How Many Liters Are In A Bag That Holds 5.0 Moles? Another Bag That Holds 45 Liters And 7.9 Moles Of Gas Is At The Same Temperature And Pressure.Before Solving:a. Which Variables Are Changing?b. What Is The Relationship Between Those Variables?

by ADMIN 245 views

1. How many liters are in a bag that holds 5.0 moles? Another bag that holds 45 liters and 7.9 moles of gas is at the same temperature and pressure.

Understanding the Problem

To solve this problem, we need to understand the relationship between the number of moles of a gas and the volume of the gas at a given temperature and pressure. The ideal gas law is a fundamental concept in chemistry that describes this relationship.

The Ideal Gas Law

The ideal gas law is given by the equation:

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

Identifying the Variables

Let's identify the variables that are changing in this problem:

  • The number of moles of gas (n) is changing in both bags.
  • The volume of gas (V) is changing in the first bag.
  • The number of moles of gas (n) and the volume of gas (V) are changing in the second bag.

The Relationship Between the Variables

The ideal gas law tells us that at a given temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas. This means that if the number of moles of a gas increases, the volume of the gas will also increase, assuming the temperature and pressure remain constant.

Solving the Problem

We are given that the second bag holds 45 liters and 7.9 moles of gas at the same temperature and pressure as the first bag. We can use the ideal gas law to find the number of moles of gas in the first bag.

Let's rearrange the ideal gas law to solve for n:

n = PV / RT

We know that the pressure (P) and temperature (T) are the same for both bags, so we can set up a proportion:

n1 / V1 = n2 / V2

Where n1 and V1 are the number of moles and volume of the first bag, and n2 and V2 are the number of moles and volume of the second bag.

a. Which variables are changing?

The variables that are changing are:

  • The number of moles of gas (n)
  • The volume of gas (V)

b. What is the relationship between those variables?

The relationship between the variables is that the volume of a gas is directly proportional to the number of moles of the gas at a given temperature and pressure.

Calculating the Number of Moles in the First Bag

We can now use the proportion to find the number of moles of gas in the first bag:

n1 / 45 = 7.9 / V1

We are given that the first bag holds 5.0 moles of gas, so we can substitute this value into the equation:

5.0 / 45 = 7.9 / V1

To solve for V1, we can cross-multiply:

5.0V1 = 45(7.9)

V1 = (45(7.9)) / 5.0

V1 = 70.5

So the first bag holds 70.5 liters of gas.

Conclusion

In this problem, we used the ideal gas law to find the number of moles of gas in a bag that holds 5.0 moles. We also used the ideal gas law to find the volume of gas in a bag that holds 45 liters and 7.9 moles of gas at the same temperature and pressure. The relationship between the variables is that the volume of a gas is directly proportional to the number of moles of the gas at a given temperature and pressure.

Discussion

This problem illustrates the importance of understanding the relationship between the number of moles of a gas and the volume of the gas at a given temperature and pressure. The ideal gas law is a fundamental concept in chemistry that describes this relationship.

Key Takeaways

  • The ideal gas law is given by the equation PV = nRT.
  • The volume of a gas is directly proportional to the number of moles of the gas at a given temperature and pressure.
  • The ideal gas law can be used to find the number of moles of gas in a bag given the volume of the gas and the temperature and pressure.
  • The ideal gas law can be used to find the volume of gas in a bag given the number of moles of gas and the temperature and pressure.

References

  • Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
  • Chang, R. (2010). Physical chemistry for the life sciences. W.H. Freeman and Company.

Further Reading

  • For a more detailed discussion of the ideal gas law, see Atkins and de Paula (2010).
  • For a more detailed discussion of the relationship between the number of moles of a gas and the volume of the gas, see Chang (2010).

Related Topics

  • The ideal gas law
  • The relationship between the number of moles of a gas and the volume of the gas
  • The importance of understanding the ideal gas law in chemistry

Keywords

  • Ideal gas law
  • Number of moles
  • Volume of gas
  • Temperature
  • Pressure
  • Chemistry
    Q&A: Understanding 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 relationship between the number of moles of a gas, the volume of the gas, the temperature, and the pressure. It is given by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

Q: What is the relationship between the number of moles of a gas and the volume of the gas?

A: The volume of a gas is directly proportional to the number of moles of the gas at a given temperature and pressure. This means that if the number of moles of a gas increases, the volume of the gas will also increase, assuming the temperature and pressure remain constant.

Q: How can I use the ideal gas law to find the number of moles of a gas?

A: To find the number of moles of a gas, you can rearrange the ideal gas law to solve for n: n = PV / RT. You will need to know the pressure, volume, and temperature of the gas, as well as the gas constant.

Q: How can I use the ideal gas law to find the volume of a gas?

A: To find the volume of a gas, you can rearrange the ideal gas law to solve for V: V = nRT / P. You will need to know the number of moles, temperature, and pressure of the gas, as well as the gas constant.

Q: What is the significance of the gas constant (R)?

A: The gas constant (R) is a fundamental constant in chemistry that relates the number of moles of a gas to the volume of the gas at a given temperature and pressure. It is a critical component of the ideal gas law and is used to calculate the number of moles of a gas or the volume of a gas.

Q: What are some common applications of the ideal gas law?

A: The ideal gas law has numerous applications in chemistry, including:

  • Calculating the number of moles of a gas in a container
  • Determining the volume of a gas in a container
  • Understanding the behavior of gases in chemical reactions
  • Calculating the pressure of a gas in a container
  • Understanding the relationship between temperature and pressure in gases

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:

  • Failing to convert units of temperature and pressure to the correct units
  • Failing to use the correct value of the gas constant (R)
  • Failing to account for the effects of non-ideal behavior in gases
  • Failing to consider the effects of temperature and pressure on the behavior of gases

Q: What are some real-world examples of the ideal gas law in action?

A: Some real-world examples of the ideal gas law in action include:

  • Calculating the number of moles of oxygen in a scuba tank
  • Determining the volume of a gas in a balloon
  • Understanding the behavior of gases in chemical reactions, such as combustion reactions
  • Calculating the pressure of a gas in a container, such as a tire
  • Understanding the relationship between temperature and pressure in gases, such as in a refrigerator or air conditioner.

Q: How can I learn more about the ideal gas law and its applications?

A: You can learn more about the ideal gas law and its applications by:

  • Reading chemistry textbooks and online resources
  • Taking chemistry courses or online tutorials
  • Practicing problems and exercises to reinforce your understanding
  • Consulting with chemistry experts or professionals
  • Conducting experiments and investigations to explore the behavior of gases.

Keywords

  • Ideal gas law
  • Number of moles
  • Volume of gas
  • Temperature
  • Pressure
  • Chemistry
  • Gas constant
  • Non-ideal behavior
  • Real-world applications