Gas law

• Gas Laws


  Relationships between volume, pressure, and temperature of gases
• Investigate the relationship between:

  1. Volume and pressure at constant temperature of a gas

  2. Volume and temperature at constant pressure of a gas

  3. Explains these relationships using kinetic molecular theory
• Kinetic Molecular Theory


  Theory that explains the behavior of gases
• States of Matter


  • 2 main factors determine state: The forces (inter/intramolecular) holding particles together, The kinetic energy present (the energy an object possesses due to its motion of the particles)
  • KE tends to 'pull' particles apart
• Properties of Gases


  • Expand to fill any container
  • Random motion, no attraction
  • Fluids (like liquids), no attraction
  • Very low densities, no volume = lots of empty space
  • Can be compressed, no volume = lots of empty space
  • Undergo diffusion & effusion (across a barrier with small holes), random motion
• Kinetic Molecular Theory


  • Gases consists of tiny molecules
  • There is no force of attraction between and among gas molecules
  • Gas molecules are constant, random, and straight line motion
  • The average KE for molecules is the same for all gases at the same temperature, and its value is directly proportional to the K temperature
• Gases have a higher kinetic energy


  Because their particles move a lot more than in a solid or a liquid
• As the temperature increases


  Gas particles move faster, and thus kinetic energy increases
• Kinetic Molecular Theory (KMT)


  Attempts to explain the properties of gases such as pressure, temperature, or volume, by looking at what they are made up of and how they move
• Kinetic


  Refers to motion
• Kinetic energy


  The energy an object has because of its motion
• Main components of kinetic theory

  • Perfectly elastic collisions, no energy is gained or lost when gas molecules collide
  • Gas molecules take up no space they are so small
  • Gas molecules are in constant, linear, random motion
• How does Kinetic Theory explain Gas Pressure?

  1. Gas Pressure results from fast moving gas particles colliding with the sides of a container

  2. More Collisions = Higher Pressure
• Temperature


  • Is a measure of the average kinetic energy of all the particles in a gas
  • Higher Energy = Higher Temperature
• Basic Laws developed through KMT

  • Boyle's Law
  • Charles' Law
  • Gay-Lussac's Law
  • Avogadro's Law
  • Ideal Gas Law – volume liters only
  • Dalton's Law
• Units used to describe gas samples


  • Volume: Liter (L), Milliliter (mL)
  • Temperature: Kelvin (K)
  • Pressure: Atmosphere (atm), Kilopascale (kPa), Torr (torr), mm of mercury (mm Hg)
• Standard Temperature and Pressure (STP)

  Standard Temperature = 273K, Standard Pressure = 1 atm
• Robert Boyle first observed the relationship between pressure and volume of a gas

  1662
• Boyle's Law


  At constant temperature, the volume of the gas increases as the pressure decreases (and the volume of the gas decreases and the pressure increases). They are inversely related.
• Boyle's Law


  1. P1V1 = P2V2

  2. Volume ↑ Pressure ↓

  3. If you squeeze a gas sample, you make its volume smaller
• When volume decreases


  Rate of collisions increases and pressure increases
• When volume increases


  Rate of collisions decreases and pressure decreases
• If you want to decrease the volume of nitrogen gas inside a cylinder, you increase the pressure
• Boyle's Law Example


