Question

\[{{H}_{2}}S\] a toxic gas with rotten egg-like smell, is used for qualitative analysis. If the solubility of \[{{H}_{2}}S\] in water at STP is \[0.195\text{ }m\], calculate Henry's law constant.

Answer 1

Hint: We need to apply Henry’s law in this question which states:
\[P=kH.x\]
where p = pressure
x = mole fraction
KH = Henry's constant

Complete Solution :
Given molarity = 0.195m.
Since, \[\text{Molority}=\dfrac{\text{No}\text{. of moles of solute}}{\text{Mass of solvent }\left( kg \right)}\]
Let us assume mass of water = 1kg
So, \[Moles\text{ }of\text{ }solute\text{ }=\text{ }Molarity~\times Mass\text{ }of\text{ }solvent\]
\[=0.195\text{ mol}\]
Molar mass of \[{{\text{H}}_{2}}S=\left( 2\times 1 \right) + 16 = 18\]
\[\text{No}\text{. of moles of water}=\dfrac{\text{mass}}{\text{molar mass}}\]
\[=\dfrac{1000}{18}\Rightarrow 55.56\text{ mol}\]
Now, we will find the mole fraction of \[{{\text{H}}_{2}}S\left( x \right)\]
\[=\dfrac{0.195}{0.195 + 55.56} = 0.0035\]
At STP \[P= 0.987 atm\]
Applying formula in equation (i) we get,
\[\Rightarrow P=kH.x\]
\[\Rightarrow kH=\dfrac{P}{x}=\dfrac{0.987}{0.035}\]
\[\therefore kH = 282 atm\]

Additional information: -Hydrogen sulfide (or\[{{H}_{2}}S\]) is a very toxic gas. It has no color but smells like rotten eggs. Excess \[{{H}_{2}}S\] can halt the breathing centre in the brain which can lead to death. The gas is also known to cause irritation in eyes, nose, lungs and throat.
-Hydrogen sulfide gas occurs naturally in crude petroleum and natural gas. It can be produced by decomposing human and animal waste and is found in sewage treatment plants and livestock areas.

Note: Henry’s law states that- “At a constant temperature, the amount of a gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of the gas in equilibrium with the liquid.” Henry’s constant depends upon the nature of the gas, nature of the solvent, temperature and pressure. This is the reason why different gases have different Henry’s laws constant in different solvents.