Solubility coefficient is actually a constant for a specific type of compound. These are empirical values that are determined by experiments. Solubilities of gas are highly dependent on temperature. So, you have to test each temperature to get the exact coefficient. The higher the temperature of the system is, the lesser the coefficient becomes. Molecules tend to escape through rapid collisions. For Carbon Dioxide, the solubility coefficient is equal to 0.0308 mmol per liter per mmHg or 0.231 mmol per liter per kPa at a temperature of 37°C.
