Gas Laws Fact Sheet

[tex]\[

\begin{tabular}{|l|l|}

\hline

Ideal gas law & $P V = n R T$ \\

\hline

Ideal gas constant &

\begin{tabular}{l}

$R = 8.314$ \\

or \\

$R = 0.0821$ \\

\end{tabular} \\

\hline

Standard atmospheric pressure & $1 \, \text{atm} = 101.3 \, \text{kPa}$ \\

\hline

Celsius to Kelvin conversion & $K = ^{\circ} C + 273.15$ \\

\hline

\end{tabular}

\][/tex]

Select the correct answer.

The gas in a sealed container has an absolute pressure of 125.4 kilopascals. If the air around the container is at a pressure of 99.8 kilopascals, what is the gauge pressure inside the container?

A. [tex]$1.5 \, \text{kPa}$[/tex]
B. [tex]$24.1 \, \text{kPa}$[/tex]
C. [tex]$25.6 \, \text{kPa}$[/tex]
D. [tex]$112.6 \, \text{kPa}$[/tex]

To solve the problem of finding the gauge pressure inside the container, follow these steps:

1. Understand the Definitions:
- Absolute Pressure: This is the total pressure inside the container, including atmospheric pressure.
- Atmospheric Pressure: This is the pressure exerted by the surrounding air on the outside of the container.
- Gauge Pressure: This is the pressure inside the container relative to the atmospheric pressure. It measures the difference between absolute pressure and atmospheric pressure.

2. Given Values:
- The absolute pressure inside the container is 125.4 kilopascals (kPa).
- The atmospheric pressure around the container is 99.8 kilopascals (kPa).

3. Calculate the Gauge Pressure:
- Use the formula for gauge pressure:
[tex]\[
\text{Gauge Pressure} = \text{Absolute Pressure} - \text{Atmospheric Pressure}
\][/tex]
- Substitute the given values:
[tex]\[
\text{Gauge Pressure} = 125.4\, \text{kPa} - 99.8\, \text{kPa}
\][/tex]
- Calculate the result:
[tex]\[
\text{Gauge Pressure} = 25.6\, \text{kPa}
\][/tex]

4. Conclusion:
- The gauge pressure inside the container is 25.6 kPa.

Therefore, the correct answer is C. 25.6 kPa.