Pressure turns a force into an intensity over an area. The same force gives a larger pressure when applied over a smaller area. In gas laws, pressure is a macroscopic measure of the repeated microscopic collisions of gas molecules with the container walls.

Pressure is defined as force per unit area acting perpendicular to a surface: P = F/A.

The SI unit is the pascal, Pa, where 1 Pa = 1 N m^-2.

Use the normal component of force and the area over which that force is distributed.

Gas pressure arises from many molecules colliding with container walls and changing momentum.

At higher molecular speed or more frequent collisions, the average force on the wall and pressure increase.

Repair the pressure misconceptions.

Spot Errors

Define pressure and explain how gas molecules produce pressure on the walls of a container.

Common mark losses are omitting “perpendicular”, using the wrong unit, or saying pressure is caused by stationary molecules.

Define pressure and explain how gas molecules produce pressure on the walls of a container.

Choose

Amount of substance is a counting quantity. It lets a macroscopic sample be linked to the number of molecules in the gas. In gas-law problems, decide whether the question gives moles n or particle number N before choosing PV = nRT or PV = NkT.

Amount of substance n is measured in moles, mol.

One mole contains Avogadro’s constant N_A = 6.02×10^23 particles.

Particle number and amount of substance are linked by N = nN_A and n = N/N_A.

The ideal gas equation can be written as PV = nRT when using moles.

It can also be written as PV = NkT when using particle number, with R = N_A k.

Build the mole-particle conversion and choose the gas-equation form.

Formula

Target formula N = nN_A; n = N/N_A; PV = nRT or PV = NkT

n

amount of substance

mol

N

number of particles or molecules

N_A

Avogadro constant

mol^-1

R

universal gas constant

J mol^-1 K^-1

k

Boltzmann constant

J K^-1

1Use N for the number of particles or molecules.N

2Use n for amount of substance in moles.n

3Connect particles and moles using Avogadro’s constant.N = nN_A

4Choose the ideal-gas equation form from the quantity given.PV = nRT or PV = NkT

Build the formula

Define amount of substance and state how it links the ideal gas equations PV = nRT and PV = NkT.

Common mark losses are confusing N with n, forgetting Avogadro’s constant, or using particle number in the mole form of the equation.

Define amount of substance and state how it links the ideal gas equations PV = nRT and PV = NkT.

Choose

The ideal gas model is not just an equation; it is a set of assumptions about particles. These assumptions work well when molecules are far apart and interactions are small. Real gases deviate at high pressure, high density, or low temperature where molecular volume and attractions become important.

The kinetic theory models a gas as many identical point particles in continuous random motion.

Particle volume is negligible compared with the container volume.

There are no intermolecular forces except during collisions, and collisions are perfectly elastic.

The time spent in collisions is negligible compared with the time between collisions.

Real gases approximate ideal behaviour best at low pressure, low density, and temperatures away from condensation.

Sort each statement by how it relates to the ideal gas model.

Sort

Unsorted

6

ideal-gas assumption

0

close to ideal behaviour

0

deviation from ideal model

0

State assumptions of the kinetic theory of ideal gases and describe when a real gas approximates ideal behaviour.

Common mark losses are listing only PV = nRT, omitting elastic collisions, or failing to mention low pressure/low density conditions for real gases.

State assumptions of the kinetic theory of ideal gases and describe when a real gas approximates ideal behaviour.

Choose

Start every gas-law question by asking what is fixed: amount of gas, then temperature, pressure, or volume. The correct law is a simplified version of PV/T = constant. Temperature must be absolute temperature in kelvin because gas-law proportionalities use absolute temperature.

For a fixed amount of ideal gas, PV/T is constant when temperature is in kelvin.

Boyle’s law: at constant temperature, PV = constant, so P1V1 = P2V2.

Charles’ law: at constant pressure, V/T = constant, so V1/T1 = V2/T2.

Gay-Lussac’s law: at constant volume, P/T = constant, so P1/T1 = P2/T2.

These empirical laws come from experimental patterns and combine into the ideal gas equation.

Build the appropriate empirical gas-law relationship.

