Question

The heat liberated when $1.89g$ of benzoic acid is burnt in a bomb calorimeter at ${25}^{o}C$ and it increases the temperature of $18.94kg$ of water by $0.632{}^{o}C$. If the specific heat of water at ${25}^{o}C$ is $0.998cal/g/deg$, the value of the heat of combustion of benzoic acid is

• A. $881.1kcal$
• B. $771.124kcal$
• C. $981.1kcal$
• D. $871.2kcal$

Answer 1

The correct option is B $771.124kcal$

(b)
Given:
$\text{Weight of benzoic acid}=1.89g;\text{Temperature of bomb calorimeter}={25}^{o}C=298K;\text{Mass of water (m)}=18.94kg=18940g;\text{Increase in temperature}\left(\Delta T\right)={0.632}^{o}C$ and
$\text{Specific heat of water, (s)}=0.998cal/g/deg$

We know that, heat gained by water or heat liberated by benzoic acid $\left(Q\right)=ms\Delta T$
$Q=18940\times 0.998\times 0.632=11946.14cal$
Since $1.89g$ of acid liberates $11946.14cal$ of heat, therefore, heat liberated by $122g$ of acid is

$=\frac{11946.14}{1.89}\times 122$
$=771126.5cal=771.12cal$
(where $122g$ is the molecular weight of benzoic acid)

Hence, option (b) is correct.