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Question: When 20 ml of a mixture of \({O_2}\) and \({O_3}\) is heated, the volume becomes 29 ml and disappear...

When 20 ml of a mixture of O2{O_2} and O3{O_3} is heated, the volume becomes 29 ml and disappears in alkaline pyrogallol solution. What is the volume per cent of O2{O_2} in the original mixture?
(A) 90 %
(B) 10 %
(C) 18 %
(D) 2 %

Explanation

Solution

The oxygen is present in a lesser amount in the mixture because heating the volume has been increased. We have the conversion reaction of ozone to oxygen as-
2O3⇄3O22{O_3} \rightleftarrows 3{O_2}
From this, it is clear that 2 moles of ozone will give rise to 3 moles of oxygen. Thus, on the heating some moles of ozone is converted into large moles of oxygen, thereby increasing the volume.

Complete step by step answer:
For such a question, let us start by writing about the behaviour of O2{O_2} and O3{O_3} and the values are given to us in the question.
We have been given :
Volume of mixture of O2{O_2} and O3{O_3}= 20 ml
On heating the mixture, the volume increased to = 29 ml
The mixture disappears in alkaline pyrogallol solution.
We need to find out :
the volume per cent of O2{O_2} in the original mixture
So, let us begin.
Volume of mixture of O2{O_2} and O3{O_3}= 20 ml
Let the volume of O2{O_2}be ‘x’ ml.
Thus, the volume of ozone = (20 - x) ml
We know that the 2O3⇄3O22{O_3} \rightleftarrows 3{O_2}
So, from the reaction, it is clear that the two moles of ozone will give us three moles of oxygen.
And one mole of ozone will give 32\dfrac{3}{2}moles of oxygen.
So, the (20 - x) ml of ozone will give = 32\dfrac{3}{2}(20 - x) ml of oxygen.
On solving the brackets, we get,
(20 - x) ml of ozone will give = (30 - 1.5 x) ml of oxygen.
We have in question the heating of the total volume = 29 ml.
So, this has ‘x’ ml of oxygen initially and the rest (29 - x) ml of oxygen which is converted from ozone to oxygen on heating.
Thus, we can write that (30 - 1.5 x) ml of oxygen = (29 - x) ml of oxygen
On solving the equation for ‘x’.
We get, (30 - 1.5 x) ml = (29 - x) ml
(30 - 29) = (-x + 1.5x)
0.5 x = 1
‘x’ = 105\dfrac{{10}}{5}
‘x’ = 2.
Thus, the volume percentage of oxygen in the mixture = 220×100\dfrac{2}{{20}} \times 100
the volume percentage of oxygen in the mixture = 10 %

So, the correct answer is the option (b).

Note: The mixture disappears in alkaline pyrogallol solution because the oxygen is soluble in alkaline pyrogallol solution. What actually happens is that initially, we have 20 ml of the total mixture. On heating the ozone converts into oxygen, thereby increasing the volume to 29. And this oxygen formed is soluble in alkaline pyrogallol solution. Thus, it disappears.