Question

What is the concentration of dissolved oxygen at $ 50{}^\circ \text{ C} $ under pressure of one atmosphere if partial pressure of oxygen at $ 50{}^\circ \text{ C} $ is $ 0\cdot 14\,\text{atm} $ .
(Henry’s law constant for oxygen $ =1\cdot 3\times {{10}^{-3}} $ mol $ \text{d}{{\text{m}}^{-5}}\text{ at}{{\text{m}}^{-1}} $ ).

Answer 1

Hint: Henry’s law: According to Henry’s law the solubility of a gas in a liquid is directly proportional to the pressure of the gas over the solution at a definite temperature.
Mathematically is expressed as
 $ \text{m}\alpha \text{P} $
m = K P
Where m = solubility of gas at definite temperature
K = Constant of proportionality
P = Pressure.

Complete step by step solution
In the given question we have to calculate the concentration of dissolved oxygen by applying henry’s law. i.e. to calculate how much oxygen soluble in water at $ 50{}^\circ \text{ C} $
Here P = $ 0\cdot 14 $ atm
K = $ 1\cdot 3\times {{10}^{-3}}\text{ mol d}{{\text{m}}^{-3}}\text{ at}{{\text{m}}^{-1}} $ [Given]
 m = ?
According to Henry’s law
 $ \text{m}\alpha \text{P} $
m = K P ….. (1)
Put the value of K and P in equation 1 we get value of m
m $ =1\cdot 3\times {{10}^{-3}}\times 0\cdot 14 $
m $ =1\cdot 82\times {{10}^{-4}}\text{ mol d}{{\text{m}}^{-3}} $
Then the stability of oxygen at $ 50{}^\circ \text{ C} $ is $ 1\cdot 82\times {{10}^{-4}}\text{ mol d}{{\text{m}}^{-3}} $ .

Note
Henry law is only applicable when the following condition is satisfied.
The pressure is not too high.
The temperature is not too low.
The gas does not combine with the solvent.
Here the word dissolved oxygen is used means that it is a measure of how much oxygen is dissolved in water i.e. the amount of oxygen available to the living organism. It also tells us about the quality of water that is present in ponds, lakes, streams etc.