Question

# When 20 ml of 2.5 M ${{\text{H}}_2}{{\text{O}}_2}$ aqueous solutions is decomposed at S.T.P. volume of oxygen obtained isa) 56 mlb) 560 mlc) 11.2 mld) 2.24 ml

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Hint:The question mentions two conditions of molarity(i.e., molarity = 2.5 M, and volume = 20 ml) and molarity is defined as the number of moles of solute dissolved per litre of solution. Hence we have to find out the third term and see if we can use it to reach our answer.

Formula used:

Morality = $\frac{{{\text{ Number of moles}}}}{{{\text{Volume(L) }}}}$

Complete step-by-step solution:First, let’s write the balanced chemical reaction and see what happens when ${{\text{H}}_2}{{\text{O}}_2}$ is decomposed,

${\text{2}}{{\text{H}}_2}{{\text{O}}_2} \to 2{{\text{H}}_2}{\text{O + }}{{\text{O}}_2}$

From the above reaction, we can conclude that in general, 2 moles ${{\text{H}}_2}{{\text{O}}_2}$ yield 1 mole of ${\text{ }}{{\text{O}}_2}$

Therefore, 1 mole ${{\text{H}}_2}{{\text{O}}_2}$ will yield $\frac{1}{2}$ moles of ${\text{ }}{{\text{O}}_2}$

But, to find out how many moles of ${{\text{H}}_2}{{\text{O}}_2}$ is formed in the given conditions of our question, we will use the formula for molarity to calculate the same,

Morality = $\frac{{{\text{ Number of moles}}}}{{{\text{Volume(L) }}}}$

$\Rightarrow {\text{Number of moles = Molarity}} \times {\text{Volume(L)}}$

We are given two values i.e., molarity and volume but the given volume is in ml we have to convert it to liter (L) by dividing it by 1000 (since 1ml = $\frac{1}{{1000}}$L). Therefore 20ml = $\frac{1}{{1000}}$$\times 20 L. Now putting up all the values in the mentioned formula, we will calculate the number of moles of {{\text{H}}_2}{{\text{O}}_2} \Rightarrow {\text{Number of moles = }} 2.5 \times \frac{1}{{1000}} \times 20 \Rightarrow {\text{Number of moles = }}$$0.05$

Therefore, for the given conditions in our question 0.05 moles of ${{\text{H}}_2}{{\text{O}}_2}$ will form,

Now we will find out how many moles of ${\text{ }}{{\text{O}}_2}$ will be yielded by 0.05 moles of ${{\text{H}}_2}{{\text{O}}_2}$

$\Rightarrow {\text{Number of moles of }}{{\text{O}}_2}{\text{ = }}\frac{1}{2} \times 0.05$

= $0.025$ moles of ${\text{ }}{{\text{O}}_2}$

We know that 1 mole of any atom has = 22.4 L of volumes.

Therefore, 0.025 moles of ${\text{ }}{{\text{O}}_2}$ has volume

$\Rightarrow$ $22.4 \times 0.025$ = $0.056{\text{ L}}$

As most of the options are given in ml we will have to convert 0.56 L in ml to check if it matches with any given answer,

$\Rightarrow$$0.056{\text{ L}}$ = $0.056 \times 1000$ =$560{\text{ ml}}$

Hence the correct answer is option (b)i.e., $560{\text{ ml}}$

Note:Carefully heed the S.I units of the measured quantity and change them as per the requirements of the question. Likewise, in this question, S.I units were changed two times first ml to L, and the L to ml both in different situations.