If A Gas Has A Volume Of 10 L, A Pressure Of 1.5 Atm, And A Temperature Of 300 K, How Many Moles Of Gas Are Present? (Given: $ R = 0.0821 , \text{L} \cdot \text{atm} / \text{K} \cdot \text{mol} $)A. 0.61 Moles B. 0.62 Moles C. 0.63 Moles

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The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is a mathematical equation that relates the pressure, volume, and temperature of a gas to the number of moles of gas present. The ideal gas law is expressed by the equation:

PV = nRT

Where:

  • P is the pressure of the gas in atmospheres (atm)
  • V is the volume of the gas in liters (L)
  • n is the number of moles of gas present
  • R is the gas constant, which is a constant value that depends on the units used to express the variables in the equation
  • T is the temperature of the gas in Kelvin (K)

In this problem, we are given the following values:

  • V = 10 L
  • P = 1.5 atm
  • T = 300 K
  • R = 0.0821 L·atm/K·mol

We are asked to find the number of moles of gas present, which is represented by the variable n.

Solving for n

To solve for n, we can rearrange the ideal gas law equation to isolate n on one side of the equation. We can do this by dividing both sides of the equation by RT:

n = PV / RT

Now, we can plug in the given values for P, V, R, and T into this equation:

n = (1.5 atm)(10 L) / (0.0821 L·atm/K·mol)(300 K)

n = 0.61 mol

Therefore, the number of moles of gas present is 0.61 moles.

Discussion

The ideal gas law is a powerful tool for predicting the behavior of gases under various conditions. By using this equation, we can calculate the number of moles of gas present in a given volume and pressure, as well as the temperature of the gas. This is useful in a wide range of applications, from chemistry and physics to engineering and biology.

In this problem, we used the ideal gas law to calculate the number of moles of gas present in a given volume and pressure. We rearranged the equation to isolate n on one side, and then plugged in the given values to solve for n. This is a common technique used in chemistry and physics to solve problems involving the ideal gas law.

Conclusion

In conclusion, the ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. By using this equation, we can calculate the number of moles of gas present in a given volume and pressure, as well as the temperature of the gas. In this problem, we used the ideal gas law to calculate the number of moles of gas present, and found that the answer is 0.61 moles.

Additional Examples

Here are a few additional examples of how to use the ideal gas law to solve problems:

  • Example 1: A gas has a volume of 20 L, a pressure of 2 atm, and a temperature of 400 K. How many moles of gas are present?
  • Solution: Using the ideal gas law equation, we can plug in the given values to solve for n: n = (2 atm)(20 L) / (0.0821 L·atm/K·mol)(400 K) n = 0.98 mol
  • Example 2: A gas has a volume of 5 L, a pressure of 1 atm, and a temperature of 200 K. How many moles of gas are present?
  • Solution: Using the ideal gas law equation, we can plug in the given values to solve for n: n = (1 atm)(5 L) / (0.0821 L·atm/K·mol)(200 K) n = 0.15 mol

Q: What is the ideal gas law?

A: The ideal gas law is a mathematical equation that describes the behavior of gases under various conditions. It is expressed by the equation:

PV = nRT

Where:

  • P is the pressure of the gas in atmospheres (atm)
  • V is the volume of the gas in liters (L)
  • n is the number of moles of gas present
  • R is the gas constant, which is a constant value that depends on the units used to express the variables in the equation
  • T is the temperature of the gas in Kelvin (K)

Q: What is the gas constant (R)?

A: The gas constant (R) is a constant value that depends on the units used to express the variables in the ideal gas law equation. The value of R is typically given as 0.0821 L·atm/K·mol.

Q: How do I use the ideal gas law to solve problems?

A: To use the ideal gas law to solve problems, you can rearrange the equation to isolate the variable you are interested in. For example, if you want to find the number of moles of gas present (n), you can rearrange the equation to:

n = PV / RT

Then, you can plug in the given values for P, V, R, and T to solve for n.

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

A: The ideal gas law has many applications in chemistry, physics, engineering, and biology. Some common applications include:

  • Calculating the number of moles of gas present in a given volume and pressure
  • Determining the temperature of a gas in a given volume and pressure
  • Predicting the behavior of gases under various conditions
  • Designing and optimizing systems that involve gases, such as engines and refrigerators

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 correctly
  • Using the wrong value for the gas constant (R)
  • Failing to account for the effects of non-ideal behavior
  • Not checking the assumptions of the ideal gas law (e.g. that the gas is an ideal gas)

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 temperature of a gas in a car engine
  • Predicting the behavior of gases in a chemical reaction
  • Designing and optimizing systems that involve gases, such as air conditioning and refrigeration systems

Q: Can the ideal gas law be used to solve problems involving non-ideal gases?

A: The ideal gas law is a simplified model that assumes the gas is an ideal gas. However, many real-world gases do not behave ideally, and the ideal gas law may not accurately predict their behavior. In these cases, more complex models and equations of state may be needed to accurately predict the behavior of the gas.

Q: What are some common equations of state that are used to describe non-ideal gases?

A: Some common equations of state that are used to describe non-ideal gases include:

  • The van der Waals equation
  • The Redlich-Kwong equation
  • The Peng-Robinson equation
  • The Soave-Redlich-Kwong equation

These equations take into account the non-ideal behavior of the gas and can provide more accurate predictions of its behavior than the ideal gas law.