Formula

Target formula P1V1/T1 = P2V2/T2 for fixed n; special cases: PV, V/T, or P/T constant

P

gas pressure

Pa

V

gas volume

m^3

T

absolute temperature

K

n

amount of gas, held fixed

mol

1Check the amount of gas is fixed.n constant

2Convert temperature to absolute temperature.T in K

3Identify whether T, P, or V is constant.Boyle / Charles / Gay-Lussac

4Use the combined gas law if none of P, V, or T is fixed.P1V1/T1 = P2V2/T2

Build the formula

State Boyle’s, Charles’, and Gay-Lussac’s laws for a fixed amount of ideal gas, including the condition for each law.

Common mark losses are forgetting the constant variable, using Celsius, or using a law for a changing amount of gas.

State Boyle’s, Charles’, and Gay-Lussac’s laws for a fixed amount of ideal gas, including the condition for each law.

Choose

The ideal gas equation links macroscopic state variables for a gas that satisfies the ideal-gas model. Before substituting, convert volume to m^3, pressure to Pa, and temperature to kelvin. Then choose nRT or Nk_B T from whether the problem gives moles or number of molecules.

The ideal gas equation in mole form is PV = nRT.

P is pressure in Pa, V is volume in m^3, n is amount in mol, and T is absolute temperature in K.

R = 8.31 J mol^-1 K^-1 is the molar gas constant.

The particle-number form is PV = Nk_B T, where N is number of molecules and k_B is the Boltzmann constant.

The two forms are equivalent because N = nN_A and R = N_A k_B.

Build the ideal gas equation in the correct form.

Formula

Target formula PV = nRT; PV = Nk_B T

P

gas pressure

Pa

V

gas volume

m^3

n

amount of substance

mol

R

molar gas constant

J mol^-1 K^-1

N

number of particles

k_B

Boltzmann constant

J K^-1

T

absolute temperature

K

1Check that the gas can be treated as ideal.ideal-gas approximation

2Convert P, V, and T into SI units.Pa, m^3, K

3If amount of gas is given in moles, use the molar form.PV = nRT

4If particle number is given, use the molecular form.PV = Nk_B T

Build the formula

A gas can be modelled as ideal. State the two equivalent forms of the ideal gas equation and define the quantities in each form.

Common mark losses are mixing particle number with moles, using Celsius, or leaving pressure and volume outside SI units.

A gas can be modelled as ideal. State the two equivalent forms of the ideal gas equation and define the quantities in each form.

Choose

The molecular model connects microscopic motion to macroscopic pressure. Faster molecules or more molecules per volume cause larger momentum transfer per second to the walls. The equation uses mean square speed, not simply mean speed, because kinetic energy and momentum-flux averages depend on speed squared.

A gas molecule colliding elastically with a wall changes momentum, so the wall experiences a force.

Pressure is the average force per unit area from many molecular collisions.

For N identical molecules of mass m in volume V, P = Nm<c^2>/(3V), where <c^2> is mean square speed.

Using mass density ρ = Nm/V, the equation can be written P = (1/3)ρ<c^2>.

The factor 1/3 comes from random motion distributed equally among three perpendicular directions.

Build the molecular pressure relation.

Formula

Target formula P = Nm<c^2>/(3V) = (1/3)ρ<c^2>

P

gas pressure

Pa

N

number of molecules

m

mass of one molecule

kg

V

gas volume

m^3

<c^2>

mean square molecular speed

m^2 s^-2

ρ

gas mass density

kg m^-3

1Start with momentum change in elastic wall collisions.Δp from reversing perpendicular velocity component

2Average many molecular collisions over time and area.P = average force/area

3Use random motion in three dimensions.<c_x^2> = <c^2>/3

4Assemble the pressure relation.P = Nm<c^2>/(3V) = (1/3)ρ<c^2>

Build the formula

Explain how molecular collisions give rise to gas pressure and state the molecular pressure equation.

Common mark losses are omitting momentum change, using mean speed instead of mean square speed, or forgetting the random-direction factor 1/3.

Explain how molecular collisions give rise to gas pressure and state the molecular pressure equation.

