The Ideal Gas Law is a fundamental principle in chemistry that describes the relationship between pressure, volume, temperature, and the amount of gas. It is expressed by the formula:
\[ PV = nRT \]
Where:
In this article, we will explore three practical examples of predicting gas behavior under varying conditions, which will help you understand the application of the Ideal Gas Law in real-world scenarios.
In this scenario, a balloon filled with helium gas is placed in an environment where the temperature changes. Understanding how the pressure inside the balloon changes with temperature is essential for applications in weather balloons and party decorations.
Assume the initial conditions of the balloon are:
To calculate the pressure when the temperature rises to 50°C (323 K), we can rearrange the Ideal Gas Law to solve for pressure:
\[ P = \frac{nRT}{V} \]
Substituting the values:
\[ P = \frac{0.08 \, \text{mol} \times 0.0821 \, \text{L·atm/(K·mol)} \times 323 \, ext{K}}{2.0 \, ext{L}} \]
\[ P \approx 1.01 \, ext{atm} \]
When the temperature increases, the pressure inside the balloon also increases, demonstrating how gas behavior changes with temperature.
This example illustrates how temperature affects gas pressure. If the volume of the balloon is kept constant, an increase in temperature will lead to an increase in pressure, adhering to Gay-Lussac’s Law.
In this example, we consider a sealed syringe containing air at room temperature. This scenario is particularly relevant in medical applications, such as administering injections or withdrawing fluids.
Assume the initial conditions are:
To find the new volume (V2) when the pressure doubles, we can apply Boyle’s Law, which states that pressure and volume are inversely proportional when temperature is held constant:
\[ P1V1 = P2V2 \]
Rearranging to find V2:
\[ V2 = \frac{P1V1}{P2} \]
Substituting the values:
\[ V2 = \frac{1 \, \text{atm} \times 10.0 \, \text{mL}}{2 \, \text{atm}} \]
\[ V2 = 5.0 \, \text{mL} \]
This calculation shows that as the pressure increases, the volume of the gas decreases, demonstrating the inverse relationship between pressure and volume.
This example highlights Boyle’s Law, which is a specific application of the Ideal Gas Law in constant temperature scenarios.
In this scenario, we will analyze a gas storage tank used in industrial applications, such as compressed natural gas (CNG) storage. Understanding how much gas can be stored under high pressure is critical for safety and efficiency.
Assume the following conditions for the gas in the tank:
To find the number of moles of gas in the tank, we can rearrange the Ideal Gas Law:
\[ n = \frac{PV}{RT} \]
Substituting the values:
\[ n = \frac{150 \, \text{atm} \times 50.0 \, \text{L}}{0.0821 \, \text{L·atm/(K·mol)} \times 298 \, ext{K}} \]
\[ n \approx 305.0 \, ext{moles} \]
This calculation indicates that approximately 305 moles of gas can be stored in the tank under high pressure.
This example demonstrates the application of the Ideal Gas Law in determining the amount of gas in a confined space, which is crucial for the design and safety of gas storage systems.