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

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,

& molarity=\dfrac{\text{volume strength}}{11.2} \\\ & molarity=\dfrac{28}{11.2}=2.5 \\\ \end{aligned}$$ Since the value of molarity obtained is 2.5 and given in the question is also the same, therefore, it is a correct option. Considering option (B), Percentage w/v can be calculated using volume strength. The formula is as follows: $\begin{aligned} & \text{percentage w/v =}\dfrac{\text{volume strength}\times \text{68}}{22.4} \\\ & \text{percentage w/v =}\dfrac{28\times 68}{224}=8.5 \\\ \end{aligned}$ The obtained value is 8.5 and the value given in the option is 17, therefore, it is an incorrect option. Considering option (C), Mole fraction of ${{H}_{2}}{{O}_{2}}$is deduced. 1 L of solution contains 2.5 moles of hydrogen peroxide.Moles of water is calculated using the formula, $$\begin{aligned} & \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{aligned}$$ Moles of water is 10 and moles of ${{H}_{2}}{{O}_{2}}$ was calculated above that is 2.5 moles, then, Mole fraction of ${{H}_{2}}{{O}_{2}}$ will be, $$\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{aligned} & molality=\dfrac{\text{moles of solute}}{\text{mass of solvent}} \\\ & molality=\dfrac{2.5}{0.180}=13.88 \\\ \end{aligned}$$ 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.