chapter ii

What is an ideal gas?

A model gas with molecules far apart and negligible intermolecular forces except during collisions.

What is the ideal gas law in terms of molecules?

pV = NkB T.

What does p represent in the ideal gas law?

Absolute pressure.

What does V represent in the ideal gas law?

Volume.

What does N represent in the ideal gas law?

Number of molecules.

What is the value of the Boltzmann constant?

1.38 × 10⁻²³ J/K.

What temperature scale is used in the ideal gas law?

Absolute temperature (Kelvin).

What is the ideal gas law in terms of moles?

pV = nRT.

What does n represent in the ideal gas law?

Number of moles.

What is the value of R in SI units?

8.31 J/mol·K.

What is the value of R in L·atm units?

0.0821 L·atm/mol·K.

What is Avogadro’s number?

6.02 × 10²³ mol⁻¹.

How are molecules and moles related?

N = nNA.

What is molar mass?

Mass of one mole of a substance.

How is molar mass related to molecular mass?

M = NA m.

What are standard temperature and pressure (STP)?

0°C (273 K) and 1.01 × 10⁵ Pa (1 atm).

What volume does one mole of ideal gas occupy at STP?

22.4 L.

When does the ideal gas law fail?

At high pressure or low temperature.

What equation describes real gas behavior?

The Van der Waals equation.

Write the Van der Waals equation.

[p + a(n/V)²](V − nb) = nRT.

What does the Van der Waals constant a represent?

Attractive forces between molecules.

What does the Van der Waals constant b represent?

Finite molecular volume.

What is a pV diagram?

A graph of pressure versus volume.

What is an isotherm?

A curve representing constant temperature.

What shape are ideal gas isotherms?

Hyperbolas.

What does pV equal along an ideal gas isotherm?

A constant value.

What is the critical temperature (Tc)?

The temperature above which a gas cannot be liquefied.

What is the critical point?

The point where liquid and gas phases become indistinguishable.

How do you convert Celsius to Kelvin?

T(K) = T(°C) + 273.

Why must Kelvin be used in gas laws?

Gas laws require absolute temperature.

What pressure must be used in gas calculations?

Absolute pressure.

How is absolute pressure calculated?

Gauge pressure + atmospheric pressure.

What combined gas law applies when n is constant?

p₁V₁/T₁ = p₂V₂/T₂.

When can the combined gas law be used?

When the amount of gas is constant.

What is the goal of kinetic theory?

To relate macroscopic gas properties to microscopic molecular motion.

What assumption is made about the number of gas molecules?

A gas contains a very large number of identical molecules.

What is assumed about molecular motion in a gas?

Molecules move randomly and isotropically.

What laws govern molecular motion in kinetic theory?

Newton’s laws of motion.

What assumption is made about molecular volume?

Molecular volume is negligible compared to container volume.

What type of collisions are assumed in kinetic theory?

Perfectly elastic collisions.

What does elastic collision mean?

Kinetic energy is conserved.

What equation relates pressure and molecular motion microscopically?

PV = (1/3) N m v̄².

What does v̄² represent?

The average of the square of molecular speeds.

What does the microscopic pressure equation show?

Pressure depends on molecular number, mass, and speed.

What is the formula for average kinetic energy of a gas molecule?

K̄ = (1/2) m v̄² = (3/2) kB T.

On what does average kinetic energy depend?

Absolute temperature only.

Does average kinetic energy depend on gas identity?

No.

What is the internal energy of a monatomic ideal gas?

Eint = (3/2) N kB T.

How can internal energy be written in terms of moles?

Eint = (3/2) nRT.

What type of energy makes up internal energy in a monatomic ideal gas?

Translational kinetic energy only.

What is RMS speed?

Root-mean-square molecular speed.

What is the RMS speed formula using molecular mass?

vrms = √(3kB T / m).

What is the RMS speed formula using molar mass?

vrms = √(3RT / M).

What does RMS speed estimate?

Typical molecular velocity.

What is partial pressure?

The pressure a gas would exert alone in the container.

What is Dalton’s law of partial pressures?

Total pressure equals the sum of partial pressures.

Write Dalton’s law mathematically.

Ptotal = P1 + P2 + … .

What is true about pressure-to-mole ratio at equilibrium?

P1/n1 = P2/n2.

What condition is required for Dalton’s law to apply?

Thermal equilibrium.

What is vapor pressure?

The partial pressure of a vapor in equilibrium with its liquid.

What is the dew point?

The temperature at which condensation begins.

What does relative humidity measure?

How close air is to saturation with water vapor.

Write the formula for relative humidity.

RH = (actual vapor pressure / saturation vapor pressure) × 100%.

What is the mean free path?

Average distance traveled between molecular collisions.

Write the mean free path formula using pressure.

λ = kB T / (4√2 π r² p).

What does r represent in mean free path equations?

Molecular radius.

What is mean free time?

Average time between collisions.

Write the mean free time formula.

τ = λ / vrms.

Why is mean free path longer in gases than liquids?

Gas molecules are much farther apart.

In which state is mean free path shortest?

Liquids.

What is molar heat capacity at constant volume (Cv)?

Heat required to raise the temperature of 1 mole of a gas by 1 K at constant volume.

Why is no work done at constant volume?

The volume does not change, so W = 0.

What happens to heat added at constant volume?

All heat increases internal energy.

What is the heat equation at constant volume?

Q = nCvΔT.

What is Cv for a monatomic ideal gas?

Cv = 3/2 R.

What is the value of R?

8.31 J/mol·K.

What theorem explains molar heat capacity values?

The equipartition theorem.

What does the equipartition theorem state?

Energy is shared equally among all degrees of freedom.

How much energy does each degree of freedom contribute per molecule?

(1/2) kB T.

What is the general formula for Cv using degrees of freedom?

Cv = (d/2) R.

What are degrees of freedom?

Independent ways a molecule can store energy.

How many degrees of freedom does a monatomic gas have?

3.

What type of motion contributes to monatomic degrees of freedom?

Translational motion only.

What is Cv for a monatomic gas using equipartition?

3/2 R.

How many degrees of freedom does a diatomic gas have at room temperature?

5.

What motions contribute to diatomic degrees of freedom?

3 translational and 2 rotational.

What is Cv for a diatomic gas at room temperature?

5/2 R.

How many degrees of freedom does a polyatomic gas have at room temperature?

6.

What motions contribute to polyatomic degrees of freedom?

3 translational and 3 rotational.

What is Cv for a polyatomic gas?

3R.

What happens to degrees of freedom at very high temperatures?

Vibrational modes become active.

How many degrees of freedom does one vibrational mode add?

2 (1 kinetic + 1 potential).

At approximately what temperature do vibrational modes activate?

Above about 3000 K.

What model describes solids in heat capacity theory?

Atoms connected by springs.

How many degrees of freedom does each atom in a solid have?

6.

What contributes to degrees of freedom in solids?

3 kinetic and 3 potential.

What law describes heat capacity of solids?

The law of Dulong and Petit.

What is the molar heat capacity of most solid elements?

Cv ≈ 3R.

What is the internal energy of a monatomic ideal gas?

(3/2) nRT.

What is the internal energy of a diatomic ideal gas?

(5/2) nRT.