Ideal gasses

Define macroscopic

The scale of objects or phenomena that are large enough to be observed with the naked eye

Define microscopic

The scale of objects and phenomena that are too small to be seen with the naked eye

Define a mole in terms of mass

The amount of substance that contains as many elementary entities as there are atoms in 0.012 kg (12 g) of carbon-12.

Define a mole in terms of number of atoms

The amount of substance that contains 6.02×10²³ elementary entities. This number is called the Avogadro constant and has symbol N_A

What is the Avogadro constant?

The number of atoms in 0.012 kg (12 g) of carbon-12 - 6.02×10²³

What is the value of the Avogadro constant?

6.02×10²³

What is the symbol for the Avogadro constant?

N_A

Define Molar Mass

The mass of one mole of a substance

What is the molar mass of CO₂ in kg? (C = carbon-12, O = oxygen-16)

1×12 + 2×16 = 44 → Molar mass of CO₂ is 44g mol^-1 = 0.044 kg mol^-1

What is the unit of molar mass?

kg mol^-1

What symbol represents the number of moles?

n

What number represents the number of particles?

N

What equation links the number of moles and the number of particles?

N = n × N_A

What are the five assumptions made in the kinetic theory of gasses?

There are a large number of particles in random motion with random speeds

Particles occupy negligible volume compared to volume of gas

Collisions between particles and with container walls are perfectly elastic

Time of collisions between particles is negligible compared to the time between collisions

Negligible electrostatic forces exist between particles except during collisions

State the assumption in the kinetic theory of gasses about the movement of particles

There are a large number of particles in random motion with random speeds

State the assumption in the kinetic theory of gasses relating to volume

Particles occupy negligible volume compared to volume of gas

State the assumption in the kinetic theory of gasses about the type of collisions

Collisions between particles and with container walls are perfectly elastic

State the assumption in the kinetic theory of gasses about the time of collisions

Time of collisions between particles is negligible compared to the time between collisions

State the assumption in the kinetic theory of gasses relating to forces

Negligible electrostatic forces exist between particles except during collisions

What is an ideal gas?

A model of a gas including assumptions that simplify the behaviour of real gases

How does the kinetic theory of ideal gases explain gas pressure on a container?

The atoms or molecules in a gas are always moving, and when they collide with the walls of a container the atoms or molecules exert a force on the walls, which we call pressure.

What is the change in momentum in a collision with a wall?

• Innitial velocity = u, so innitial momentum = mu

• Velocity after collision = -u (speed doesn’t change but directions is opposite), so momenutum after collision = -mu

• ∆p = (-mu) - (mu) = -2mu

How do you derive pressure from the collision momentum?

• Atoms in the gas bounce between the container walls, making frequent collisions.

• According to Newton's second law, the force acting on the atom F_atom = ∆P / ∆t, where ∆p = -2mu and ∆t is the time between collisions with the wall. From Newton's third law, the atom also exerts an equal but opposite force on the wall.

• A large number of atoms collide randomly with the walls of the container. If the total force they exert on the wall is F, then the pressure they exert on the wall is given by p = F / A where A is the cross-sectional area of the wall.

What is Boyle’s Law as an equation?

If mass and temperature of gas are constant:

• p ∝ 1/V

• pV = constant

• p₁/T₁ = p₂/T₂

What is Boyle’s Law in words?

The pressure of an ideal gas is inversely proportional to its volume, provided that the mass of the gas and its temperature remain constant.

What must remain constant for Boyle’s Law and how is this achieved?

• Mass and temperature of gas must remain constant

• Temperature can me kept roughly the same be slowly compressing the gas

What is the graph of P against V (pressure against volume)?

What is the graph of P against 1/V (pressure against 1/volume)?

What apparatus is used to test Boyle’s Law?

What is the graph of P against T (pressure against temperature)?

Describe the Pressure Law (relationship between P and T) in words

If the volume and mass of gas remain constant, the pressure of an ideal gas is directly proportional to its absolute (thermodynamic) temperature in kelvin.

What equation describes the relationship between P and T (the Pressure Law)?

If mass and volume of gas is constant:

• p ∝ T

• p/T = constant

• p₁V₁ = p₂V₂

What needs to remain constant for the Pressure Law? How do we achieve this?

• The volume and mass of the gass must remain constant

• Add how this can be achieved

How can the experiment used to test the Pressure Law be used to find an estimate for absolute zero?

Plotting a graph of pressure against temperature θ in Celsius from the experimental results gives a line that can be extrapolated back to a point where the pressure is zero. At absolute zero the particles are not moving so the pressure of the gas must be zero.

Sketch and label the apparatus used to test the Pressure Law

To be completed

What is the ideal gas equation involving n and what do the terms mean?

• pV = nRT

• p is pressure

• V is volume of gas

• n is the number of moles of gas

• R is the molar gas constant

• T is the temperature of the gas in kelvin

What is the ideal gas equation involving N and what do the terms mean?

• pV = NkT

• p is pressure

• V is volume of gas

• N is the number of atoms or molecules in the gas

• k is Boltzmann constant (given in formula book)

• T is the temperature of the gas in kelvin

What is the molar constant?

The constant in the equation of state of an ideal gas - symbol R, 8.31JK^-1mol^-1

What is Charle’s Law?

If the pressure and mass of a gas is constant:

• V ∝ T

• V/T = constant

• V₁/T₁ = p₂V₂/T₂

How can Boyle’s Law and the Pressure Law be combined into a single equation?

• Boyle’s law → pV = constant → p₁/T₁ = p₂/T₂

• Pressure law → p/T = constant → p₁V₁ = p₂V₂

• Charle’s law → V ∝ T → V/T = constant → V₁/T₁ = V₂/T₂

• Hence pV/T = constant

What is the internal energy of an ideal gas?

The sum of the (randomly distributed) kinetic energies of the molecules in an ideal gas.