Question

A Sample of ${{H}_{2}}{{O}_{2}}$ solution labeled as 28 volume has density of 265g/L. Mark the correct option(s) representing concentration of same solution in other units.
(A) Molarity of ${{H}_{2}}{{O}_{2}}$=2.5
(B) Percentage w/v = 17
(C) Mole fraction of ${{H}_{2}}{{O}_{2}}$ = 0.2
(D) Molality of ${{H}_{2}}{{O}_{2}}$= 13.88

Answer 1

Hint: Volume strength is a term used for the volume of oxygen gas liberated from 1 Volume of ${{H}_{2}}{{O}_{2}}$ solution. Percentage w/v is a measurement of the concentration of a solution. Solubility is sometimes given in units of grams of solute per 100mL of water.

Complete step by step answer: Since it is a multiple answer type question therefore, we will calculate each of the options one by one.
Considering option (A), Volume strength of solution is given as 28. Therefore molarity will be,
\[\begin{align}
  & molarity=\dfrac{\text{volume strength}}{11.2} \\
 & molarity=\dfrac{28}{11.2}=2.5 \\
\end{align}\]
Since the value of molarity obtained is 2.5 and given in the question is also the same, therefore, it is a correct option.
Considering option (B), Percentage w/v can be calculated using volume strength. The formula is as follows:
$\begin{align}
 & \text{percentage w/v =}\dfrac{\text{volume strength}\times \text{68}}{22.4} \\
 & \text{percentage w/v =}\dfrac{28\times 68}{224}=8.5 \\
\end{align}$
The obtained value is 8.5 and the value given in the option is 17, therefore, it is an incorrect option.
 Considering option (C), Mole fraction of ${{H}_{2}}{{O}_{2}}$is deduced. 1 L of solution contains 2.5 moles of hydrogen peroxide.Moles of water is calculated using the formula,
\[\begin{align}
& \text{Number of moles of water = }\dfrac{\text{mass of solution- mass of }{{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}}{\text{molecular mass}} \\
 & \text{Number of moles of water =}\dfrac{265\times 1-2.5\times 34}{18}=10moles \\
\end{align}\]
Moles of water is 10 and moles of ${{H}_{2}}{{O}_{2}}$ was calculated above that is 2.5 moles, then, Mole fraction of ${{H}_{2}}{{O}_{2}}$ will be,
\[\text{mole fraction=}\dfrac{2.5}{10+2.5}=0.2\]
Therefore, mole fraction obtained is 0.2, which is the value as given in the option C. therefore, Option C is the correct answer.
Considering option (D), molality is calculated using the formula,
\[\begin{align}
& molality=\dfrac{\text{moles of solute}}{\text{mass of solvent}} \\
& molality=\dfrac{2.5}{0.180}=13.88 \\
\end{align}\]
Obtained value of molality is 13.88 which is the same as given in the question, therefore, C option is also the correct answer.

Thus, the correct answer is the A, C and D option.

Note: Molarity is the measure of concentration. It is defined as the moles of solute per litre of a solution.It is also known as the molar concentration of a solution.Molality is defined as the number of moles of solute per kilogram of solvent.