A student shakes a gas with 1.000 kg of water at 293 K until the amount dissolved stops changing…

Step 1. The test. The ratios are $\dfrac{0.74}{1.0} = \dfrac{1.48}{2.0} = \dfrac{2.22}{3.0} = \dfrac{2.96}{4.0} = 0.74\ \text{mmol/bar}$. The amount is proportional to the pressure, so the gas obeys Henry's law.

Step 2. The mole fraction. At $4.0\ \text{bar}$, the gas is $2.96\ \text{mmol}$ in $55.56\ \text{mol}$ of water: $x = \dfrac{2.96 \times 10^{-3}}{55.56} = 5.33 \times 10^{-5}$.

Step 3. The constant. We want $K_H$, so $K_H = \dfrac{p}{x} = \dfrac{4.0\ \text{bar}}{5.33 \times 10^{-5}} = 75\,100\ \text{bar} = 75.1\ \text{kbar}$.