Answer:
A). Percentage of gold by mass of the jewellery =
(6.059÷9.85) × 100 = 61.5%
B). Purity of the gold = 0.615 × 24 = 14.76 karat ~ 15 karat gold
Explanation:
Mass of jewellery = 9.85g Volume of jewellery = 0.675cm^3.
Density of gold = 19.3g/cm^3 and density of silver = 10.5g/cm^3
Let the volume of gold in the jewellery be X and the volume of silver in the jewellery be Y
Hence we have
Density = mass/volume or mass = volume × density = for gold = X × 19.3g/cm^3 and for the silver = Y × 10.5g/cm^3
19.3X +10.5Y = 9.85g
Also volume of jewellery is given by
Volume of silver in the jewellery + volume of gold in the jewellery = 0.675cm^3.
X + Y = 0.675cm^3.
Solving the above equations we have
Y = 0.675 - X
Which gives
19.3X + 10.5Y = 9.85g
19.3X + 10.5 × (0.675 - X) =9.85g
19.3X + 7.0875 - 10.5X = 9.85
8.8X + 7.0875 = 9.85
8.8X = 2.7625
or X = 0.3139 cm^3
But Y = 0.675 - X
Hence Y = 0.675 - 0.3139 = 0.3611 cm^3
Mass of gold in the jewellery = volume of gold × Density of gold = 0.3139 × 19.3 = 6.059 g
Also mass of silver = 10.5 × 0.3611 = 3.7913g
A). Percentage of gold by mass of the jewellery =
(6.059÷9.85) × 100 = 61.5%
B). Purity of the gold = 0.615 × 24 = 14.76 karat ~ 15 karat gold
