Question

A 50.00 g sample of an unknown metal is heated to 45.00°C. It is then placed in a coffee-cup calorimeter filled with water. The calorimeter and the water have a combined mass of 250.0 g and an overall specific heat of 1.035 cal/g•°C. The initial temperature of the calorimeter is 10.00°C. The system reaches a final temperature of 11.08°C when the metal is added.

Which of the following equations is the correct one to use to calculate the specific heat of the metal?

C subscript p metal equals StartFraction m metal delta T metal over m calories C subscript p calorites delta T calories EndFraction.
C subscript p metal equals StartFraction negative m calories C subscript p calories delta T calories over m metal delta T metal EndFraction.

What is the specific heat of the metal?
cal/g•°C

Answer 1

The correct equation is the second one:
C_p,metal = −(m_cal · C_p,cal · ΔT_cal) / (m_metal · ΔT_metal),
because heat lost by the metal + heat gained by the calorimeter = 0.

Compute ΔT:
ΔT_metal = 11.08 − 45.00 = −33.92 °C
ΔT_cal = 11.08 − 10.00 = 1.08 °C

Then
C_p,metal = −(250.0 g · 1.035 cal/g·°C · 1.08 °C) / (50.00 g · −33.92 °C)
= 279.45 / 1696.0
= 0.1647 cal/g·°C

Rounded to three significant figures: 0.165 cal/g·°C.