Gases

Question 1

What is absolute zero?

Answer 1

It is the lowest temperature possible, defined as 0 K or -273.15 °C.

Question 2

Can a temperature be lower than 0 K?

Answer 2

No, it is not possible to have a temperature lower than 0 K.

Question 3

What does a temperature of 0 K mean for the particles in a substance?

Answer 3

The molecules in a substance have zero kinetic energy.

Question 4

What is the temperature in space?

Answer 4

Roughly 2.7 K, just above absolute zero.

Question 5

How do you convert from Celsius to Kelvin?

Answer 5

T (K) = θ (°C) + 273.15

Question 6

How do you convert from Kelvin to Celsius?

Answer 6

θ (°C) = T (K) − 273.15

Question 7

What does it mean that the divisions on the Celsius and Kelvin scales are equal?

Answer 7

A change in temperature of 1 K is equal to a change of 1 °C.

Question 8

Why doesn’t Δθ in Q = mcΔθ require conversion to Kelvin?

Answer 8

Because the temperature difference is the same in both Celsius and Kelvin.

Question 9

What is the Celsius equivalent of room temperature (300 K)?

Answer 9

26.85 °C.

Question 10

What is Boyle’s Law?

Answer 10

For a constant temperature, the pressure of a gas is inversely proportional to its volume.

Question 11

What is the equation for Boyle’s Law?

Answer 11

P₁V₁ = P₂V₂

Question 12

What is Charles’s Law?

Answer 12

At constant pressure, the volume of a gas is proportional to its absolute temperature.

Question 13

What is the equation form of Charles’s Law?

Answer 13

V₁/T₁ = V₂/T₂

Question 14

Draw and explain a graph of pressure vs volume for Boyle’s Law.

Answer 14

See document for answer.

Question 15

Draw and explain a graph of volume vs temperature for Charles’s Law.

Answer 15

See document for answer.

Question 16

What is the Pressure Law?

Answer 16

At constant volume, pressure is proportional to absolute temperature.

Question 17

What is the equation for the Pressure Law?

Answer 17

P₁/T₁ = P₂/T₂

Question 18

Draw and explain a graph of pressure vs temperature for Pressure Law.

Answer 18

See document for answer.

Question 19

What does pV ∝ T describe?

Answer 19

The relationship between pressure, volume and temperature for an ideal gas.

Question 20

How do gas molecules behave in a container?

Answer 20

They move randomly at high speeds, collide with surfaces, and exert pressure.

Question 21

How does temperature relate to molecular speed?

Answer 21

The hotter the gas, the faster the molecules move.

Question 22

How does pressure relate to collisions?

Answer 22

Faster and more frequent collisions result in more force per unit area, increasing pressure.

Question 23

What happens to pressure if volume decreases and temperature remains constant?

Answer 23

Pressure increases due to more frequent collisions.

Question 24

What defines pressure in an ideal gas?

Answer 24

The frequency of collisions per unit area of the container.

Question 25

What is the ideal gas equation?

Answer 25

pV = nRT

Question 26

What does pV = nRT represent?

Answer 26

The state equation for an ideal gas, relating pressure, volume, and temperature.

Question 27

What is an ideal gas?

Answer 27

A gas that obeys the equation of state pV = nRT at all conditions.

Question 28

What is the equation for work done by a gas at constant pressure?

Answer 28

W = pΔV

Question 29

What does W = pΔV describe?

Answer 29

The work done by a gas when it changes volume at constant pressure.

Question 30

How is work done derived from pressure and volume?

Answer 30

W = F × s, where F = pA and A × s = ΔV, leading to W = pΔV.

Question 31

What happens when a gas expands?

Answer 31

It does work on the surroundings.

Question 32

What happens when a gas is compressed?

Answer 32

Work is done on the gas.

Question 33

What is Avogadro’s constant?

Answer 33

6.02 × 10²³ mol⁻¹, the number of atoms in 12 g of carbon-12.

Question 34

How is the mass of an atom related to atomic mass unit?

Answer 34

1 u ≈ mass of a proton or neutron = 1.66 × 10⁻²⁷ kg.

Question 35

How many atoms are in 2.0 mol of nitrogen?

Answer 35

2.0 × 6.02 × 10²³ = 1.20 × 10²⁴ atoms.

Question 36

How do you calculate molar mass?

