1A The Perfect Gas Flashcards
What is the key idea of the chapter?
The perfect gas law is a limiting law that is obeyed increasingly well as the pressure of a gas tends to zero.
In molecular terms, a gas consists of…
…a collection of molecules that are in ceaseless motion and which interact significantly with one another only when they collide.
What defines the physical state of a substance (its physical condition)?
Its physical properties.
When are two samples in the same state?
- When they are made of the same substance.
2. When they have the same physical properties.
What are the variables that specify the state of a system?
- n (the amount of substance it contains);
- V (the volume it occupies);
- p
- T
Why the pressure of a gas is steady, even though the molecules are battering on the walls of the container without interruption?
Because the collisions are so numerous that they exert an effectively steady force, which is experienced as a steady pressure.
What is the standard pressure for reporting data?
1 bar
When do two gases of different pressures reach mechanical equilibrium?
- In a container with a piston, the gas that has the higher pressure will compress the gas of lower pressure.
- The pressure of the high-pressure gas will fall and the pressure of the low-pressure gas will increase.
- There will come a stage when the two pressures are equal and the wall will have no tendency to move.
- This condition of equality of pressure on either side of a movable wall is a state of MECHANICAL EQUILIBRIUM.
A fact: the perfect-gas temperature scale is identical to the thermodynamic temperature scale.
Different liquids expand to different extents, that is why thermometers constructed from different materials can show different numerical values of temperature.
A gas can be used to construct a PERFECT-GAS temperature scale that is independent of the identity of the gas.
Definition of Celsius scale
T/K = θ/°C + 273.15
How to write zero pressure and zero temperature in an absolute scale?
T=0 and p=0
NO UNITS!
However, t=0°C (because Celsius is not an absolute scale)
The state of a pure substance is defined by n, p, V, T, however, it is sufficient to specify only…
…three of the variables, so then the fourth is fixed (constant).
General form of an equation of state
p = f (T, V, n)
Perfect gas equation of state
p = nRT/V
a limiting law
Boyle’s Law
Boyle’s Law:
LIMITING LAW
pV = const
(when n,T - constant)
What specific graph can be plotted from Boyle’s Law?
An isotherm: y-axis: pressure (p) x-axis: volume (V) Looks like a hyperbola The higher the line, the HIGHER its temperature.
How to plot a straight line out of Boyle’s Law?
Plot: y-axis: pressure (p) x-axis: 1/V T - still constant Looks like a straight line Extrapolates from 0 (dashed line) The higher the line, the HIGHER its temperature.
Charles’s Law
Charles’s Law:
LIMITING LAW
V = const x T (when n, p - constant)
p = const x T (when n, V - constant)
What specific graph can be plotted from Charles’s Law?
n, p - constant
An isobar: y-axis: volume (V) x-axis: temperature (T) Looks like a straight line Extrapolates from 0 (dashed line) The higher the line, the LOWER its pressure.
What specific graph can be plotted from Charles’s Law?
n, V - constant
An isochore: y-axis: pressure (p) x-axis: temperature (T) Looks like a straight line The higher the line, the LOWER its volume.
What is an isotherm?
A line in a graph that shows the variations of properties at a single temperature.
What is an isochore?
A line in a graph that shows the variations of properties at a single volume.
What is an isobar?
A line that shows the variations of properties at a single pressure.
What is a perfect gas?
A gas that obeys the PERFECT GAS EQUATION OF STATE under all conditions.
When does a real gas behave more like a perfect gas?
The lower the pressure.
Expression for the (molar) gas constant.
R = k x Na
k - Boltzmann’s constant
Na - Avogadro’s constant
Avogadro’s Principle
Equal volumes of gases at the same temperature and pressure contain the same number of molecules.
In a perfect gas, all interactions between the particles are…
…not only all the same, but also all equal to zero!
The p, V, T surface
x-axis: volume (V)
y-axis: pressure (p)
z-axis: temperature (T)
(į mane)
1. The surface depicts all possible states of a perfect gas.
2. The gas cannot exist in states that do not correspond to points on the surface.
The combined gas law
pV/nT = pV/nT
gas 1) (gas 2
What does SATP stand for?
SATP: Standard ambient temperature and pressure
T = 298.15K (25°C)
p = 1 bar
What does STP stand for?
STP: Standard temperature and pressure
It’s an older version!
T = 273.15K (0°C)
p = 1 atm
Why according to Boyle’s law pV - const?
+ Molecular explanation
If a sample of gas is compressed to half its volume, the pressure increases twice (twice as many molecules hit the walls of the container).
Thus the numerical value of pV is still the same - constant.
Molecular explanation of Charles’s Law
Raising the temperature of a gas increases the average speed of its molecules and they collide with the walls more frequently and with greater impact.
Thus the molecules exert a greater pressure on the walls of the container.
The partial pressure pj of a gas J in a mixture
pj = xj p
pj - partial pressure of a gas J in a mixture
xj - mole fraction of a gas J in a mixture
p - total pressure of the mixture
The mole fraction xj of the component J in a mixture
xj= nj/n
nj - moles of J
n - total number of moles
The sum of partial pressures is…
…equal to the total pressure of the mixture.
The sum of mole fractions is…
…equal to the total number of moles of the mixture.
What is the definition of partial pressure in perfect gases?
Dalton’s Law
The pressure exerted by a mixture of (perfect) gases is also the pressure that each gas would exert if it occupied the same container alone at the same temperature.
What is mechanical equilibrium?
Mechanical equilibrium is the condition of equality of pressure on either side of a shared movable wall.
What is an equation of state?
An equation of state is an equation that interrelates the variables that define the state of the substance.
