Q. 8.74 - An Introduction to General, Organic, and Biological Chemistry

Question

A fire extinguisher has a pressure of $10atm$ at $25°C$. What is the final pressure, in atmospheres, when the fire extinguisher is used at a temperature of $75°C$, if $V and n$ do not change?

Step-by-Step Solution

Answer

The final pressure of fire extinguisher is $11.67atm$.

Step 1: Given Information

We have given the pressure of the fire extinguisher is $10atm$ and the temperature is $25°C$.

Step 2: Explanation

Considering the Gay- Lussac's Law that if a constant volume and amount of gas are maintained, the pressure will be increased. In the temperature-pressure relationship which is known as Gay-Lussac's law, the pressure of a gas decreases, and a decrease in temperature decreases the pressure of the gas till the volume of the gas doesn't change. i.e.

$\frac{P_1}{T_1}=\frac{P_2}{T_2} ... \left(1\right)$

Step 3: Calculation

Here we have the quantities available, that is

the initial temperature $T_1=25°C=\left(25+273\right)K=298K$,

initial pressure $P_1=10atm$

and the final temperature $T_2=75°C=\left(75+273\right)K=348K$

Calculating the final pressure $P_2$, from equation $\left(1\right)$

$P_2=\frac{P_1\times T_2}{T_1}$

Using the values

$$\begin{gathered} P_2=\frac{10atm\times 348K}{298K} \\ {P}_2=11.67atm \end{gathered}$$