3. Electrum is an ancient alloy of silver and gold with a variable composition d

Question

3. Electrum is an ancient alloy of silver and gold with a variable composition dependent on geographical location and time period. A coin made of electrum is discovered in Tunisia, near the ancient site of Carthage, it is dated to ca. 200 BCE. The volume of the coin is measured at 0.9254 cm' and has a mass of 13.0555 g. Using the densities of gold and silver (19.3 g/cm and 10.5 g/cm^3, respectively) and assuming no change in volume occurs when the two metals are mixed, calculate the percentage of gold in the coin and the equivalent karat rating (24 karats corresponds to 100% gold.)

Explanation / Answer

mass of gold in the coin = m1 and mass of silver in the coin = m2

Since Volume is constant

Mass / Density remains constant

0.9254 = (m1 / 19.3) + ( m2 / 10.5)

0.9254 = m1 * 0.052 + m2 * 0.095 ------------(1)

Again,

Mass of coin = m1 + m2

13.0555 = m1 + m2 --------------(2)

m1 = 13.0555 - m2

Putting value of m1 in eqn (1) we get

0.9254 = (13.0555 - m2) * 0.052 + m2 * 0.095

0.9254 = 0.68 + 0.043*m2

m2 = (0.9254 - 0.68) / 0.043 = 5.71 g

m1 = 13.0555 - 5.71 = 7.35 g

% of gold = (m1 / 13.0555) * 100 = (7.35 / 13.0555) * 100 = 56.3%

100% = 24 karat

56.3% = (24/100) * 56.3 = 13.51 karat

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