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 your response differs significantly from the correct answer. rework your solution from the beginning and check each step carefully. m3 volume of copper your response differs significantly from the correct answer. rework your solution from the beginning and check each step carefully. m3 (c) calculate the density of the british sovereign coin. kg/m3

(a) Mass of gold = 0.0073223 kg.

(b) V of gold 3.79 x 10⁻⁷ m³ & ∴ V of copper = 7.438 x 10⁻⁸ m³.

(c) The density of the British sovereign coin 17,620 kg/m³.

Explanation:

(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).

∵ the number of karats = 24 (mass of gold)/(total mass)

the number of karats = 22-karat gold,

mass of gold = ??? g,

total mass = 7.988 g.

∴ mass of gold = (the number of karats)(total mass)/24 = (22)(7.988 g)/(24) = 7.3223 g = 0.0073223 kg.

(b) Calculate the volumes of gold and copper, respectively.

∵ Mass of coin = 7.988 g.

∵ mass of gold = 7.3223 g.

∴ mass of Cu = Mass of coin - mass of gold = 7.988 g - 7.3223 g = 0.6657 g = 0.6657 x 10⁻³ kg.

V = m/d.

where, V is the volume of the material,

m is the mass of the material,

d is the density of the material.

Density of gold = 19,320 kg/m³, mass of gold = 0.0073223 kg.

∴ V of gold = m/d = (0.0073223 kg)/(19,320 kg/m³) = 3.79 x 10⁻⁷ m³.

Density of copper = 8,950 kg/m³, mass of copper = 0.6657 x 10⁻³ kg.

∴ V of copper = m/d = (0.6657 x 10⁻³ kg)/(8,950 kg/m³) = 7.438 x 10⁻⁸ m³.

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

d = m/V.

mass of the British sovereign coin = 7.988 g = 0.007988 kg.

Volume of the British sovereign coin = V of gold + V of copper = (3.79 x 10⁻⁷ m³) + (7.438 x 10⁻⁸ m³) = 4.534 x 10⁻⁷ m³.

∴ Density of the British sovereign coin = m/V = (0.007988 kg)/(4.534 x 10⁻⁷ m³) = 17,620 kg/m³.

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