15 - Ideal Gasses Flashcards

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1
Q

What is the SI unit for the amount of a substance?

A

Mole (mol)

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2
Q

Define the mole.

A

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

The Avogadro constant.

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3
Q

What is the sign for the Avogadro constant?

Also what is it?

A

Nₐ

6.02x10²³

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4
Q

What does one mole of any substance contain?

A

The Avogadro constant of individual molecules.

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5
Q

How do you calculate the number of molecules in a substance?

A

N = n x Nₐ

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6
Q

What is the molar mass of a substance?

A

The mass of a single mole of the substance.

M

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7
Q

How do we calculate the mass of a substance from the molar mass?

A

m = n x M

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8
Q

What is the kinetic theory of gases?

A

A model used to describe the behaviour of the atoms / molecules in an ideal gas.

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9
Q

Why do we use the kinetic theory of gases?

A

Because real gases have complex behaviour which we must simplify.

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10
Q

What are the assumptions made in the kinetic theory of gases?

A
  • Very large number of molecules moving in random directions with random speeds
  • Molecules occupy a negligible volume compared to the volume of the gas
  • Collision of molecules and sides of container are perfectly elastic
  • Time of colisions is negligible compared to time between collisions
  • Electrostatic forces between molecules are negligible except during collisions
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11
Q

What is the relationship between the volume of a container and the pressure inside it?

(What are the other conditions for this to be true?)

A

P ∝ 1/v

If temperature and mass of gas remains constant

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12
Q

What is Boyle’s law?

A

P ∝ 1/v

If temperature and mass of gas remains constant

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13
Q

What is the relationship between the pressure of an ideal gas and the temperature?

(What are the other conditions for this to be true?)

A

P ∝ T

If volume and mass of gas remain constant

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14
Q

How does the relationship between the pressure of an ideal gas and the temperature help us find the value of absolute zero.

A

Plot graph of pressure against temperature.

Extrapolate backwards to where pressure = 0.

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15
Q

How do we combine the relationships between pressure and volume and pressure and temperature?

A

PV / T = Constant

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16
Q

What is the molar gas constant?

What is its symbol?

A

The constant from the equation PV / T for one mole of gas.

R

17
Q

What is the equation of state of an ideal gas?

A

PV = nRT

P = Pressure
V = Volume
n = number of moles
R = molar gas constant
T = Temperature
18
Q

What is the SI unit of temperatute?

A

Kelvin

K

19
Q

What is the SI unit for pressure?

A

Pascal

Pa

20
Q

What is the SI unit for volume?

A

21
Q

On a graph of PV against T, what does the gradient represent?

A

nR

y = mx + c

Pv = (nR)T + 0

22
Q

How do we calculate root mean square speed?

A

Square all velocity values
Find mean of squared values
Square root mean

23
Q

Why do we use root mean square speed?

A

Because velocities are vectors and just the mean would cancel out to equal 0.

Squaring the velocities removes the negative.

24
Q

What is the Maxwell-Boltzmann distribution?

A

The range of speeds of particles in a gas at a constant temperature.

25
Q

Where is the most probable speed on the Maxwell-Boltzmann distribution curve?

A

At the peak

26
Q

Where is the mean speed on the Maxwell-Boltzmann distribution curve?

A

Slightly to the right of the peak,

Between the peak and the RMS.

27
Q

Where is the root mean square speed on the Maxwell-Boltzmann distribution curve?

A

Further right of the peak.

Right of the mean speed.

28
Q

How does changing the temperature affect the Maxwell-Boltzmann distribution?

A

It becomes more spread out.

All three speed values become larger.

29
Q

Define the Boltzmann constant.

A

Molar gas constant divided by the Avogadro constant.

k = R / Nₐ

30
Q

What is the symbol of the Boltzmann constant?

A

k

LOWERCASE

31
Q

How can the Boltzmann constant be incorporated into the equation of state of an ideal gas?

A

PV = nRT (equation of state of an ideal gas)

R = kNₐ (Rearrange formula for Boltzmann constant)

PV = knNₐT (Sub in formula above)

n x Nₐ = N (number of moles x Avogadro = number of molecules)

PV = NkT

32
Q

What does the symbol “k” represent?

A

Boltzmann constant

33
Q

What does the symbol “R” represent?

A

Molar gas constant

34
Q

What does the symbol “Nₐ” represent?

A

Avogadro constant

35
Q

What is the derivation of the equation:
(1/2)mc̅ ²kT = (3/2)kt?

Probably use paper

A

1/3 Nmc̅ ² = NkT
1/3mc̅ ² = kT (Cancel N)

REWRITE LHS

(2/3)(1/2mc̅ ²) = kt

1/2mc̅ ² = 3/2kt

36
Q

What does the equation 1/2mc̅ ² equal?

A

The mean average kinetic energy of the particles in the gas.

1/2 mv²

37
Q

What is the relationship between the mean kinetic energy of particles in the gas and the temperature of the gas?

A

Eₖ ∝ T

38
Q

What is the internal energy of an ideal gas and why?

A

A sum of the kinetic and potential energies of the particles in the gas.

Ee assume that the electrostatic forces between particles are negligible.

Internal energy of ideal gas = kinetic energy of all of the particles.

39
Q

What would happen to the internal energy of an ideal gas if you doubled the temperature?

A

It would also double.

Eₖ ∝ T
THEREFORE
Internal E ∝ T