Gas Laws .....

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Gas laws

Constant temperature (Boyle's law)

P₁V₁ = P₂V₂

Constant pressure (Charles's law)

V₁/T₁ = V₂/T₂

Constant volume (Gay-Lussac's law)

P₁/T₁ = P₂/T₂

Combined Gas law

P₁V₁/T₁ = P₂V₂/T₂

pressure and temperature are absolute

Avogadro's law

V₁/n₁ = V₂/n₂

n = number of moles

Work on a gas at constant pressure

Volume increases with temperature. Take a cylinder with

the top a piston of area A moving up by distance d

W = Fd = (F/A)(Ad)

W = P(Ad) = PΔV

Work on a gas at constant volume

no work is done

Work on a gas at constant temperature

Take a cylinder with the top a piston of area A moving up

by distance d. We can keep the temperature constant by having

the system in contact with a heat reservoir.

W = nRT ln(Vf/Vi)

n = number of moles

R = gas constant = 0.08206 (atm∙L)/(mol∙K)

T = temperature in kelvins

P = absolute pressure in atm

V = volume in liters

Ideal gas law

PV = nRT

n = number of moles

R = gas constant = 0.08206 (atm∙L)/(mol∙K)

T = temperature in kelvins

P = absolute pressure in atm

V = volume in liters

One mole of any ideal gas at STP has a volume of 22.4L

One mole of any ideal gas at RTP has a volume of 24L

STP = 0ºC and 1 ATM RTP = 25ºC and 1 ATM

alternate:

R = 8.314 J/K•mol

P = absolute pressure in Pa

V = volume in m³

Alternate:

PV = kNT

k = Boltzmann constant, 1.381e-23 J/K

N is number of gas molecules

P is absolute pressure in Pa

V is volume in m³

alternate:

P = ρRsT

ρ = density

Rs = specific gas constant, = R/M

M = molar mass in g/mole