Molecular kinetics

Amount of substance (moles)

$$\nu = \frac{N}{N_{A}}$$

ν - amount of substance
N - number of molecules
N_A - Avogadro constant

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Molar mass

$$M = \frac{m}{\nu}$$

M - molar mass
m - mass
ν - amount of substance

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Mass of the molecule

$$m_0 = \frac{m}{N}$$

m₀ - mass of the molecule
m - mass
N - number of molecules

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Calculate 'm0'

Molar mass

$$M = m_0\cdot N_{A}$$

M - molar mass
m₀ - mass of the molecule
N_A - Avogadro constant

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Calculate 'M'

Number of molecules

$$N = \frac{m\cdot N_{A}}{M}$$

N - number of molecules
m - mass
N_A - Avogadro constant
M - molar mass

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Calculate 'N'

Kinetic theory formula

$$p = \frac{1}{3}\cdot n\cdot m_0\cdot v^{2}$$

p - pressure
n - concentration
m₀ - mass of the molecule
v - speed (velocity)

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Inner energy of molecules

$$E = \frac{m\cdot v^{2}}{2}$$

E - energy
m - mass
v - speed (velocity)

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Pressure of perfect gas

$$p = \frac{2}{3}\cdot n\cdot E$$

p - pressure
n - concentration
E - energy

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Concentration of molecules

$$n = \frac{N}{V}$$

n - concentration
N - number of molecules
V - bulk (volume)

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Gas pressure, volume and average kinetic energy

$$\frac{p\cdot V}{N} = \frac{2\cdot E}{3}$$

p - pressure
V - bulk (volume)
N - number of molecules
E - average kinetic energy

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Gas: pressure, volume, temperature

$$\frac{p\cdot V}{N} = k\cdot T$$

p - pressure
V - bulk (volume)
N - number of molecules
k - Boltzmann constant
T - temperature

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Calculate 'p'

Average kinetic energy

$$E = \frac{3\cdot k\cdot T}{2}$$

E - average kinetic energy
k - Boltzmann constant
T - temperature

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Calculate 'E'

Gas: pressure, concentration, temperature

$$p = n\cdot k\cdot T$$

p - pressure
n - concentration
k - Boltzmann constant
T - temperature

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Calculate 'p'

Gas: amount of substance, volume

$$\nu = \frac{V}{V_{M}}$$

ν - amount of substance
V - bulk (volume)
V_M - molal (gram-molecular) volume

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Calculate 'ν'

Root-mean-square velocity of a gas molecule

$$v = \sqrt {\frac{3\cdot k\cdot T}{m_0}}$$

v - speed (velocity)
k - Boltzmann constant
T - temperature
m₀ - mass of the molecule

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Calculate 'v'

Ideal gas law (Mendeleev - Clapeyron equation)

$$p\cdot V = \frac{m\cdot R\cdot T}{M}$$

p - pressure
V - bulk (volume)
m - mass
R - ideal gas constant
T - temperature
M - molar mass

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Ideal gas law (Mendeleev - Clapeyron equation)

$$\frac{p\cdot V}{T} = \nu\cdot R$$

p - pressure
V - bulk (volume)
T - temperature
ν - amount of substance
R - ideal gas constant

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Calculate 'p'

Boyle and Mariotte law (isothermal process)

$$p_1\cdot V_1 = p_2\cdot V_2$$

p1, p2 - pressures
V1, V2 - volumes

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Calculate 'p1'

Gay-Lussac\'s law (isobaric process)

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

T1, T2 - temperatures
V1, V2 - volumes

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Calculate 'V1'

Thermal expansion of gas

$$V = V_0\cdot \alpha\cdot T$$

V - bulk (volume)
V₀ - volume when temperature is 0 C
α - coefficient of volume expansion
T - temperature

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Charles\'s law (isochoric process)

$$\frac{p_1}{T_1} = \frac{p_2}{T_2}$$

p1, p2 - pressures
V1, V2 - volumes

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Calculate 'p1'

The temperature dependence of the gas pressure

$$p = p_0\cdot \gamma\cdot T$$

p - pressure
p₀ - pressure when temperature is 0 C
T - temperature
γ - thermal coefficient of gas pressure

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