Answer to Question #144800 in General Chemistry for Joshua

Question

A sample of unknown metal with a mass of 192 g heated to a temperature of 100°C was immersed into a brass calorimwter with a mass of 0.128 kg containing of water at a temperature of 8.4°C. Provided that the water temperature stabilized at 21.5 °C, calculate the specific heat capacity of the metal anf based on this value of capacity, identify the metal by using the law of Dulong and Petit. Assume that the specific heat capacity of brass is 394 J kg-1 K-1.

Answer 1

mass of metal (m1) = 192g

T1 = 100°C

c1 (shc of metal) = ?

mass of calorimeter (m2) = 0.128kg = 128g

c2 (shc of calorimeter) = 394 J/kg.K = 0.394 J/g.K

mass of water (m3) = 240g

c3 (shc of water) = 4.184 J/g.K

T2 (Temperature of water and calorimeter) = 8.4°C

T3 (Final Temperature) = 21.5°C

heat lost = heat gained

m1c1(T1-T3) = m2c2(T3-T2) + m3c3(T3-T2)

192 × c1 × (100-21.5) = 128 × 0.394 × (21.5-8.4) + 240 × 4.184 × (21.5 - 8.4)

15,072c1 = 660.7 + 13,154.5

15,072c1 = 13815.2

c1 = 13815.2/15,072

c1 = 0.916 J/g.C

According to Dulong and Petit's law,

Atomic mass × specific heat = 3R

Atomic mass × c = 24.942

Atomic mass = 24.942/0.916 = 27.23g

Therefore, the unknown metal is probably Aluminium. Since the atomic mass of Aluminium is 27g.