Chapter 6, Problem 6.50P

Interpretation Introduction

Interpretation:

$\Delta E$ for the combustion of $1.750\text{g}$ ethanol sample that is burned in a bomb calorimeter with a heat capacity $12.05\text{ kJ/K}$ is to be calculated.

Concept introduction:

Calorimeter is a device that is employed to measure the heat absorbed or released by the system. Calorimeter is of two types:

1. Coffee cup calorimeter

2. Bomb calorimeter

Bomb calorimeter is employed to determine the heat absorbed or released by the substance placed in the calorimeter at constant volume. Bomb calorimeter is generally used in case of combustion reactions. The heat lost by the reaction is gained by the calorimeter.

$-q_{\text{rxn}}=q_{\text{calorimeter}}$

Specific heat capacity $\left(c\right)$ of a substance is the amount of heat needed to raise the temperature of $1\text{g}$ of a substance by $1\text{K}$. The formula to calculate heat required is as follows:

$q=\left(\text{mass}\right)\left(c\right)\left(\Delta T\right)$        (1)

Here,

$\Delta T$ is the temperature difference.

$q$ is the heat released or absorbed.

$c$ is the specific heat capacity of the substance.

The formula to calculate heat required in case of calorimeter is as follows:

$q_{\text{calorimeter}}=\left(C_{\text{calorimeter}}\right)\left(\Delta T_{\text{calorimeter}}\right)$        (2)

Here,

$\Delta T_{\text{calorimeter}}$ is the temperature difference.

$q_{\text{calorimeter}}$ is the heat released or absorbed by calorimeter.

$C_{\text{calorimeter}}$ is the specific heat capacity of the calorimeter.

At the constant volume the value of heat $\left(q_{\text{v}}\right)$ is equal to internal energy $\left(\Delta E\right)$.

The formula to calculate $\Delta T$ of the system is as follows:

$\Delta T=T_{\text{Final}}-T_{\text{Initial}}$        (3)