Gold is alloyed with other metals to increase its hardness in making jewelery. a) Consider a piece of gold jewelry the weighs 9.85g and has a volume of 0.675cm^3. The jewelery contains only gold and silver which have densities of 19.3g/cm^3 and 10.5g/cm^3. Assuming that the total volume of the jewelery is the sum if the volumes of the gold and silver that it contains, calculate the percentage of gold (by mass) of the jewelery. b) The relative amount of gold in an alloy is commonly expressed in units of karats. Pure gold is 24 karats, and the percentage of gold in an alloy is given as the percentage of this value. For example: an alloy that is 50 percent gold is 12 karats. State the purity of the gold jewelery in karats.

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