Question

The British gold sovereign coin is an alloy of gold and copper having a total mass of 7.988 g, and is 22-karat gold.

(a) Find the mass of gold in the sovereign in kilograms using the fact that the number of karats = 24 ✕ (mass of gold)/(total mass).
kg

(b) Calculate the volumes of gold and copper, respectively, used to manufacture the coin.

volume of gold	m3
volume of copper	m3

(c) Calculate the density of the British sovereign coin.
kg/m³

Answer 1

Density of gold = 19.32 gm/cm^3 = 19320 kg /m^3
Density of copper = 8.95 gm/cm^3 = 8950 kg /m^3
Mass of coin = 7.988 gm

(a)
Find the mass of gold in the sovereign in kilograms using the fact that the number of karats =
= (22 / 24) * 7.988
= 7.3223 gm
= 7.3223 * 10^-3 kg

(b)
Volume = Mass/Density
Volume of gold = (7.3223 * 10^-3)/19320
Volume of gold = 3.79 * 10^-7 m^3

Volume of copper = (7.988 - 7.322) / 8950 * 10^-3
Volume of copper = 7.44 * 10^-8 m^3

(c)
Density = Mass/Volume
Density = ( 7.988 * 10^-3) / (3.79 * 10^-7 + 7.44 * 10^-8) kg /m^3
Density = 17618 kg/m^3