A coffee cup (or constant pressure) calorimeter contains 108.0 g of water at an initial temperature of 25.0°C. 118.7 g of tin metal at a temperature of 100°C is added. The final temperature in the calorimeter is 29.2°C. What is the molar heat capacity of the tin? The molar heat capacity of water is 75.4 J / (mol•°C). Assume that the heat capacity of the coffee cup is negligible.

Explanation:

The molar mass of water is

Here the mass of water is

So the number of moles of water in the cup is:

The amount of heat released by absorbed by the water in the process is:

where

n = 6 mol is the number of moles

C = 75.4 J / (mol•°C) is the molar heat capacity of water

is the change in temperature of the water

Substituting,

According to the law of conservation of energy, this is also equal to the energy released by the hot tin metal, which can be rewritten as

where:

is the number of moles of tin, where

m = 118.7 g is the mass of tin

is the molar mass of tin

So,

C is the molar heat capacity of tin

is the change in temperature of the tin

Solving for C, we find the molar heat capacity of tin: