$A$ mixture of $O_2$ and gas $Y$ (molecular weight $80$) in the mole ratio $a : b$ has a mean molecular weight of $40$. What would be the mean molecular weight if the gases are mixed in the ratio $b : a$ under identical conditions? (The gases are non-reacting)

What quantity (in $mL$) of a $45\%$ acid solution of a mono-protic strong acid must be mixed with a $20\%$ solution of the same acid to produce $800 \ mL$ of a $29.875\%$ acid solution?

Mole fraction of $O_2$ in an $O_2$ and $O_3$ mixture is $0.25$. Hence,the percentage concentration $\left( \frac{w}{W}\% \right)$ of $O_2$ in the mixture is:

Partially dried soil contains $50 \%$ silica and $7 \%$ water. If the original soil contained $12 \%$ water,then the percentage of silica in the original soil is .............. $\%$.

$1 \, L$ aqueous solution of $H_{2}SO_{4}$ contains $0.02 \, mmol$ $H_{2}SO_{4}$. $50 \%$ of this solution is diluted with deionized water to give $1 \, L$ solution $(A)$. In solution $(A)$,$0.01 \, mmol$ of $H_{2}SO_{4}$ are added. Total $mmol$ of $H_{2}SO_{4}$ in the final solution is $...... \times 10^{-3} \, mmol$.

State whether the following statements are true or false:
$(i)$ The molarity of a $0.6 \ N$ aqueous solution of ${H_3PO_3}$ is $1.2 \ M$.
$(ii)$ $\text{Empirical formula} = n \times \text{Molecular formula}$.
$(iii)$ In ${Cl_2O}$,the weight of chlorine combining with $8 \ g$ of oxygen is $35.5 \ g$.