Gas Law Test Review Notes

Gas Law Test Review

I. Kinetic Molecular Theory (How Ideal Gases Behave)

• Gas Particles Do Not Attract or Repel: This implies that intermolecular forces are negligible in gas behavior, making them ideal gases under the right conditions.

• Gas Particles Have No Volume: This means that the actual volume occupied by gas particles is considered to be insignificant compared to the volume of the container.

• Kinetic Energy is Maintained During Elastic Collisions: Collisions between gas particles, or between gas particles and container walls, are elastic, indicating that there is no loss of kinetic energy in these collisions.

• Gas Particles are in Constant, Random Motion: This characteristic leads to the diffusion and mixing of gases, as particles do not have a fixed position.

• All Gases Have the Same Kinetic Energy at a Given Temperature: The average kinetic energy of gas particles is directly proportional to the temperature of the gas in Kelvin.

• Real Gases Behave More "Ideal" Under Low Pressures and High Temperatures: Under these conditions, the assumptions of the kinetic molecular theory hold more accurately, with minimized intermolecular forces and greater particle separation.

II. Gas Laws

• List the 4 Variables and Acceptable Units:

  • Temperature (K)

  • Pressure (atm, kPa, mmHg)

  • Volume (L, m³)

  • Amount of gas (n, in moles)

A. Boyle's Law

1. Temperature and Moles are Held Constant: This law applies when temperature and quantity of gas do not change.

2. Found Inverse Relationship Between Pressure and Volume: When the pressure increases on a gas, its volume decreases proportionally.

3. As Pressure Increases, Volume Decreases: Mathematically, this can be expressed as one variable increasing while the other decreases, such that: $P_1V_1 = P_2V_2$.

4. Why?: This occurs because gas particles are compressed, leading to more frequent collisions with container walls, thus increasing pressure.

5. Equation: $PV = ext{constant}$.

B. Charles's Law

1. Pressure and Moles are Held Constant: This law describes the relationship between volume and temperature when pressure and amount of gas remain unchanged.

2. Found Direct Relationship Between Volume and Temperature: As one increases, so does the other, resulting in a proportional increase.

3. As Temperature Increases, Volume Increases: This implies that heating a gas causes it to expand if pressure remains constant.

4. Why?: Increased temperature means greater kinetic energy, causing gas particles to occupy a larger volume.

5. Equation: $rac{V_1}{T_1} = rac{V_2}{T_2}$.

C. Gay-Lussac's Law

1. Volume and Moles are Held Constant: This law is applicable when only pressure and temperature change.

2. Found Direct Relationship Between Pressure and Temperature: As temperature rises, pressure also rises when the volume remains fixed.

3. As Temperature Increases, Pressure Increases: This means heating a gas at constant volume increases its pressure due to increased kinetic energy of particles.

4. Why?: Heated gas particles collide more often and with greater force against the container walls, increasing pressure.

5. Equation: $rac{P_1}{T_1} = rac{P_2}{T_2}$.

D. Avogadro's Principle

1. Equal Volumes of Gases at the Same Temperature and Pressure: This principle states that equal volumes of different gases contain the same number of particles when subjected to equal temperature and pressure.

2. Found Direct Relationship Between Moles and Volume: Increasing the number of moles of gas increases its volume at constant temperature and pressure.

3. As Moles Increase, Volume Increases: Thus, the volume occupied by a gas is directly proportional to the number of moles.

4. Why?: More gas particles lead to increased space needed to accommodate the particles at constant conditions.

5. Equation: $V ext{ is proportional to } n$, or more formally expressed as $V = kn$, where k is a constant.

E. The Combined Gas Law

1. Amount of Gas (Moles) Held Constant: This law unifies Boyle's, Charles's, and Gay-Lussac's laws into one equation.

2. Equation: $rac{P_1V_1}{T_1} = rac{P_2V_2}{T_2}$. This can be used to relate the pressure, volume, and temperature of a fixed amount of gas.

F. Conversion Factors

1. Molar Volume at STP: The molar volume of an ideal gas at standard temperature and pressure (STP) is $22.4 ext{ L/mol}$.

2. STP Temperature: Standard temperature is defined as $0 °C$ or $273 ext{ K}$.

3. Pressure Conversion: 1 atm is equivalent to:

   • $101.3 ext{ kPa}$

   • $760 ext{ mmHg}$

   • $760 ext{ torr}$

4. Gas Constant (R): Different values for R depending on the units used:

   • $R = 0.08206 rac{ ext{L} imes ext{atm}}{ ext{K} imes ext{mol}}$ when using atmospheres.

   • $R = 8.314 rac{ ext{J}}{ ext{K} imes ext{mol}}$ or when pressure is in kPa.

5. 760 torr is equivalent to 1 atm.

G. The Ideal Gas Law

1. Equation: The ideal gas law is represented as $PV = nRT$, where n is the number of moles and R is the ideal gas constant.

2. When to Use This: Applicable when the gas is not at standard temperature and pressure (not STP). This equation describes the state of an ideal gas.

H. Dalton's Law of Partial Pressure

1. Where: This law states that in a mixture of non-reacting gases, each gas exerts pressure independently of the others.

2. Equation: The total pressure is given by: $P_T = P_1 + P_2 + P_3 + ext{…}$, where each pressure must be in the same units.

3. When to Use This: Useful when calculating the total pressure in a system of gases, allowing for the understanding of how different gas pressures contribute to the overall pressure in a mixture.