A pure gold ring and pure silver ring have a total mass of 15.8 g . The two ring

Question

A pure gold ring and pure silver ring have a total mass of 15.8 g . The two rings are heated to 71.0 C and dropped into a 12.2 mL of water at 22.7 C. When equilibrium is reached, the temperature of the water is 25.2 C.

What is the mass of gold ring? (Assume a density of 0.998 g/mL for water.)

Express your answer to two significant figures and include the appropriate units.

What is the mass of silver ring? (Assume a density of 0.998 g/mL for water.)

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

We know that,

Cp fro silver = 0.235 J / g K

Cp for gold = 0.129 J / g K

Cp for water = 4.18 J / g K

Given,

Total Mass = 15.8 g

Volume of water = 12.2 mL

Density = 0.998 g / mL

=> Mass of water = 12.2 x 0.998 = 12.1756 g

Let,

Mass of gold ring = m

Mass of silver ring = 15.8 - m

Heat lost by gold ring = m x 0.129 x (71 - 25.2) = 5.9082 m

Heat lost by silver ring = (15.8 - m) x 0.235 x (71 - 25.2) = 170.0554 - 10.673 m

Heat gained by water = 12.1756 x 4.18 x (25.2 - 22.7) = 127.235

Heat gained = Heat lost

=> 5.9082 m + 170.0554 - 10.673 m = 127.235

=> m = 8.99 g

=> Mass of gold ring = 8.99 g

Mass of silver ring = 15.8 - 8.99 = 6.81 g

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