Answer 36

It is the mass in grams of one mole of a substance, unit is g mol⁻¹.

Question 37

How do you calculate moles from mass and molar mass?

Answer 37

n = mass / molar mass

Question 38

What is the Boltzmann constant?

Answer 38

It relates macroscopic temperature to microscopic kinetic energy, k = R / NA.

Question 39

What is the unit of Boltzmann constant?

Answer 39

J K⁻¹.

Question 40

Why is the Boltzmann constant small?

Answer 40

Because a small increase in temperature causes a tiny increase in kinetic energy.

Question 41

What is the difference between gas laws and kinetic theory?

Answer 41

Gas laws are empirical, based on observation. Kinetic theory is theoretical, based on assumptions.

Question 42

What are examples of gas laws?

Answer 42

Boyle’s Law, Charles’s Law, Pressure Law, and the ideal gas equation.

Question 43

What does the internal energy of an ideal gas depend on?

Answer 43

It depends only on the kinetic energy of the gas particles.

Question 44

What is the relation between change in internal energy and temperature for an ideal gas?

Answer 44

ΔU ∝ ΔT

Question 45

Define internal energy (ΔU) and its units.

Answer 45

ΔU = change in internal energy (Joules, J)

Question 46

Define change in temperature (ΔT) and its units.

Answer 46

ΔT = change in temperature (Kelvin, K)

Question 47

What is the effect of heating a container of gas molecules?

Answer 47

Molecules move faster, kinetic and internal energy increase.

Question 48

Why do ideal gases have only kinetic energy?

Answer 48

Ideal gases assume no intermolecular forces, hence no potential energy.

Question 49

What are the assumptions of kinetic theory?

Answer 49

Gas consists of identical molecules, perfect elastic collisions, negligible volume compared to the container, continuous random motion, obey Newton’s laws. Time of collision is negligible compared to the time between collisions. Very large number of molecules. No intermolecular forces between molecules.

Question 50

What is the significance of root mean square speed (crms)?

Answer 50

It represents the average speed of gas molecules accounting for direction.

Question 51

Draw and explain the derivation of the kinetic theory of gases equation.

Answer 51

It is provided in the document.

Question 52

What is the kinetic theory of gases equation?

Answer 52

pV = 1/3 Nm(crms)^2

Question 53

What are the units and meanings of p, V, N, m, crms?

Answer 53

p = pressure (Pa), V = volume (m³), N = number of molecules, m = mass of one molecule (kg), crms = root mean square speed (m/s)

Question 54

What is the kinetic theory equation in terms of density?

Answer 54

p = 1/3 ρ(crms)^2

Question 55

What is the average kinetic energy of a molecule in an ideal gas?

Answer 55

Ek = (3/2)kT

Question 56

What is k in the equation Ek = (3/2)kT?

Answer 56

k = Boltzmann constant (1.38 × 10⁻²³ J/K)

Question 57

What is the relationship between kinetic energy and temperature?

Answer 57

Ek ∝ T

Question 58

Define Brownian motion.

Answer 58

Random motion of small particles suspended in a fluid due to collisions with fast-moving molecules.

Question 59

What does Brownian motion provide evidence for?

Answer 59

Existence and movement of molecules in fluids, supports kinetic theory.

Question 60

Why do small molecules affect larger particles in Brownian motion?

Answer 60

Small molecules move faster and transfer momentum during collisions.

Question 61

What is the historical significance of Democritus in gas theory?

Answer 61

He proposed that matter is made of indivisible atoms (atomos).

Question 62

What did Robert Boyle discover?

Answer 62

The inverse relationship between pressure and volume at constant temperature (Boyle’s Law).

Question 63

What did Amontons and Gay-Lussac discover?

Answer 63

The relationship between pressure and temperature at constant volume (Pressure Law).

Question 64

What did Jacques Charles discover?

Answer 64

The relationship between volume and temperature at constant pressure (Charles’s Law).

Question 65

What did Daniel Bernoulli propose?

Answer 65

Gases consist of particles in motion, a foundation of kinetic theory.

Question 66

What was Robert Brown known for?

Answer 66

Discovery of Brownian motion.

Question 67

What did Einstein contribute to gas theory in 1905?

Answer 67

Used kinetic theory to make predictions for Brownian motion, supporting atomic theory.

Question 68

Why are scientific theories not accepted immediately?

Answer 68

They require validation through repeated experiments and peer consensus.