Question

A glass of cold water contains 0.45mM ${{O}_{2}}$. How many millilitres of oxygen gas at STP are dissolved in 300.0mL of this water?

Answer 1

The answer is obtained by converting milli molar into molar form and millilitres into litres and then calculating the amount of dissolved oxygen in solution followed by using the ideal gas equation $PV=nRT$ and find the volume of oxygen dissolved by this equation.

Complete step by step solution:
In the previous classes, we have come across the physical chemistry concepts which deal with the basic part such as calculation of dissolved oxygen in water and also the oxygen demand and some of the related entities.
We shall calculate the volume of oxygen dissolved in water at standard temperature and pressure that is nothing but at STP.
- To start with, let us firstly convert milli molar to molar with the help of data given and that is,
$0.45mM({{O}_{2}})=\dfrac{1M({{O}_{2}})}{1000mM({{O}_{2}})}=0.00045M({{O}_{2}})$
We know that molarity of the solution is the ratio of number of moles of solute present in one litre of the solution, the above molar quantity can also be written as, 0.0045 mol/L.
Similarly we shall convert milliliters into litres of solution and that will be,
$300mL(solution)\times \dfrac{1L}{1000mL}=0.300L(solution)$
Now we shall determine the moles of oxygen dissolved in 0.3L of solution and that is calculated as shown below,
$0.3L(solution)\times \dfrac{0.00045mol({{O}_{2}})}{1L(solution)}=0.000135mol({{O}_{2}})$
Thus, at STP, we know that the value of temperature and pressure respectively are, 273.15K and 100kPa
By, using the ideal gas equation, we have
$PV=nRT$
where P is the pressure, V is the volume, T is the temperature, n is the number of moles of gas and R is the gas constant which is equal to $8.314L-kPa{{K}^{-1}}mo{{l}^{-1}}$
We have P = 100kPa and T = 273.15K and also the number of moles of${{O}_{2}}$
Substituting these values in ideal gas equation and calculating for ‘V’, we get
$V=\dfrac{0.000135\times 8.314\times 273.15}{100}=0.00307L({{O}_{2}})$
By converting the above obtained value into millilitres, we get the correct answer as 3.1 mL

Note:
Note that dissolved oxygen also abbreviated as DO is the measure of the amount of oxygen which is dissolved in the water that is the amount of oxygen available for the living aquatic species. This also gives information regarding the water quality.