A deep diver breathes a mixture of 80 % helium and 20 % oxygen by moles, at a total pressure of 5.0…

Step 1. Partial pressures. Helium: $\dfrac{80}{100} \times 5.0 = 4.0\ \text{bar}$. Oxygen: $\dfrac{20}{100} \times 5.0 = 1.0\ \text{bar}$.

Step 2. Helium. $x = \dfrac{4.0}{144\,970} = 2.76 \times 10^{-5}$. In $1\ \text{kg}$ of water that is $2.76 \times 10^{-5} \times 55.56 = 1.53 \times 10^{-3}\ \text{mol} = 1.53\ \text{mmol}$.

Step 3. Oxygen. $x = \dfrac{1.0}{34\,860} = 2.87 \times 10^{-5}$, which is $2.87 \times 10^{-5} \times 55.56 = 1.59\ \text{mmol}$.

What does it show? The helium has four times the partial pressure of the oxygen, yet about the same amount dissolves. Helium is much less soluble, so it adds little dissolved gas to the blood.