Phases Flashcards
What are some basic differences between solids, liquids, and gases?
Solids have greater intermolecular forces or attraction and much less space in between molecules
- Solids favored at high pressures and compression
Gases have lower intermolecular forces and much more space
- Higher kinetic energies of molecules (and T) are likely to break free of intermolecular bonds and exist in liquid or gas phase
Real gas
Typical real gas is a loose collection of weakly attracted atoms or molecules moving rapidly in random directions
Volume of molecules is ~0.1% of total volume occupied by gas
Fairly spread out at STP
Attractive forces between molecules decreases as distance increases (attractive forces can almost be ignored)
Average speed of O2 is ~481 m/s, mean free path is 10^-4 mm, 2.5 billion collisions / s
Why is a mixture of compounds in gas phase homogeneous regardless of polarity differences?
Molecules are so far apart that they exert negligible attractive or repulsive force on each other
However, density at lower temperatures can cause denser gases to settle beneath less dense gases
Hot air rises because it is less dense than cold air
Kinetic Molecular Theory
An ideal gas lacks certain real gas characteristics:
1. Gas molecules have no size, (0 molecular volume)
2. Gas molecules do not exert attractive or repulsive forces on one another
3. Gas molecules have completely elastic collisions
4. Avg KE of gas molecule is directly proportional to temperature of gas
Ideal gas molecules use all of energy to collide with sides of container and exert pressure
Ideal Gas Law
PV = nRT
R is universal gas constant = 0.08206 L atm /K mol = 8.314 J /K mol
Simple Mercury Barometer
Measures atmospheric pressure
Tube of mercury that is closed at one end is inverted and placed in an uncovered mercury bath open to the atmosphere
Some mercury will fall down into bath, remainder suspended above in the tube
Amount of mercury left in the tube is related to atmospheric pressure pushing down on the mercury bath by:
P_atm = /rho g h
/rho is density of mercury in kg /m^3, g is gravitational constant 9.8 m/s^2, P_atm is measured in Pascals
Historically, height of mercury so important that it became own units, mm Hg which are equivalent to torr
760 torr = 760 mm Hg = 1 atm
What is the density of water?
/rho_H2O = 1000 kg/m^3 = 1 g/mL
Boyles Law
PV = constant
Pressure and volume are inversely proportional
Charle’s Law
V / T = constant
Volume of gas directly proportional to temperature
Think of a constant pressure situation, such as in a balloon
The atmospheric pressure will always necessarily equal the pressure exerted by the balloon on the atmosphere
If not, the balloon would be expanding or contracting
Avogadro’s Law
V / n = constant
Volume is directly proportional to moles of gas
Balloon would expand if more air added to the balloon
Isovolumetric Process
Change in volume of a process is zero
Therefore the work done is zero
Delta E = w + q = 0 + q
Delta E = q
Adiabatic Process
A process that occurs without the transfer of heat, such as with a heavily insulated system
No heat transfer:
Delta E = q + w = w
If gas expanding, w < 0
Gas does work on environment and loses kinetic energy by expansion, decreasing temperature, and pressure also decreases with decreased T and increased V
Isothermal Process
Gas remains in thermal equilibrium with surroundings, heat can be exchanged between gas and surroundings
No change in internal energy
Delta E = q + w = 0
If surroundings heated, both temperature and volume of gas will increase in accordance with gas law
Work is done by the gas during expansion, but compensated for by transfer of heat
For an ideal gas, work is equal to internal energy
Standard molar volume
AT STP, one mole of any ideal gas will occupy that standard molar volume of 22.4 L
P = 1 atm, T = 273K (STP)
Partial Pressure
(Of a particular gas) is total pressure of gaseous mixture multiplied by the mole fraction of the particular gas
P_a = \Chi_a P_total
P_a is partial pressure for gas a, \Chi_a is mole fraction of gas a
In a mixture of gases, each gas contributes to pressure in same proportion as it contributes to number of molecules of gas
Mole fraction: number of moles of gas a divided by total number of moles of gas in sample
Dalton’s Law
Total pressure exerted by a gaseous mixture is sun of partial pressures of each of its gases
P_total = P_1 + P_2 + P_3 + …
Partial Pressure Equilibrium Constant
Equilibrium constant can be written in terms of partial pressures for reactions involving gases
K_p = P_C^c P_D^d / P_A^a P_B^b = products^coeff / reactants^coeff
To convert between K_p and K_c:
K_p = K_c (RT)^\delta n
\delta n: sum of coefficients of products minus the sum of the coefficients of reactants
Partial pressure equilibrium constants ONLY vary with temperature as with K_c
When do real gases deviate from ideal gas behavior?
When their molecules are close together either due to low temperatures or high pressures
Generally deviate above 10 atm
Van der Waals’ equation
[P + (n^2 a / V^2)] (V - nb) = nRT
Approximates real pressure and real volume of a gas, where a and b are constants for specific gases
Variable b: accounts for actual volume occupied by a mole of gas
Variable a: reflects strength of intermolecular attractions
Generally both increase with molecular mass and molecular complexity of a gas, so complex gases deviate significantly from ideal behavior
Explain the deviations from ideal gases that Van der Waals’ expresses
Molecules of real gas do have volume, so volume must be added to ideal volume:
V_real > V_ideal, where V_ideal is calculated from PV = nRT
Molecules in a real gas do exhibit forces on each other (mostly attractive):
Gas molecules are pulled inward toward center of gas and slow before colliding with container walls (strike the container wall with less force than predicted by kinetic molecular theory, and thus exert less pressure):
P_real < P_ideal, where P_ideal is calculated from PV=nRT
If PV/RT is greater than 1 for one mole of a real gas, what does this mean? If PV/RT is less than 1 for one mole of real gas, what does this mean?
For greater than 1, this means the contribution of the volume of the gas itself is contributing more to deviations from ideal gases (increased volume in ratio)
For less than 1, this means that the deviation due to intermolecular forces must be greater than the deviation due to molecular volume
What are some general rules of thumb for what molecules are gas at room temperature, and which tend to be liquids or solids?
The more polar a molecule, the greater the dipole moments, and consequently the stronger the intermolecular forces, and so the more likely it is to be liquid or solid at room temperature (e.g. H2O)
The larger a molecule, the more likely it is to have strong intermolecular forces, independent of polarity
Simplest alkane, methane (CH4) is a gas at STP, C6H14 is a liquid, and eicosane (C20H42) is a solid
Heat Capacity
Added energy required to increase the temperature of a given substance by one Kelvin (or equivalently, one degree Celsius)
Different substances can absorb different amounts of energy before their temperature increases a certain amount
C = q / delta T
Remember that heat is a process of energy transfer, not something that can be stored so ‘Internal energy capacity’ would be a better name
Two types of heat capacities for a substance
Constant volume heat capacity (Cv) = q / delta T_{constant volume}
If volume constant, no PV work and all energy change must be in form of heat
None of energy going into system can escape as work done by system
Constant pressure heat capacity (Cp) = q / delta T_{constant pressure}
When pressure is held constant, and substance is allowed to expand, some energy can leave system as PV work done on surroundings as volume changes
Cp > Cv because delta T is greater for Cv than for Cp, difference only significant for molecules in gas phase
