Forms of Henry's law versus ideal gas law

Question

This might be a slightly daft question as I'm a physicist rather than a chemist, but I have a slight problem in using Henry's law which I think I can circumvent using the ideal gas law – I'd be grateful if anyone can confirm or deny my logic!

I have an equation that yields the volume of oxygen gas per unit mass of tissue. We'll call this quantity $C$ with S.I units of $\mathrm{m^3\: kg^{-1}}$. We also have the partial pressure $p$ measured in $\mathrm{mmHg}$ and we wish to relate the two; several texts have suggested using Henry's law of the form $C = kp$ where $k$ is Henry's constant for oxygen. However, this causes a problem, as I can find no form of Henry's law with the correct units to allow this conversions (units of $\text{vol} / ({\text{pressure} \times \text{mass}})$).

My first question is does such a series of constants exist and does anyone know where?

In the interim, I decided to try to circumvent this problem by using the ideal gas law, which I believe holds at the relatively low pressures in very shallow water. Knowing one mole of oxygen gas has a mass of $32\:\mathrm{g}$, and occupies a volume of $22.4\:\mathrm{l}$ at standard temperature and pressure of $760\:\mathrm{mmHg}$, I re-wrote the expression for the mass of $\ce{O_2}$ in a given volume;

$m_{\ce{O_2}} = \frac{0.024\,p}{(0.032)760RT} = \frac{0.7\,p}{760RT}$

Using the ideal gas constant, and a temperature of $310.15\:\mathrm{K}$, I get

$m_{\ce{O_2}} = 3.572 \times 10^{-7} \cdot p$

If I define $M_{\ce{O_2}}$ as the unitless mass fraction of $m_{\ce{O_2}}$ per unit mass, then knowing the density of oxygen gas is around $1.331\:\mathrm{kg/m^3}$, I can divide this into $M_{\ce{O_2}}$ to get the expression

$C = 2.6835 \times 10^{-7} \cdot p$

which has the correct units. My second question is then is this valid, and if not, why not?

Answer 1

I wrote out an answer to this but realized I was wrong. But I've noticed a number of things:

First off, your form of the ideal gas law has the Molar Mass inverted. If you make the substitution that $n=m/M$, then the rearrangement reads $m = MVp/RT$, you have the $M$ on the bottom.

Secondly, You are selecting a Volume of 1 Liter, so your calculation will solve for a relation of mass and pressure @ 1L, which I don't think you want.

Thirdly (?), I'm guessing that the 760 in the denominator is there so you can use a gas constant in terms of atm? Or did I miss something?

So those are my observations about your attempt with the ideal gas law. I also am concerned over the bit with the mass fraction, as I think you converted a tissue mass into an $\ce {O2}$ volume using $\ce {O2}$'s density, which would be wrong if that was the case.

Looking again at Henry's law in the $p=kC$, you can see that in order to use the standard k units available, you would need to convert the $C$ you have from $L/kg$ to $mol/L$. You can convert $L$ to $mol$ using the ratio you used earlier, and you end up with $C$ in terms of $mol/kg_{tissue}$. The trick here is that you need the density of the tissue (not of $\ce {O2}$) to convert this into the volume you're looking for in order to use the equation. I think haha.