Gases Chapter 10

Review Temperature Pressure Volume Number of Moles, n Average kinetic energy Pressure Collisions of gas particles between each other and container walls Volume Amount of space Number of Moles, n

Review Boyle’s Law Charles’s Law Gay-Lussac’s Law Avogadro’s Law

Boyle’s Law V P Inverse

Charles’s Law T V Direct

Gay-Lussac's Law T P Direct

Avogadro’s Law n V Direct

Kinetic Molecular Theory The particles in a gas are constantly moving in rapid, random, straight-line motion. Gas particles have no volume compared to the volume of the gas. No attraction between particles All collisions are completely elastic

All Together Now Constant If we add Avogadro’s Law into the Combined Gas Law: Constant

Ideal Gas Law PV = nRT R = Universal Gas Constant Ideal Gases follow assumptions of the Kinetic Molecular Theory

Ideal Gases When do real gases act most like an ideal gas? High Temperature Low Pressure When do real gases act least like an ideal gas? Low Temperature High Pressure

Units of Pressure Atmospheres (atm) Pound / inch2 (psi) Pascal (Pa) = N/m2 millimeters of Mercury (mmHg) Torr

Atmospheric pressure Pressure exerted by the air above us 1 atm 14.7 psi 101.325 kPa 760 mmHg or torr

Measuring Pressure Barometer Measures atmospheric pressure Invented by Torricelli in 1600’s

Measuring Pressure Manometer Measures pressure in a sealed container

Ideal Gas Law PV = nRT R = Universal Gas Constant

𝑃𝑉=𝑛𝑅𝑇 𝑉= 𝑛𝑅𝑇 𝑃 Molar Volume 1 mole of ANY gas occupies 22.4L of volume at STP 𝑉= 𝑛𝑅𝑇 𝑃

Ideal Gas Law 𝑃𝑉=𝑛𝑅𝑇 𝑛 𝑉 = 𝑃 𝑅𝑇 𝑛𝑀 𝑉 = 𝑃𝑀 𝑅𝑇

Ideal Gas Law 𝑛𝑀 𝑉 = 𝑃𝑀 𝑅𝑇 𝑚 𝑉 = 𝑃𝑀 𝑅𝑇 𝐷= 𝑃𝑀 𝑅𝑇

Ideal Gas Law 𝐷= 𝑃𝑀 𝑅𝑇 𝑀= 𝐷𝑅𝑇 𝑃 = 𝑚𝑅𝑇 𝑃𝑉

Gaseous Mixtures What is the composition of the air that you breathe? Does air behave like an ideal gas? Does the size of the gas molecules affect the volume of an Ideal gas? Is there a factor in the Ideal Gas Law to account for different amounts of gas in a mixture?

Dalton’s Law Mole Fraction (XA) Partial Pressure (PA) Amount of one gas compared to total sample of gas Partial Pressure (PA) Pressure exerted by one gas in a sample of gas

Dalton’s Law of Partial Pressures How does partial pressure relate to total pressure? Sum of partial pressures equals total pressure PT = PA + PB + PC…

Dalton’s Law of Partial Pressures How can we relate mole fraction to partial pressure and total pressure?

In Class Practice #61, 63, 65, 69 from Ch 10

Question Which balloons are better for birthday parties? Latex or Mylar Which balloons stay inflated longer? Why?

Temperature Average Kinetic Energy A gas at any given temperature will have molecules with a wide range of speeds Range of speeds is calculated by a Maxwell-Boltzman distribution

Maxwell-Boltzmann Dist.

Molecular speed Root Mean Square velocity Speed of molecule with average kinetic energy

Root Mean Square velocity As molar mass increases, rms velocity decreases Remember: 𝑢= 3𝑅𝑇 𝑀 𝐾𝐸= 1 2 𝑚 𝑣 2

Root Mean Square velocity

Molecular Movement Diffusion Effusion Movement of molecules throughout a space or throughout a second substance Effusion Process in which a gas escapes through a tiny hole in a container

Graham’s Law of Effusion Relates the rate of effusion of two gases 𝑟=𝑢= 3𝑅𝑇 𝑀 𝑟 1 𝑟 2 = 3𝑅𝑇/ 𝑀 1 3𝑅𝑇/ 𝑀 2 = 𝑀 2 𝑀 1

Graham’s Law of Effusion 𝑟 1 𝑟 2 = 𝑀 2 𝑀 1 Gases with lower molar masses will effuse faster Gases with higher molar masses will effuse slower

Kinetic Molecular Theory The particles in a gas are constantly moving in rapid, random, straight-line motion. Gas particles have no volume compared to the volume of the gas. No attraction between particles All collisions are completely elastic

Real Gases When do real gases behave more like an Ideal Gas? High Temperature Low Pressure When do real gases behave least like an Ideal Gas? Low Temperature High Pressure

Real Gases Why don’t real gases act like ideal gases at low temp and high pressures? What assumptions of the KMT are no longer accurate?

𝑃+ 𝑛 2 𝑎 𝑉 2 Real Gases Real gases do have attractions Real gases exert less pressure due to attractions between molecules a – constant unique to each substance 𝑃+ 𝑛 2 𝑎 𝑉 2

𝑉−𝑛𝑏 Real Gases Real gases do have volume The amount of free space that molecules actually have is less than an ideal gas b – constant unique to each substance 𝑉−𝑛𝑏

van der Waals Equation 𝑃+ 𝑛 2 𝑎 𝑉 2 𝑉−𝑛𝑏 =𝑛𝑅𝑇

van der Waals Equation 𝑃+ 𝑛 2 𝑎 𝑉 2 𝑉−𝑛𝑏 =𝑛𝑅𝑇