The British gold sovereign coin is an alloy of gold and copper having a total ma

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). (b) Calculate the volumes of gold and copper, respectively, used to manufacture the coin. (c) Calculate the density of the British sovereign coin. Useful values: density of gold = 19.3 × 10^3 kg/m3 , density of copper = 8.92 × 10^3 kg/m3

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Explanation / Answer

Density of gold = 19.32 grams / cu cm
(19,320 kg / cu m)
Density of copper = 8.95 grams / cu cm
(8,950 kg / cu m)
Mass of coin = 7.988 grams

The mass of gold from :
(22 / 24) * 7.988
= 7.3223 grams (0.0073223 kg)
( ANSWER (a) )

The mass of copper = 7.988 - 7.3223
= 0.6757 grams ( 0.0006757 kg )

Volume of gold = mass / density = 7.3223 / 19.32
= 0.379 cu cm ( 0.000000379 cubic meter )
( ANSWER (b) )

Volume of copper = mass / density = 0.6757 / 8.95
= 0.0755 cu cm ( 0.0000000755 cubic meter )
( ANSWER (b) )

Density = mass / volume = 7.988 / ( 0.379 + 0.0755 )
= 17.575 g / cu cm
( 17,575 kg / cu m )
(ANSWER (c) )

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