Concentrated H₂O₂ solution is used as oxidant in rocket fuel and diluted H₂O₂ solution is used as hair bleach.  A 30% H₂O₂ (w/w) aqueous solution has density 1.11 gm/mL.  What is the molarity and mole fraction of the H₂O₂ solution ?   

$\begin{array}{l}30 \%\left(\frac{w}{w}\right)=x \%\left(\frac{w}{w}\right) \\ \begin{aligned} \therefore S & =\frac{10 x}{M} \times s \\ & =\frac{10 \times 30}{34} \times 1.11 \\ & =9.79 \mathrm{M}\end{aligned}\end{array}$

$\begin{aligned} \mathrm{mole ~of~} \mathrm{H}_{2}\mathrm{O}_{2} ~=30 \div 34 ~=0.088\end{aligned}$

$\begin{aligned} \text { moles of } \mathrm{H}_{2} \mathrm{O} & =70 / 18 \\ & =3.88 \\ \therefore \text { Total moles } & =0.88+3.88 \\ & =4.76\end{aligned}$

$\therefore$ mole Fraction of,

$\begin{aligned} \mathrm{H}_{2} \mathrm{O}_{2} & =\frac{0.088}{4.76} \\ & =0.185 \end{aligned}$