\begin{tabular}{|l|l|}
\hline
& [tex]$R=0.0821 \frac{L \cdot atm}{mol \cdot K}$[/tex] \\
\hline
Standard atmospheric pressure & [tex]$1 atm = 101.3 kPa$[/tex] \\
\hline
\end{tabular}

The gas in a sealed container has an absolute pressure of 9.25 atmospheres. If the air around the container is at standard pressure, what is the gauge pressure inside the container?

A. 0.759 atm
B. 8.25 atm
C. 10.25 atm



Answer :

To determine the gauge pressure inside the container, first understand the difference between absolute pressure and gauge pressure.

1. Absolute Pressure: This is the total pressure exerted on the walls of a container, including atmospheric pressure. Here, the absolute pressure in the sealed container is given as [tex]\( 9.25 \)[/tex] atmospheres.

2. Standard Atmospheric Pressure: This is the average pressure exerted by the earth's atmosphere at sea level, which is given as [tex]\( 1 \)[/tex] atmosphere.

3. Gauge Pressure: This is the pressure relative to the atmospheric pressure. It can be calculated by subtracting the atmospheric pressure from the absolute pressure.

Formally, the relationship can be written as:
[tex]\[ \text{Gauge Pressure} = \text{Absolute Pressure} - \text{Atmospheric Pressure} \][/tex]

Given:
[tex]\[ \text{Absolute Pressure} = 9.25 \, \text{atm} \][/tex]
[tex]\[ \text{Atmospheric Pressure} = 1 \, \text{atm} \][/tex]

Now, substitute the given values into the equation:
[tex]\[ \text{Gauge Pressure} = 9.25 \, \text{atm} - 1 \, \text{atm} \][/tex]

Perform the subtraction:
[tex]\[ \text{Gauge Pressure} = 9.25 \, \text{atm} - 1 \, \text{atm} = 8.25 \, \text{atm} \][/tex]

The gauge pressure inside the container is [tex]\( \boxed{8.25 \, \text{atm}} \)[/tex].

Therefore, the correct answer is:
[tex]\[ \mathbf{B. \, 8.25 \, \text{atm}} \][/tex]