Chapter 1: 1.2 The Ideal Gas Law Flashcards
Avogadro’s law states that one mole of any ideal gas always…
Occupies the same volume at a given temperature and pressure, regardless of the gas in question
According to Avogadro’s Law, equal volumes of different gases at the same temperature and pressure…
Contains the same number of moles
Define:
Molar volume of a gas
Volume occupied by one mole of any gas
Define:
STP
Give units
Standard temperature and pressure
= 1 atm (101.324 kPa) and 273.15 K
Define and state the formula for:
Density
(in terms of gases)
Mass per unit volume
d = m/V
Show the relation and state the formula for:
Mass, molar mass, and moles
m = MM * n
What are the two forms of the ideal gas equation that can be used to derive relationship between gas density and its molar mass?
d = (MM)P / RT
OR
MM = dRT / P
State the relationships between gas density/molar mass at constant temperature
Gas density is directly proportional to its pressure
State the relationships between gas density/molar mass at constant temperature AND pressure
Density is related to molar mass of the gas
Define and state the formula for:
Dalton’s Law of Partial Pressures
A mixture of gases behaves as a single gas
PV = nRT or P(total) * V(total) = n(total) * R * T
Define:
Dalton’s Law of Partial Pressures
The total pressure exerted by a mixture of gases is the sum of all the partial pressures of these gases
State the formula for:
Mole fraction of any one gas in a mixture
X(i) = n(i)/n(T)
[mole fraction = # of moles of individual constituent / # of total moles in mixture]
State the proportionality in:
Mole Fractions
State constants
Pressure (P) is directly proportional to moles (n)
At constant temperature (T) and volume (V)
What must the mole fraction (ratio) equal to?
Must equal to the pressure ratio
What does the sum of all mole fractions equal?
1
At constant temperature and pressure, what is the relation between volume and moles?
Directly proportional
Define:
Vapour pressure
The partial pressure of water vapour
What does the vapour pressure of water depend on?
Only depends on the temperature of the water
Does higher temperature mean more or less vapour pressure?
More
Define:
Boiling point
Temperature at which the vapour pressure equals the atmospheric pressure
(Explains why water boils at lower temperatures at higher altitudes)
True or False:
Solvents that are more volatile (have lower boiling points) have lower vapour pressures
False, solvents that are more volatile have higher vapour pressures
Define:
Average Molar Mass of a mixture of different gases
The weighted average of the molar masses of the different components
State the formula for:
Average molar mass of a gas mixture
MM (with a line above to represent weighted average) = XaMMa + XbMMb + XcMMc …
State the assumptions of:
Kinetic Molecular Theory of Gases
- Size of particles is negligible
- Molecules are point particles (only Ek)
- Elastic collisions
- No intermolecular forces
- Kinetic energy (Ek) is proportional to temperature (Ek [line above] = 1/2mu^2 [u has line])
What do bars/lines above values mean?
Average values
What does the term u[bar]^2 mean? How is it found?
Mean-square speed
Found by taking an average of the squares of the speeds of the molecules
What are the factors that determine the pressure of a gas in a container?
- Mass of each molecule (m)
- Speed of the molecules (u)
- Frequency of collisions/the number of collisions per second
What does the frequency of collision relate to?
- The number of molecules (N)
- The volume of the container (V)
- The speed of the molecules (u)
State:
The basic equation of the kinetic theory of gases
P = 1/3 (N/V)(mu[bar]^2)
State the proportionalities of:
Mean-square speed of gas molecules, temperature, molar mass
Directly proportional to the temperature
Inversely proportional to the molar mass
True or False:
If a gas is heated the molecules will move faster
True
True or False:
If two gases are at the same temperature, the lighter gas molecules move slower, on average, then the heavier gas molecules
False, the lighter gas molecules move faster, on average, than the heavier gas molecules
What does the Maxwell-Boltzmann distribution govern?
The distribution of the speeds of the molecules
State the term and formula for:
The more commonly used form of the mean-square speed term
Root-mean-square (rms) speed
(sqrt)(3RT/MM)
State the proportionality between:
rms speed and square root ratio of molar masses
The rms speed for the two gases is inversely proportional to the square root of the ratio of their molar masses
What are the units for rms speed? In this scenario, state the units for molar mass and R
rms speed: metres per second
Molar mass: kilograms
R: 8.314 J/mol K OR 8.314 kg m^2/s^2 mol K
Define:
Effusion
The flow of gas molecules at low pressures through tiny pores or pinholes in a container
What is the rate of effusion defined as?
Number of moles of the gas escaping the container per unit of time
State:
Graham’s Law
The rate of effusion of a gas is inversely proportional to the square root of its molar mass
State the proportionality of:
Rate of effusion, Molar Mass
Rate of effusion is inversely proportional to the square root of its molar mass
r(effusion) proportional to 1/(sqrt)MM
How is Graham’s Law written when two gases A and B with equal partial pressure effuse through a porous material or a small hole?
r(A)/r(B) = (sqrt)[ MM(B) / MM(A) ]
True or False:
Lighter molecules effuse faster than heavier molecules
True
What is the special about the gas that emerges from the container in effusion?
It is enriched in the lighter component
What does the quantity f = (sqrt) [MM(B) / MM(A)] called?
Enrichment factor (how much of one gas is part of the effusion)
