Ideal gases Flashcards
Mole
1 mole is the amount of matter that contains a number of particles equal to the Avogadro constant.
The mole is an SI base quantity for the amount of substance, base unit mol
Avogadro constant
the number of particles in one mole of any substance, denoted Nₐ *A
Boyle’s Law
the pressure exerted by a fixed mass of gas is inversely proportional to its volume, provided the temperature remains constant
p.V = constant
p₁V₁ = p₂V₂
Charles’s Law
the volume occupied by a gas at constant pressure is directly proportional to its absolute temperature
V/T = constant
V₁/T₁ = V₂/T₂
Combined equation for fixed mass of gas
pV/T = constant
p₁V₁/T₁ = p₂V₂/T₂
Ideal gas
a gas that behaves according to the equation pV = nRT
Equation of state
pV = nRT
pressure x volume = number of moles x universal molar gas constant x temperature
pV = NkT
N is the number of molecules
k is the Boltzmann constant
Number of moles (n)
mass / molar mass
[g] / [g mol⁻¹]
Kinetic theory of gases
a model based on the microscopic motion of atoms or molecules of a gas
Key equations of force and pressure
F = change in momentum / time
P = F / A
Pressure of an ideal gas
p = 1/3 (Nm/V)<c²>
or
pV = 1/3 x Nm x <c²>
Nm is the mass of all the molecules of the gas hence Nm/V is density
p = 1/3ρ<c²>
Boltzmann constant
k = R/Nₐ
the gas constant per molecule, a fundamental constant
Relation between kinetic energy and temperature
mean translational kinetic energy of atom ∝ T
Kinetic energy of a molecule
3/2 kT
Root-mean-square speed
the square root of the average of the squares of the speeds of all the molecules in a gas
cᵣ.ₘ.ₛ = √<c²>
