

To express your 4ppm of oxygen in water, as molarity you'll need to convert ppm to moles/L.

This might be the long way around, but the way I do it is like this:

Changing from grams of sample (presume 4ppm oxygen is 4grams of oxygen dissolved in 1,000,000 g of water, which is entirely okay since no grams of solute or solvent are given) to moles.

number of moles is mass of sample/molar mass. So presuming 4g, divided by 32g/mole molar mass of O2, we have 0.125 moles of oxygen.

Now, we use the equation for molarity.

I use n=CV, but others use different variations. The idea is that n=number of moles. C=concentration in moles/L. V=volume in Litres.

So we rearrange this, remembering we have 0.125 moles of Oxygen and 10^6g of solvent (water). Since the density of water is 1g/mL, 1 gram has a volume of 1mL and therefore 1 million grams occupy 1 million millilitres.

But the n=CV equation asks for volume in Litres, so

1*10^6 mL = 1000L.

Now rearrange, for C:

C=n/V

n=0.125 moles

V=1000

concentration in moles/L = 1.25*10^-4

So we have Sg.

Pg is pretty clear: Pg is partial pressure of the specified gas (oxygen in this case) and we know from Dalton's law that total pressure equals the sum of constituent partial pressures.

So Ptotal = P1 + P2 + P3 etc.

We are given the total pressure, and we are given the mole fraction of the oxygen constituent, so X (mole fraction) oxygen=0.21 = 0.21 atm.

Now we have Sg and Pg, and we solve Sg/Pg= k for k,

(1.25x10^-4 M )/(0.21 atm)

k = 5.95 x 10^-4

Now, that's showing you how to solve it the way I would.

hopefully you can see what your Professor has done and why he has used 1000*4/1,000,000. But next time ask him if he could put units onto his problem solutions or if he could go through them step by step - the main thing is, he's converting sample mass to molarity (by presuming a sample mass of 4,000g).

If hope I haven't confused you, let me know if you need any more help