Question

10mL of a solution of ${{H}_{2}}{{O}_{2}}$ liberated 0.5g of iodine from KI solution. The percentage of ${{H}_{2}}{{O}_{2}}$ in the solution is:
A. 0.27%
B. 0.669%
C. 0.47%
D. 0.87%

Answer 1

Hint: Try to check the reaction of ${{H}_{2}}{{O}_{2}}$ with the $KI$solution and find out the moles of them which are produced. Then use the concept of stoichiometry to find out the volume, which can be substituted in the formula for volume strength.

Complete step by step solution:
In order to answer our question, we need to learn about the moles, molar mass and stoichiometry. Mole is simply a unit for measuring quantitatively the objects at the microscopic level (i.e., atoms, molecules, particles, electrons, ions, etc., just as we use one dozen for twelve objects . In SI system, mole was introduced as base seven quantity for the amount of a substance, One mole is defined as "the amount of a substance that contains as many particles or substances as there are atoms in approximately 12 g (or 0.012 kg) of the $^{12}C$ isotope". No matter what the substance may be, the mole of a substance always contains the same number of substances. In order to determine this number accurately, the mass of a carbon-12 atom was determined by a spectrometer. The mass of one molecule or compound that contains $6\times {{10}^{23}}$ particles or Avogardo’s number is called molar mass. It is different for all substances. Volume strength is defined for ${{H}_{2}}{{O}_{2}}$ as, if, at STP condition we have one volume strength of ${{H}_{2}}{{O}_{2}}$, then it liberates 1 volume of ${{O}_{2}}$. Now, let us come to the question. We can write:
\[{{H}_{2}}{{O}_{2}}+2{{H}^{+}}+2{{I}^{-}}\to {{I}_{2}}+2{{H}_{2}}O\]
So, 1 mole of hydrogen peroxide produces 1 mole of iodine. Molar mass of ${{H}_{2}}{{O}_{2}}$ is 34 gram and molar mass of ${{I}_{2}}$ is 254 gram, that means 254g of iodine relates to 34 gram of ${{H}_{2}}{{O}_{2}}$. So, 0.5 gram will correspond to:
\[\dfrac{34}{254}\times 0.5=0.0669gram\]
Now, we know that $vol\,strength{{h}_{{{H}_{2}}{{O}_{2}}}}=\dfrac{weigh{{t}_{{{H}_{2}}{{O}_{2}}}}}{volume}$
So, on substituting the values, we get:
\[vol\,strength{{h}_{{{H}_{2}}{{O}_{2}}}}=\dfrac{0.0669}{10}\times 100=0.669\]

So, the percentage of ${{H}_{2}}{{O}_{2}}$ in the solution is 0.669%, which gives us option B as the correct answer.

Note: For finding the molar mass of a compound or a diatomic molecule, the individual molar masses are added for example, oxygen element has a molar mass of 16, but diatomic oxygen molecule has molar mass of $2\times 16$=32grams.