The reaction between zinc and gold can be represented by the following equation:
$$Zn(s) + 2Au^3+(aq) → 2Au(s) + Zn^2+(aq)$$
In this reaction, the zinc atoms are oxidized from a neutral state to a +2 oxidation state, while the gold ions are reduced from a +3 oxidation state to a neutral state. The solid gold atoms then precipitate out of the solution, while the zinc ions remain in solution.
The ability of zinc to displace gold is due to its lower reactivity compared to gold. This means that zinc is more easily oxidized than gold, and therefore it is more willing to give up its electrons. This difference in reactivity is what drives the cementation process.
The process of cementation is commonly used in the mining industry to extract gold from ores. The ore is first leached with a cyanide solution, which dissolves the gold. The gold-rich solution is then passed through a bed of zinc shavings, where the zinc atoms displace the gold ions from the solution. The gold atoms then precipitate out of the solution and can be collected.