Ideal Gas Law: Pressure Calculation Examples

Understanding the Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that describes the relationship between pressure, volume, temperature, and the number of moles of a gas. It is expressed as:

\[ PV = nRT \]

Where:

• P = Pressure (in atmospheres or pascals)
• V = Volume (in liters)
• n = Number of moles of the gas
• R = Ideal gas constant (0.0821 L·atm/(K·mol) or 8.314 J/(K·mol))
• T = Temperature (in Kelvin)

In this article, we will look at three diverse examples of calculating pressure using the Ideal Gas Law, providing clear context and detailed explanations.

Example 1: Calculating Pressure of a Balloon

In a fun science experiment, you might want to know the pressure inside a balloon filled with helium. Let’s say the balloon has a volume of 3 liters, contains 0.2 moles of helium gas, and is at a temperature of 25°C.

To find the pressure, we first convert the temperature to Kelvin:

\[ T = 25 + 273.15 = 298.15 \, K \]

Now, we can apply the Ideal Gas Law:

\[ P = \frac{nRT}{V} \]

Substituting the known values:

• n = 0.2 moles
• R = 0.0821 L·atm/(K·mol)
• T = 298.15 K
• V = 3 L

\[ P = \frac{(0.2)(0.0821)(298.15)}{3} \approx 1.63 \, atm \]

This tells us that the pressure inside the balloon is approximately 1.63 atmospheres.

Notes:

• If the balloon were to be heated, the pressure would increase if the volume remains constant.
• If you used a different gas, ensure that you adjust the number of moles accordingly.

Example 2: Pressure in a Tire

Consider a scenario where you want to determine the pressure in a car tire. The tire has a volume of 30 liters, contains 0.5 moles of air, and the temperature is at a comfortable 20°C.

First, convert the temperature to Kelvin:

\[ T = 20 + 273.15 = 293.15 \, K \]

Using the Ideal Gas Law, we find the pressure:

\[ P = \frac{nRT}{V} \]

Substituting in the values:

• n = 0.5 moles
• R = 0.0821 L·atm/(K·mol)
• T = 293.15 K
• V = 30 L

\[ P = \frac{(0.5)(0.0821)(293.15)}{30} \approx 0.43 \, atm \]

This calculation indicates that the pressure in the tire is approximately 0.43 atmospheres, which is below the standard tire pressure.

Notes:

• Tire pressure is generally measured in psi (pounds per square inch), so you may need to convert atmospheres to psi for practical applications (1 atm ≈ 14.7 psi).
• Regular monitoring of tire pressure can improve fuel efficiency and safety.

Example 3: Gas Cylinder Pressure Calculation

In a laboratory setting, you might have a gas cylinder filled with nitrogen gas. If the cylinder has a volume of 50 liters, contains 4 moles of nitrogen, and is maintained at a temperature of 15°C, we can calculate the pressure.

Convert the temperature to Kelvin:

\[ T = 15 + 273.15 = 288.15 \, K \]

Now, applying the Ideal Gas Law:

\[ P = \frac{nRT}{V} \]

Using the provided information:

• n = 4 moles
• R = 0.0821 L·atm/(K·mol)
• T = 288.15 K
• V = 50 L

\[ P = \frac{(4)(0.0821)(288.15)}{50} \approx 2.29 \, atm \]

Thus, the pressure inside the gas cylinder is approximately 2.29 atmospheres.

Notes:

• Safety precautions should be taken when working with gas cylinders, as they can be under high pressure.
• The Ideal Gas Law assumes ideal behavior; real gases may deviate from this under high pressure or low temperature conditions.