Determine the Number of Moles of Air Present in a Given Volume

Oct 13, 2025 by recoveryshake.com 75 views

Determine the Number of Moles of Air Present in a Given Volume

Understanding the Ideal Gas Law

The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is expressed by the formula: 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, and T is the temperature of the gas in Kelvin. In this article, we will use the ideal gas law to determine the number of moles of air present in a given volume.

Given Conditions

We are given the following conditions:

Volume (V) = 1.35 L
Pressure (P) = 750 torr
Temperature (T) = 17.0°C

Converting Temperature to Kelvin

Before we can use the ideal gas law, we need to convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is: T(K) = T(°C) + 273.15. Therefore, the temperature in Kelvin is:

T(K) = 17.0°C + 273.15 = 290.15 K

Choosing the Correct Equation

The ideal gas law formula is: PV = nRT. However, we are given the pressure in torr, which is not the standard unit of pressure. Therefore, we need to convert the pressure from torr to atm. The conversion factor is: 1 atm = 760 torr. Therefore, the pressure in atm is:

P(atm) = 750 torr / 760 torr/atm = 0.987 atm

Using the Ideal Gas Law

Now that we have the pressure in atm, we can use the ideal gas law to determine the number of moles of air present in the given volume. Rearranging the ideal gas law formula to solve for n, we get:

n = PV / RT

Substituting the given values, we get:

n = (0.987 atm)(1.35 L) / (62.396 L·torr/mol·K)(290.15 K)

Calculating the Number of Moles

Now, we can calculate the number of moles of air present in the given volume:

n = (0.987 atm)(1.35 L) / (62.396 L·torr/mol·K)(290.15 K) n = 0.00551 mol

Conclusion

In this article, we used the ideal gas law to determine the number of moles of air present in a given volume. We converted the temperature from Celsius to Kelvin and the pressure from torr to atm. We then used the ideal gas law formula to calculate the number of moles of air present in the given volume. The result is 0.00551 mol.

Understanding the Significance of the Result

The result of 0.00551 mol represents the number of moles of air present in a volume of 1.35 L at a pressure of 750 torr and a temperature of 17.0°C. This result can be used to understand the behavior of gases under various conditions and to make predictions about the behavior of gases in different situations.

Real-World Applications

The ideal gas law has many real-world applications, including:

Calculating the volume of a gas in a container
Determining the number of moles of a gas present in a container
Understanding the behavior of gases under various conditions
Making predictions about the behavior of gases in different situations

Conclusion

In conclusion, the ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. We used the ideal gas law to determine the number of moles of air present in a given volume. The result is 0.00551 mol. This result can be used to understand the behavior of gases under various conditions and to make predictions about the behavior of gases in different situations.
Frequently Asked Questions (FAQs) About the Ideal Gas Law

Q: What is the ideal gas law?

A: The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is expressed by the formula: 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, and T is the temperature of the gas in Kelvin.

Q: What are the units of the ideal gas law?

A: The units of the ideal gas law are:

Pressure (P): atm or torr
Volume (V): L
Number of moles (n): mol
Gas constant (R): L·torr/mol·K
Temperature (T): K

Q: How do I convert temperature from Celsius to Kelvin?

A: To convert temperature from Celsius to Kelvin, you can use the following formula: T(K) = T(°C) + 273.15.

Q: How do I convert pressure from torr to atm?

A: To convert pressure from torr to atm, you can use the following conversion factor: 1 atm = 760 torr.

Q: What is the gas constant (R)?

A: The gas constant (R) is a constant that relates the pressure, volume, and temperature of a gas. It is equal to 62.396 L·torr/mol·K.

Q: How do I use the ideal gas law to calculate the number of moles of a gas?

A: To use the ideal gas law to calculate the number of moles of a gas, you can rearrange the formula to solve for n: n = PV / RT.

Q: What are some real-world applications of the ideal gas law?

A: Some real-world applications of the ideal gas law include:

Calculating the volume of a gas in a container
Determining the number of moles of a gas present in a container
Understanding the behavior of gases under various conditions
Making predictions about the behavior of gases in different situations

Q: What are some common mistakes to avoid when using the ideal gas law?

A: Some common mistakes to avoid when using the ideal gas law include:

Not converting temperature from Celsius to Kelvin
Not converting pressure from torr to atm
Not using the correct units for the gas constant (R)
Not rearranging the formula to solve for the correct variable

Q: How do I troubleshoot common errors when using the ideal gas law?

A: To troubleshoot common errors when using the ideal gas law, you can:

Check your units to ensure that they are correct
Double-check your calculations to ensure that they are correct
Use a calculator or computer program to check your calculations
Consult a reference book or online resource for help

Conclusion

In conclusion, the ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. By understanding the ideal gas law and how to use it, you can calculate the number of moles of a gas present in a container, determine the volume of a gas in a container, and make predictions about the behavior of gases in different situations.