Gas Laws/Formulas Remember

Boyle's Law

• P₁ V_{1 =} P₂ V₂

• _{tells us that the volume of gas increases as the pressure decreases}

Charles’ Law

• V₁ / T₁ = V₂ / T₂

• the volume of gas increases as the temperature increases

Avogadro’s Law

• V₁ / n₁ = V₂ / n₂

• tell us that the volume of gas increases as the amount of gas increases

Combine Gas Law

• P₁ V₁ / T_{1 =} P₂ V₂ / T₂

• the combination of the three simple gas laws

PV = nRT

• P = Pressure ( atm )

• V = Volume ( L )

• n = moles ( mol )

• R = Constant ( R = 0.08206 L x atm / mol x K )

• T = Temperature ( K ; K = 273 + °C )

Molar mass = dRT / P

• d = density ( g / L )

• R = Constant ( R = 0.08206 L x atm / mol x K )

• T = Temperature ( K ; K = 273 + °C )

• P = Pressure ( atm )

Open Manometers ONLY Formulas

• P_atm = P_gas + P_Hg ( **use if atm arm has more pressure)

• P_gas = P_atm + P_Hg ( **use if gas arm has more pressure )

Pressure and Manometers

• Pressure = Force / Area

• As P goes up F goes up

• As P goes up A goes down

Important Conversions

Standard Atmospheric Pressure ( @ sea level & ALWAYS 1 atm !! )

• = 14.7 psi

• = 101325 Pa

• = 1 atm

• = 760 mm Hg

• = 760 torr

** ALL EQUAL each other can be converted anywhere **

Gas Stoichiometry

• STP = standard Temperature ( 273 K ) and standard Pressure ( 1 atm )

• 1 mol of any gas = 22.4 L at STP

• An excess signals that the reagent is not the limited reagent

• All gas element that anit noble gas MUST HAVE subscript 2 (e.g: Nitrogen gas → N₂ & Hydrogen gas → H₂

Kinetic Molecular Theory of Gas

• The gas particles are so small compared to the distances separating them that we assume their volume is negligible (zero). Ideal Gases

• The gas particles are in constant motion and their collisions cause the pressure exerted by the gas.

• The particles are assumed to exert no attractive / repulsive forces on each other. Ideal Gases

• The average Kinetic Energy (KE) is directly proportional to temperature.

Avg. Kinetic Energy (KE) Formula

• KE = ½ mv² (m = m/s; meters per sec & v = velocity; speed + direction)

• KE = 3/2RT where R = 8.31 J/(mol x K)

• 1 joule = 1 Newton x meter

• 1 Newton = 1 (kg x m) / s²

Root Mean Square Velocity

= provide measurement of avg. volocity of all gas particles

• KE = 1/2mv² = 3/2RT

  mv² = 3RT

  v² = 3RT/m

vrms = √(3RT/m) **molar mass must be in kg/mol, velocity in m/s)

Diffusion

• mixing of 2 gases

Effusion

• filling of a gas into a chamber by a hole

Graham’s Law of Effusion

• Rate of effusion for gas #1 = Vrms #1 = √(3RT/m1) = √(1/m1) = √m2

• gas #2 = Vrms #2 = √(3RT/m2) = √(1/m2) = √m1

• Rate gas #1/Rate gas #2 = √m2/√m1

• Rate must be in volume/time, but units din’t matter if they agree

• √J/kg (J = N x M) —> √(kg x m²/s²) —> m/s