  1. P1V1 = P2V2

  2. 2.00L x 740.0 mmHg = 760.0 mm Hg x V2

  3. V2 = 1.95 L
• Boyle's Law Problems


  • 2.00 L of a gas is at 740.0 mmHg pressure. What is its volume at 760.0 mmHg pressure?
  • A sample gas occupies a volume of 145 mL at 560 torr and 20 degrees Celsius. Calculate the new pressure if its volume is increased to 290 mL at constant temperature.
  • A gas occupies 12.3 liters at a pressure of 40.0 mmHg. What is the volume when the pressure is increased to 60.0 mmHg?
  • If a gas at 25.0 °C occupies 3.60 liters at a pressure of 1.00 atm, what will be its volume at a pressure of 2.50 atm?
  • To what pressure must a gas be compressed in order to get into a 3.00 cubic foot tank the entire weight of a gas that occupies 400.0 cu. ft. at standard pressure?
  • A gas occupies 1.56 L at 1.00 atm. What will be the volume of this gas if the pressure becomes 3.00 atm?
  • A gas occupies 11.2 liters at 0.860 atm. What is the pressure if the volume becomes 15.0 L?
  • 500.0 mL of a gas is collected at 745.0 mmHg. What will the volume be at standard pressure?
  • When the pressure on a gas increases, will the volume increase or decrease?
  • 10. If the pressure on a gas is decreased by one-half, how large will the volume change be?
• French physicist Jacques Charles observed the effect of temperature on the volume of a gas

  1787
• Charles' Law


  At a constant pressure, the volume of a gas increases as the temperature of the gas increases (and the volume decreases when the temperature decreases). They are directly related.
• Charles' Law


  1. V1/T1 = V2/T2

  2. V1T2 = V2T1

  3. Increasing the temperature of a gas increases the speed of gas particles which collide more often and with more force causing the walls of a flexible container expand.
• Charles' Law Problems


  • Three liters of hydrogen at 20˚C is allowed to warm to 27˚C . What is the volume if the pressure remains constant?
  • Carbon dioxide is usually formed when gasoline is burned. If 30.0 L of CO2 is produced at a temperature of 1.00 x 103 °C and allowed to reach room temperature (25.0 °C) without any pressure changes, what is the new volume of the carbon dioxide?
  • A 600.0 mL sample of nitrogen is warmed from 77.0 °C to 86.0 °C. Find its new volume if the pressure remains constant.
  • What volume change occurs to a 400.0 mL gas sample as the temperature increases from 22.0 °C to 30.0 °C?
  • A gas syringe contains 56.05 milliliters of a gas at 315.1 K. Determine the volume that the gas will occupy if the temperature is increased to 380.5 K
  • When 50.0 liters of oxygen at 20.0 °C is compressed to 5.00 liters, what must the new temperature be to maintain constant pressure?
  • If 15.0 liters of neon at 25.0 °C is allowed to expand to 45.0 liters, what must the new temperature be to maintain constant pressure?
  • 3.50 liters of a gas at 727.0 K will occupy how many liters at 153.0 K?
  • When the temperature of a gas decreases (with pressure and amount held constant), does the volume increase or decrease?
  • 10. If the Kelvin temperature of a gas is doubled, the volume of the gas will increase by ____.
• Joseph Louis Gay-Lussac proposed the relationship between temperature and pressure


  1802
• Gay-Lussac's Law


  At a constant volume, the pressure of a gas increases as the temperature of the gas increases (and the pressure decreases when the temperature decreases). They are directly related.
• If the temperature is increased

  The KE of the molecules will increase, as will the pressure since the volume occupied by the gas is constant
• Charle's Law


  Relationship between temperature and volume of a gas at constant pressure
• Charle's Law Problems


  1. If 15.0 liters of neon at 25.0 °C is allowed to expand to 45.0 liters, what must the new temperature be to maintain constant pressure?

  2. 3.50 liters of a gas at 727.0 K will occupy how many liters at 153.0 K?

  3. When the temperature of a gas decreases (with pressure and amount held constant), does the volume increase or decrease?

  4. If the Kelvin temperature of a gas is doubled, the volume of the gas will increase by ____.
• In 1802, Joseph Louis Gay-Lussac proposed the relationship between temperature and pressure
• Kinetic molecular theory


  If the temperature is increased, the KE of the molecules will increase, as will the pressure since the volume occupied by the gas is constant
• Gay-Lussac's Law


  • Pressurized can, such as one that contains hair spray, deodorant, or insecticide
• When you climb a mountain


  Changes in pressure and temperature
• • Steel cylinder (2L) contains 500 molecules of O2 at 400 K
  • Steel cylinder (2L) contains 500 molecules of O2 at 800 K
• Average kinetic energy


  Higher at 800 K