Question

A 12.8 g sample of ethanol (C2H5OH) is burned in a calorimeter with a heat capacity of 5.65 kJ/°C. Assume the heat from the sample is negligible compared to the calorimeter. Determine the initial temperature of the calorimeter if the final temperature is 85.7°C. The molar mass of ethanol is 46.07 g/mol.

Answer 1

18.78° C

Step-by-step explanation:

We are given;

• Mass of ethanol as 12.8 g
• Heat capacity of the calorimeter as 5.65 kJ/°C
• Final temperature of the calorimeter is 85.7°C
• Molar mass of ethanol as 46.07 g/mol

We are required to determine the initial temperature of the calorimeter;

Step 1: Calculate the heat released by ethanol

First, we determine moles of ethanol

Moles = Mass ÷ Molar mass

Moles = 12.8 g ÷ 46.07 g/mol

= 0.278 moles

But. molar enthalpy of ethanol is 1360 kJ/mol

Thus,

Heat released, Q = n × ΔHc

= 0.278 mole × 1360 kJ/mol

=378.08 kJ

Step 2: Calculate the heat energy absorbed by the calorimeter

Assuming the initial temperature of the calorimeter is X

Heat absorbed, Q = C × ΔT, Where C is the heat capacity

Change in temperature, ΔT = (85.7 - X)°C

Therefore;

Q = 5.65 kJ/°C × (85.7 - X)°C

= 484.205 - 5.65 X kilo Joules

Step 3: Determine the initial temperature of the calorimeter

• We know that, the heat absorbed is equivalent to the heat released.

Thus;

484.205 - 5.65 X Joules = 378.08 kJ

5.65 X = 106.125

X = 18.78° C

Thus, the initial temperature of the calorimeter 18.78° C