Question

Exercise 7.46 We can determine the purity of solid materials by using calorimetry. A gold ring (for pure gold, specific heat = 0.1291 J⋅g−1⋅K−1 ) with mass of 10.5 g is heated to 78.3 ∘C and immersed in 50 g of 23.7 ∘C water in a constant-pressure calorimeter. The final temperature of the water is 31.0 ∘C. You may want to reference ( page ) Section 7.1 while completing this problem.

Answer 1

So, the question would would probably ask if the gold ring is indeed pure gold. Let's calculate the specific heat capacity of the calorimeter. If this is equal to the given specific heat for pure gold, then the the gold ring is pure gold.

Qwater = mCdT = (50 g)(4.18 J/gC)(31 - 23.7) = 1525.7 J
Through conservation of energy,
Qwater = Qcalorimeter = mCdT = 1525.7
1525.7 = (10.5)(C)(78.3 - 31)
Solving for C,
C = 3.072 J/gC

Since the specific heat of the calorimeter is not equal to that of the pure gold (0.1291 J/gC), then the gold ring is not pure.