# A gas has a solubility in water at 0°C of 3.5 g/L at a pressure of 0.80 atm. What pressure is needed to produce an aqueous solution containing 8.9 g/L of the same gas at 0°C?

##### 1 Answer

#### Explanation:

You're dealing with *pressures* and *gas solubility*, which should automatically tell you that this is an example of a **Henry's Law** problem.

As you know, **Henry's Law** states that the *solubility* of a gas in a liquid is **directly proportional** to its **partial pressure** of the gas above the liquid.

#color(blue)("solubility " prop " partial pressure")#

This means that *increasing* the pressure of the gas above the liquid will **Increase** its solubility.

Likewise, *decreasing* the pressure of the gas above the liquid will **decrease** its solubility.

Mathematically, you can express Henry's Law like this

#color(blue)(S_1/P_1 = S_2/P_2)" "# , where

You'll often be dealing with the **molar solubility** of the gas, measured in *moles per liter*, but for this problem you can use the solubility in *grams per liter*.

So, the solubility of the gas **increased** from **must have increased** as well.

Plug your values into the above equation and solve for

#P_2 = S_2/S_1 * P_1#

#P_2 = (8.9 color(red)(cancel(color(black)("g L"^(-1)))))/(3.5color(red)(cancel(color(black)("g L"^(-1))))) * "0.80 atm" = color(green)("2.0 atm")#

The answer is rounded to two **sig figs**.