A bottle of sulfuric acid is labelled 49.0% by mass, with density 1.40 g mL⁻¹…

(a) $100\ \text{g}$ has volume $100 / 1.40 = 71.43\ \text{mL}$ and holds $0.50\ \text{mol}$ of $\text{H}_2\text{SO}_4$. Molarity $= 0.50 / (71.43 \times 10^{-3}) = 7.00\ \text{mol L}^{-1}$.

(b) The water is $51.0\ \text{g} = 0.0510\ \text{kg}$, so molality $= 0.50 / 0.0510 = 9.80\ \text{mol kg}^{-1}$.

(c) Water is $51.0 / 18.0 = 2.833\ \text{mol}$, so $x = 0.50 / (0.50 + 2.833) = 0.150$.

(d) Mass of the mixture $= 100.0 \times 1.40 + 300.0 \times 1.00 = 440.0\ \text{g}$, so its volume is $440.0 / 1.12 = 392.9\ \text{mL}$. This is less than the $400.0\ \text{mL}$ that simply adding would give.

(e) The portion held $7.00 \times 0.1000 = 0.70\ \text{mol}$, so the molarity is $0.70 / (392.9 \times 10^{-3}) = 1.78\ \text{mol L}^{-1}$. Adding volumes would have given $1.75\ \text{mol L}^{-1}$, which is wrong by about $2\%$.