ACTIVITY 5 - According To The LawRead Each Problem Carefully And Answer It According To The Gas Laws Being Discussed. Show Your Complete Solution. Express The Units In Standard Form.1. A Sample Of Helium Gas Has A Volume Of 0.250 L At 800 Torr. If The

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Understanding the Gas Laws

In this activity, we will apply the gas laws to solve problems related to the behavior of gases. The gas laws are a set of principles that describe the relationships between the pressure, volume, and temperature of a gas. These laws are essential in understanding various chemical and physical phenomena involving gases.

Problem 1: Applying Boyle's Law

Problem Statement

A sample of helium gas has a volume of 0.250 L at 800 torr. If the pressure is increased to 1200 torr, what is the new volume of the gas?

Solution

To solve this problem, we will use Boyle's Law, which states that the volume of a gas is inversely proportional to the pressure at a constant temperature. Mathematically, this can be expressed as:

P1V1 = P2V2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Given values:

P1 = 800 torr V1 = 0.250 L P2 = 1200 torr V2 = ?

Rearranging the equation to solve for V2, we get:

V2 = P1V1 / P2

Substituting the given values, we get:

V2 = (800 torr)(0.250 L) / (1200 torr) V2 = 0.167 L

Therefore, the new volume of the gas is 0.167 L.

Units

The units of volume are in liters (L), and the units of pressure are in torr.

Conclusion

In this problem, we applied Boyle's Law to find the new volume of a gas when the pressure is increased. The law states that the volume of a gas is inversely proportional to the pressure at a constant temperature.

Problem 2: Applying Charles' Law

Problem Statement

A sample of oxygen gas has a volume of 2.00 L at 20°C. If the temperature is increased to 50°C, what is the new volume of the gas?

Solution

To solve this problem, we will use Charles' Law, which states that the volume of a gas is directly proportional to the temperature at a constant pressure. Mathematically, this can be expressed as:

V1 / T1 = V2 / T2

where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.

Given values:

V1 = 2.00 L T1 = 20°C + 273 = 293 K T2 = 50°C + 273 = 323 K V2 = ?

Rearranging the equation to solve for V2, we get:

V2 = V1T2 / T1

Substituting the given values, we get:

V2 = (2.00 L)(323 K) / (293 K) V2 = 2.21 L

Therefore, the new volume of the gas is 2.21 L.

Units

The units of volume are in liters (L), and the units of temperature are in Kelvin (K).

Conclusion

In this problem, we applied Charles' Law to find the new volume of a gas when the temperature is increased. The law states that the volume of a gas is directly proportional to the temperature at a constant pressure.

Problem 3: Applying Avogadro's Law

Problem Statement

A sample of nitrogen gas has a volume of 1.00 L at STP (Standard Temperature and Pressure). If the number of moles of gas is doubled, what is the new volume of the gas?

Solution

To solve this problem, we will use Avogadro's Law, which states that equal volumes of gases at the same temperature and pressure contain an equal number of moles. Mathematically, this can be expressed as:

V1 / n1 = V2 / n2

where V1 and n1 are the initial volume and number of moles, and V2 and n2 are the final volume and number of moles.

Given values:

V1 = 1.00 L n1 = 1 mole n2 = 2 moles V2 = ?

Rearranging the equation to solve for V2, we get:

V2 = V1n2 / n1

Substituting the given values, we get:

V2 = (1.00 L)(2 moles) / (1 mole) V2 = 2.00 L

Therefore, the new volume of the gas is 2.00 L.

Units

The units of volume are in liters (L), and the units of number of moles are in moles.

Conclusion

In this problem, we applied Avogadro's Law to find the new volume of a gas when the number of moles is doubled. The law states that equal volumes of gases at the same temperature and pressure contain an equal number of moles.

Problem 4: Applying the Ideal Gas Law

Problem Statement

A sample of carbon dioxide gas has a volume of 3.00 L at 25°C and 1.00 atm. If the temperature is increased to 50°C and the pressure is increased to 2.00 atm, what is the new volume of the gas?

Solution

To solve this problem, we will use the Ideal Gas Law, which states that the volume of a gas is directly proportional to the temperature and inversely proportional to the pressure. Mathematically, this can be expressed as:

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.

Given values:

P1 = 1.00 atm V1 = 3.00 L T1 = 25°C + 273 = 298 K P2 = 2.00 atm T2 = 50°C + 273 = 323 K V2 = ?

Rearranging the equation to solve for V2, we get:

V2 = P1V1T2 / (P2T1)

Substituting the given values, we get:

V2 = (1.00 atm)(3.00 L)(323 K) / ((2.00 atm)(298 K)) V2 = 3.45 L

Therefore, the new volume of the gas is 3.45 L.

Units

The units of volume are in liters (L), the units of pressure are in atmospheres (atm), and the units of temperature are in Kelvin (K).

Conclusion

In this problem, we applied the Ideal Gas Law to find the new volume of a gas when the temperature and pressure are increased. The law states that the volume of a gas is directly proportional to the temperature and inversely proportional to the pressure.

Conclusion

Frequently Asked Questions

In this article, we will answer some frequently asked questions related to the gas laws.

Q: What is the difference between Boyle's Law and Charles' Law?

A: Boyle's Law states that the volume of a gas is inversely proportional to the pressure at a constant temperature. Charles' Law states that the volume of a gas is directly proportional to the temperature at a constant pressure.

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

A: According to Avogadro's Law, equal volumes of gases at the same temperature and pressure contain an equal number of moles.

Q: What is the Ideal Gas Law?

A: The Ideal Gas Law is a mathematical equation that describes the behavior of an ideal gas. It states that the volume of a gas is directly proportional to the temperature and inversely proportional to the pressure.

Q: What are the units of measurement for the gas laws?

A: The units of measurement for the gas laws are:

  • Volume: liters (L)
  • Pressure: atmospheres (atm), pascals (Pa), or torr
  • Temperature: Kelvin (K), Celsius (°C), or Fahrenheit (°F)
  • Number of moles: moles (mol)

Q: How do the gas laws apply to real-world situations?

A: The gas laws apply to a wide range of real-world situations, including:

  • Scuba diving: The pressure of the surrounding water affects the volume of the air in a scuba tank.
  • Weather forecasting: Changes in temperature and pressure can affect the volume of air in the atmosphere.
  • Industrial processes: The gas laws are used to design and operate industrial processes, such as chemical reactions and gas separation.

Q: What are some common applications of the gas laws?

A: Some common applications of the gas laws include:

  • Air conditioning and refrigeration: The gas laws are used to design and operate air conditioning and refrigeration systems.
  • Gas turbines: The gas laws are used to design and operate gas turbines, which are used to generate electricity.
  • Medical equipment: The gas laws are used to design and operate medical equipment, such as ventilators and anesthesia machines.

Q: How can I apply the gas laws in my daily life?

A: You can apply the gas laws in your daily life by:

  • Understanding the behavior of gases in different situations
  • Using the gas laws to design and operate systems that involve gases
  • Recognizing the importance of the gas laws in various industries and applications

Conclusion

In this article, we have answered some frequently asked questions related to the gas laws. We hope that this information has been helpful in understanding the gas laws and their applications.