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

GIVEN DATA

Total mass of British gold sovereign is: M_T = 7.988 g =0.007988 kg

Quality of gold is: K_T = 22 karat

a)

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

K_T=24×(M_G)/ (M_T)

M_G=(K_T×M_T) / 24 =( 22×7.998 ) /24 =7.322 g = 0.007322 kg

M_G = 0.007322 kg

Thus, the mass of gold is 0.007322 kg

(b)

Density of gold is: ρ_G =19.32 g/cm³ = 19320 kg/m³

Density of copper is: ρ_CU =8.95 g/cm³ = 8950 kg/m³

volume of the gold = (mass of gold )/ (Density of gold)

volume of gold = 0.007322 / 19320 = 3.789 ×10^-7 m³

volume of gold= 3.789 ×10^-7 m³

similarly volume of copper = (mass of copper )/ (density of copper)

volume of copper = (total mass - mass of gold ) /( density of copper )

volume of copper =( 0.007988 - 0.007322 ) / (8950)

volume of copper = 7.44 ×10^-8 m³

volume of gold= 3.789 ×10-7 m3 volume of copper = 7.44 ×10-8 m3

c)

density of the sovereign

ρ sovereign = M_TOTAL / V_total = M_TOTAL / (V _GOLD +V_COPPER )

ρ sovereign = 0.007988 / ( 3.789 ×10^-7 m³ + 7.44 ×10^-8 m³ ) = 17622 kg/m³

ρ sovereign = 17622 kg/m3

answers

a)

the mass of gold is 0.007322 kg

b)

volume of gold= 3.789 ×10^-7 m³

volume of copper = 7.44 ×10^-8 m³

c)

ρ sovereign = 17622 kg/m³

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