Ideal Gas Law Worksheet Answers Made Easy

Understanding the Ideal Gas Law

The ideal gas law is a fundamental concept in chemistry and physics that describes the behavior of gases. It is a mathematical equation that relates the pressure, volume, temperature, and number of moles of a gas. The ideal gas law is expressed as:

PV = nRT

Where:

• P is the pressure of the gas
• V is the volume of the gas
• n is the number of moles of the gas
• R is the gas constant
• T is the temperature of the gas in Kelvin

Breaking Down the Ideal Gas Law

To better understand the ideal gas law, let’s break it down into its individual components.

• Pressure (P): The pressure of a gas is the force exerted by the gas molecules on the walls of the container. It is typically measured in units of atmospheres (atm) or pascals (Pa).
• Volume (V): The volume of a gas is the amount of space occupied by the gas molecules. It is typically measured in units of liters (L) or cubic meters (m³).
• Number of Moles (n): The number of moles of a gas is a measure of the amount of gas present. It is defined as the ratio of the mass of the gas to its molar mass.
• Gas Constant ®: The gas constant is a universal constant that relates the pressure and volume of a gas to its temperature. It is typically expressed in units of joules per mole per kelvin (J/mol·K).
• Temperature (T): The temperature of a gas is a measure of the average kinetic energy of the gas molecules. It is typically measured in units of kelvin (K) or degrees Celsius (°C).

Using the Ideal Gas Law to Solve Problems

Now that we have a good understanding of the ideal gas law, let’s use it to solve some problems.

Problem 1: A gas cylinder contains 2.5 moles of oxygen at a pressure of 10 atm and a temperature of 300 K. What is the volume of the gas?

Solution: Rearrange the ideal gas law to solve for volume:

V = nRT / P

Plugging in the values, we get:

V = (2.5 mol)(0.0821 L·atm/mol·K)(300 K) / (10 atm) V = 6.15 L

Problem 2: A gas bubble has a volume of 500 mL at a pressure of 1 atm and a temperature of 25°C. What is the number of moles of gas present?

Solution: Rearrange the ideal gas law to solve for number of moles:

n = PV / RT

Plugging in the values, we get:

n = (1 atm)(0.5 L) / (0.0821 L·atm/mol·K)(298 K) n = 0.020 mol

Problem 3: A gas tank contains 5 moles of nitrogen at a pressure of 5 atm and a volume of 10 L. What is the temperature of the gas?

Solution: Rearrange the ideal gas law to solve for temperature:

T = PV / nR

Plugging in the values, we get:

T = (5 atm)(10 L) / (5 mol)(0.0821 L·atm/mol·K) T = 121 K

Important Notes

💡 Note: The ideal gas law is only applicable to ideal gases, which are hypothetical gases that obey the gas laws perfectly. Real gases deviate from ideal behavior due to intermolecular forces and other factors.

💡 Note: The gas constant R is not a universal constant, but rather a conversion factor that depends on the units used. Make sure to use the correct value of R for the units you are using.

Conclusion

The ideal gas law is a powerful tool for understanding the behavior of gases. By rearranging the equation and plugging in the values, we can solve a variety of problems involving pressure, volume, temperature, and number of moles. Remember to always use the correct units and to be mindful of the assumptions and limitations of the ideal gas law.

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