Question

A tank contains isoflurane, an inhaled anesthetic, at a pressure of $1.8atm$and $5°C$. What is the pressure, in atmospheres, if the gas is warmed to a temperature of$22°C$, if$V,n$do not change?

Short answer

The final pressure of the gas is$1.9atm$.

Step-by-step solution

Given Information 

We need to find the final temperature of the gas.

Simplify

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.

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

Calculation

Here we have the quantities available, that is

the initial temperature $T_1=5°C=\left(5+273\right)K=278K$

initial pressure$P_1=1.8atm$

the final temperature$T_2=22°C=\left(22+273\right)K=295K$

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

$$\begin{gathered} \frac{P_1}{T_1}=\frac{P_2}{T_2} \\ {P}_2=\frac{P_1\times T_2}{T_1} \end{gathered}$$

Putting the values:

$$\begin{gathered} P_2=\frac{1.8atm\times 295K}{278K} \\ {P}_2=\frac{531atm}{278} \\ =1.9atm \end{gathered}$$

The final pressure is $1.9atm$.