Choose

A monatomic ideal gas has only translational kinetic energy in this model. Because ideal gas particles do not exert intermolecular forces except during collisions, there is no intermolecular potential energy term. This is why internal energy depends only on absolute temperature, not directly on pressure or volume.

For an ideal gas, intermolecular potential energy is ignored because there are no forces except during collisions.

For a monatomic ideal gas, internal energy is the total translational kinetic energy of the atoms.

The average translational kinetic energy per atom is (3/2)k_B T.

Total internal energy is U = (3/2)Nk_B T = (3/2)nRT.

For a fixed amount of monatomic ideal gas, ΔU = (3/2)nRΔT, so U changes only when temperature changes.

Build the monatomic ideal-gas internal energy equation.

Formula

Target formula U = (3/2)Nk_B T = (3/2)nRT; ΔU = (3/2)nRΔT

U

internal energy

J

N

number of atoms

k_B

Boltzmann constant

J K^-1

n

amount of gas

mol

R

gas constant

J mol^-1 K^-1

T

absolute temperature

K

1Check the gas is monatomic and ideal.monatomic ideal gas

2Use average translational kinetic energy per atom.<E_k> = (3/2)k_B T

3Multiply by the number of particles or use moles.N or n

4Assemble internal energy and change in internal energy.U = (3/2)Nk_B T = (3/2)nRT; ΔU = (3/2)nRΔT

Build the formula

For a monatomic ideal gas, state the internal energy equation and explain why internal energy depends only on temperature.

Common mark losses are using the formula for non-monatomic gases without checking, saying U depends directly on volume, or forgetting Kelvin temperature.

For a monatomic ideal gas, state the internal energy equation and explain why internal energy depends only on temperature.

Choose

The ideal gas approximation is a judgement about whether the assumptions are acceptable. If molecules are far apart, they mostly ignore each other except during brief collisions. If the gas is compressed or cooled close to liquefaction, molecular size and attractions change the pressure-volume-temperature behaviour.

The ideal gas model assumes negligible molecular volume and no intermolecular forces except during collisions.

Real gases approximate ideal behaviour when pressure and density are low, so molecules are far apart.

The approximation is better when the gas is far from condensation, so attractive forces have little effect.

At high pressure or high density, molecular volume becomes a significant fraction of the container volume.

At low temperature near liquefaction, intermolecular attractions make real gases deviate from ideal behaviour.

Sort each condition by whether the ideal-gas approximation is more or less reliable.

Sort

Unsorted

7

closer to ideal

0

deviation likely

0

assumption violated

0

Describe conditions under which a real gas approximates an ideal gas and conditions where the approximation breaks down.

Common mark losses are saying only “use PV = nRT”, or failing to connect deviations to finite molecular volume and intermolecular forces.

Describe conditions under which a real gas approximates an ideal gas and conditions where the approximation breaks down.

Choose

B.3 links microscopic gas particles to macroscopic gas equations. Start with ideal-gas assumptions, keep units and Kelvin temperature clean, choose the equation form from the given amount variable, and always attach gas laws to their constant-variable conditions.

Define pressure as normal force per unit area and link gas pressure to molecular momentum changes.

Convert between amount of substance n and particle number N using N = nN_A.

State ideal-gas assumptions before using ideal-gas equations.

Choose Boyle, Charles, Gay-Lussac, or the combined gas law by checking which variable is constant.

Use PV = nRT for moles and PV = Nk_B T for particle number, with T in kelvin.

Explain molecular pressure using P = Nm<c^2>/(3V) = (1/3)ρ<c^2>.

Use U = (3/2)nRT = (3/2)Nk_B T for a monatomic ideal gas.

Judge when real gases approximate or deviate from ideal behaviour.

Match each B.3 retrieval cue to the physics move it should trigger.

Match

Reasons

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IB Physics SL B.3 Gas laws Notes

Use Pressure

Use Amount of substance

Use Ideal gas model

Use Empirical gas laws

Use Ideal gas equations

Use Molecular pressure model

Use Ideal gas internal energy

Use Ideal gas approximation limits

Retrieve the B.3 Gas laws Model