Question

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en 7 of 10 > Red gold is a gold-copper alloy used to make jewelry, A piece of jewelry made of red gold weighs 8.28 g and has a volume of 0.503 cm. Gold has a density of 19.3 g/cm' and copper has a density of 8.96 g/cm'. 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. carats purity:

Answer 1

Answer -

Given,

Mass of Red Gold (Gold-Copper Alloy) = 8.28 g

Volume of Red Gold = 0.503 cm³

density of Gold = 19.3 g/cm³

density of Copper = 8.96 g/cm³

Percentage by mass of Gold = ?

Percentage by mass of Copper = ?

Let Mass of Gold = X g and Mass of Copper = Y g

X + Y = 8.28 g (given)

X = 8.28 g - Y ---------------A

Now,

Density = Mass/Volume

Volume = Mass/ Density

So, Volume of Gold = X /19.3 g/cm³

Volume of Copper = Y /8.96 g/cm³

Total Volume = 0.503 cm³ = X/19.3 g/cm³ + Y/8.96 g/cm³ (given) -----B

Put A in B

0.503 cm³ = (8.28 g - Y )/19.3 g/cm³ + Y/8.96 g/cm³

0.503 cm³ - Y/(8.96 g/cm³) = (8.28 g - Y )/19.3 g/cm³

(4.51 - Y)/(8.96 g/cm³) = (8.28 g - Y )/19.3 g/cm³

(4.51 - Y) *19.3 g/cm³ = (8.28 g - Y ) *8.96 g/cm³

87.043 g/cm³ - Y *19.3 g/cm³ =74.1888 - Y *8.96 g/cm³

87.043 g/cm³ - 74.1888 = Y *19.3 g/cm³ - Y *8.96 g/cm³

12.8542 g/cm³ = Y *10.34 g/cm³

Y = 12.8542 g/cm³ / 10.34 g/cm³ = 1.24

Y = 1.24 g ------------C

Put C in A

X = 8.28 g - 1.24 g

X = 7.04 g

So, Mass of Gold in alloy = 7.04 g

Mass of Copper in alloy = 1.24 g

% by mass = (Mass/ Total mass) * 100

So, % by mass of Gold = (7.04 g / 8.28 g) * 100

% by mass of Gold = 85.02 % [Answer]

% by mass of Copper = (1.24 g / 8.28 g) * 100

% by mass of Copper = 4.98 % [Answer]

Purity of Gold is measured in Carats- 100% = 24 Carat

50% pure = 12 carats

So, 1 % pure = 24/100 = 0.24 carat

Percentage of Gold in jewellery = 85.02 %

So, Purity = 85.02 * 0.24

Purity = 20.40 carat [Answer]