(a) (i) State Boyle's law. (ii) Give the mathematical expression of Boyle's law. (iii) Sketch the graphical representation of Boyle's law. (b) A given mass ...

(a)(i) Boyle's law states that, at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.

(ii) \[V\propto\frac{1}{P}\] Hence, \[PV=k\] where \(k\) is a constant for a fixed mass of gas at constant temperature.

(iii) The graph of pressure against volume is a rectangular hyperbola.

(b) Using the combined gas law:

\[\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\]

\[V_2=\frac{P_1V_1T_2}{P_2T_1}\]

\[V_2=\frac{(6.5\times10^4)(500)(273)}{(1.01\times10^5)(273+30)}\]

\[V_2=289.8\ \text{cm}^3\]

\[\boxed{V_2\approx290\ \text{cm}^3}\]

(c) In warm water, the air particles inside the balloon gain kinetic energy and move more rapidly. They collide more frequently and forcefully with the wall of the balloon, causing the balloon to expand until the internal and external pressures balance.

(d)(i) Vapour density is the ratio of the mass of a given volume of a gas or vapour to the mass of an equal volume of hydrogen at the same temperature and pressure.

(d)(ii)

\[M_r(\mathrm{SO_2})=32+(2\times16)=64\]

\[\text{Vapour density}=\frac{M_r}{2}=\frac{64}{2}=\boxed{32}\]

(e)(i)

1. Upward delivery: \(\mathrm{NH_3}\).
2. Downward delivery: \(\mathrm{SO_2}\).

(e)(ii)

1. \(\mathrm{SO_2}\) dissolves in water to form an acidic solution.
2. \(\mathrm{NH_3}\) dissolves in water to form a basic or alkaline solution.

(e)(iii)

1. \(\mathrm{SO_2}\) acts as an oxidising agent.
2. \(\mathrm{NH_3}\) acts as a reducing agent.

(f)(i) Two alloys of tin are:

1. Bronze, an alloy of copper and tin.
2. Soft solder, an alloy of tin and lead.

(f)(ii)

1. Bronze is used for making coins, medals and ornaments.
2. Soft solder is used for joining metals, for example in electrical connections and plumbing.