Gas Laws Fact Sheet

[tex]\[

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

\hline

\text{Ideal gas law} & P V = n R T \\

\hline

\multirow{3}{*}{\text{Ideal gas constant}} & R = 8.314 \frac{\text{J}}{\text{mol K}} \\

\hline

& \text{or} \\

& R = 0.0821 \frac{\text{L atm}}{\text{mol K}} \\

\hline

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

\hline

\text{Celsius to Kelvin conversion} & K = ^{\circ}\text{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]

To solve for the gauge pressure inside the container, we need to understand the difference between absolute pressure and gauge pressure.

1. Understand the Terms:
- Absolute Pressure: This is the total pressure exerted by the gas, including atmospheric pressure. In this problem, it's given as 125.4 kilopascals (kPa).
- Atmospheric Pressure: This is the pressure of the air outside the container, provided as 99.8 kPa.
- Gauge Pressure: This is the pressure of the gas inside the container relative to the atmospheric pressure. It is the pressure reading typically shown on a pressure gauge.

2. Calculate Gauge Pressure:
- The formula to calculate gauge pressure is:
[tex]\[
\text{Gauge Pressure} = \text{Absolute Pressure} - \text{Atmospheric Pressure}
\][/tex]
- Plug in the provided values:
[tex]\[
\text{Gauge Pressure} = 125.4 \, \text{kPa} - 99.8 \, \text{kPa} = 25.6 \, \text{kPa}
\][/tex]

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

Therefore, the correct answer is:
C. [tex]\(25.6 \, \text{kPa}\)[/tex]