Question

A piece of copper has a temperature of 75.6 0C. When the metal is placed in 100.0 grams of water at 19.1 0C, the temperature rises by 5.5 0C. What is the mass of the metal?

Answer 1

Answer:

115.58 g ≅ 115.6 g.

Explanation:

• Knowing that:

Heat lost by copper (Qc) = Heat gained by the water (Qw) ,

- (Qc) = (Qw).

• We can calculate the amount of heat (Qw) gained by water using the relation:

Qw = m.c.ΔT,

where, Qw is the amount of heat released to water (Q = ??? J).

m is the mass of water (m = 100.0 g).

c is the specific heat capacity of solution (c = 4.18 J/g.°C).  

ΔT is the difference in T (ΔT = final temperature - initial temperature = 24.6°C - 19.1°C = 5.5°C).

∴ Q = m.c.ΔT = (100.0 g)(4.18 J/g.°C)(5.5°C) = 2299 J.

 

• Now, the amount of heat lost by copper (Qc) = - 2299 J.

(Qc) = m.c.ΔT,

where, Qc is the amount of heat lost by substance (Qc = - 2299 J).

m is the mass of water (m = ??? g).

c is the specific heat capacity of solution (c = 0.39 J/g.°C).

ΔT is the difference in T (ΔT = final temperature - initial temperature = 24.6°C - 75.6°C = - 51.0°C).

∴ (- 2299 J) = (m)(0.39 J/g.°C)(- 51.0°C).  

∴ m of copper = (- 2299 J)/(0.39 J/g.°C)(- 51.0°C) = 115.58 g ≅ 115.6 g.