Question

Red gold is a gold‑copper alloy used to make jewelry. A piece of jewelry made of red gold weighs 8.80 g and has a volume of 0.594 cm3. Gold has a density of 19.3 g/cm3 and copper has a density of 8.96 g/cm3

. Calculate the percentage by mass of each metal in the jewelry. Assume the total volume of the jewelry is the sum of the volumes of the two metals it contains.

gold:

%

copper:

%

Pure gold is defined as having 24 carats. When mixed in an alloy, the carats of gold are given as a percentage of this value. For example, a piece of jewelry made with 50% gold has 12 carats. State the purity of this piece of red gold jewelry in carats.

purity:

carats

Answer 1

solution - In this question, we have - weight of red Gold Jewelry = 8.80g - volume of Jewelry = 0.594 cm3, Density of Gold = 19.3 g/cm? Density of copper = 8.96 g/cm3 Let volume of Grold = x cm² & copper ay cm3 volume of red Gold Jewelry ist - volume of Gold used (x) cms - & volume of copper used s 0.594cm3 = xty y ) cm3 So, y = (0.594 x 3 cm3 volume volume of of Gold =-xcm3 used copper usce = (0.594-u) cm3 so, mass of Jewelry - l density & volume ) of Gold) tl density & volume) of copper) - 8.80g = (19. 39/m3 * * ( m ) + (8-96 / m X (0.594-2) Eims 8.80g = (19.39 -8.96 g) + 5.32 g 3.489= 10.34g. x x= 0.337

So, volume of gold used = 4 cm² - 0.337 cm3 volume of copper used = y cm3 = (0.594-2) (m3 = (0.594 -0.337) cm = 0,257 cm - mass of to para gold used in Je welry :- density of gold & volume of gold used - in Jewelry 19.3 g/cm3 x 0.337 cm3 = 6.5 g 9 gotd used Similarly, mass of copper used in Jewelry - =) 8.96 g/cm3 x 0. 257 cm3 - 3 g of copper used) mass % of old in Tewelry: - masst of old = mass of gold in Jewelry mass of Jewelry mass t. of gold = 6. 5 g x 100% 8. 88 mass% of gold = 73.9% X 1007

similarly, mass % of copper :- » mass t of copper = 2,3 g x 100% 8.89 mass % of copper = 26.1% If jewelry is made up of 100% Gold then - it defined as having 24 carats. In this case, Tewelry is made up of obwh 73.9% Gold. so, burity = 24 x 73.9% purity = 17,736 carats