Physical Chemistry Exam 1
Principle of Corresponding States
- different gases have same reduced compression factors if they have the same reduced variables (volume & temp) -real gases :samereduced temperature and volume = same reduced pressure
If Vf > Vi
- gas expands - work done to expand = system loses internal energy w < 0
Heat capacity at constant pressure
Cp = (∂H/∂T)
Enthalpy (H)
- The heat content of a system at constant pressure - state function
If Z = 1
- gas is ideal -no molecular forces
∆H0( A -> B) =
-∆H0(B -> A) * bc state function
Standard Enthalpy Change ∆H0
- change in enthalpy for a process where initial and final substances are in standard states - sum of H products - sum of H reactants
standard reaction enthalpy ∆rH0
- change in enthalpy when reactants in standard states change to products in standard states ex: CH4 (g) + 2O2 (g) ---> CO2 (g) + 2H2O (l) ∆rH0 = -890 kJ/mol
Van der Waals Equation
- describes behavior of real gases, accounts for attractive forces and volume p =(nRT/V - nb ) - a(n/V)^2 or p = (nRT/ Vm - b) - a/Vm^2 a = pressure correction, magnitude of attractive forces between particles b = volume correction, related to particle size
Virial Equation
- equation of state for real gases that expresses the compression factor as a power series of either the pressure or molar volume - compression factor acts linear to pressure Z = 1 + B'P B' = temperature dependent constant for specific gas - B' < 0 at low temp - B' > 0 at high temp
Temperature
- indicates the flow of energy in the form of heat through thermally conductive, rigid wall - flows from higher to lower temp
First Law of Thermodynamics
- internal energy of an isolated system is constant - energy cannot be created nor destroyed
If Z > 1
- occurs at high pressure -repulsive forces = expansion
If Z < 1
- occurs at low pressure - attractive forces = compression
Van der Waals Loops
- oscillations which occur for temperatures below the critical temperature - suggests pressure increases with volume ( violates Boyle's) - Maxwell Constructions: replace loops with horizontal lines
Path Functions
- properties that relate to the preparation of the state of the substance ex: w & q
Repulsive Forces
- short range interactions - occurs at HIGH PRESSURE, molecules in close contact - gas is less compressible than ideal bc repulsive forces drives the molecules apart
Standard Enthalpy of Transition ∆trsH0
- standard enthalpy change accompanying a phase change
∆rH0 Formula
- sum of forming and unforming elements \ ∆rH0 = Σprod ∆rH0 + Σreactants ∆rH0
What changes occur when a gas expands adiabatically?
- work is done - internal energy falls - temperature of the working gas falls - kinetic energy of the molecules falls w/ avg speed of the molecules
Hess' Law
- ∆H0 of an overall rxn is the sum of the ∆H0's of the individual rxns into which the overall rxn may be divided
A sample consisting of 2.00 mol He is expanded isothermally at 22C from 22.8 dm3 to 31.7 dm3 reversibly. Calculate W
-1.62 x 10^3 J
85.0 moles of Argon undergo an isothermal, reversible expansion from an initial volume of 75.0 m3 to a final volume of 175.0 m3. The temperature is a constant 400.0 K. Calculate Won, the work done on the system, and report the answer in J.
-239,525.17 J
The Joule-Thompson coefficient for a certain freon gas is 4.7 oC atm-1. Calculate the change in temperature( oC) if the freon is subjected to a 7.4 atm pressure drop.
-34.78 C
Towards the end of WWII the Nazis employed rocket-powered fighter planes (with minimal success). The hydrazine/hydrogen peroxide reaction powering the planes, along with the Heats of Formation in kJmol^-1 appear below: N2H4 + 2 H2O2 → N2 + 4 H2O 50.63 -187.78 0 -241.82 Calculate ∆HRXN for this reaction.
-642.35
Thermal Equilibrium
-flow of energy continues until both objects are of equal temperature -established if no change of state occurs when two objects are in contact with one another through a diathermic boundary
Critical Point
-horizontal points of isotherms merged to single point - critical constant s: temp, pressure, and molar volume @ CP
Attractive Forces
-long range interactions - occurs @ LOW TEMP, molecules so slow they can be captured by one another -gas is more compressible than ideal gas bc attractive forces pull molecules together
State Function
-properties are independent of how the substance is prepared & are functions of variables like P and T - define the state of the system ex: U & H
100.0 moles of CO2 gas undergoes a reversible adiabatic expansion from 0.400 L to 4.000 L. The initial temperature is 298.2 K. Calculate the final temperature (K) of the gas. C v,m (CO2) = 28.80 Jmol^-1K^-1
153 K
Mole Fraction
xj = nj/ntotal
Cp @ measurable changes in T
ΔH = Cp*ΔT
With constant V & no additional work, ΔU =
ΔQ
Joule-Thompson Effect μ
ΔT = μ Δp p1 > p2 μ = (∂T/∂P)
ΔU Adiabatic Expansion
ΔU = CvΔT
Internal Energy Formula
ΔU = ΔQ + ΔWexp + ΔWe - ΔQ = heat transferred - ΔWexp = expansion work - ΔWe = extra work (electrical current)
Isothermal Compressibility kT
ΔV = -kTΔpV kT = -1/v*(∂V/∂p)
Thermal Expansion Coefficient α
ΔV = α ΔTV α = 1/V*(∂V/∂T)
Force on outer face of piston (formula)
F = pex*A - pex = exertnal pressure
Combined Gas Law
P1V1/T1=P2V2/T2
Boyle's Law
P1V1=P2V2 - at constant T & n
Ideal Gas Law
PV = nRT
Ideal Gas Constant (R)
constant of proportionality
An equation of state of a non-deal gas is P(V-nb) = nRT. The coefficient of thermal expansion, α, of any gas is defined as this. Therefore α for this gas is: α = 1/V*(∂V/∂T) a) 1/T b) R/T + bP c) nRT + nb d) (R/P)/((RT/P)+b)
d
Changes in H @ constant V
dH = (∂H/∂P)dp + (∂H/∂T)dT
Cp @ infinitessimal changes in T
dH = Cp*dT
Change in Volume (expansion work formula)
dV = Adz
Endothermic Process in Diathermic Container
decreases temperature of surroundings
Adiabatic Boundary
does not allow the flow of energy (heat) between two objects
Exothermic Process in Diathermic Container
increases temperature of surroundings
Dalton's Law of Partial Pressures
the pressure exerted by a mixture of gases us the sum of the partial pressures of the gaseous components - p = pa + pb + ...
Calculate Won, the work done on the gas, when a sample of CO2 is compressed by a constant external pressure of 75 Pa. The volume of the gas decreases by 225 m3. Notice that one J = 1 Pa*m3. Report your answer in J
16875
Baker, California claims to be the home of the world's largest thermometer. Assume (falsely) that the working fluid is mercury and that the volume of mercury in the thermometer is 10.00 L. Mercury has a coefficient of thermal expansion α equal to 1.82 x 10-4 K-1. Calculate the change in volume of the mercury for a 10.0 K increase in temperature. Report your answer in mL.
18.2 mL
A perfect gas undergoes isothermal compression, which reduces its volume by 2.20 dm3. The final pressure and volume of the gas are 5.04 bar and 4.65 dm3, respectively. Calculate the original pressure of the gas in the bar.
3.42 bar
The average college student exhales 800.0 L of air per hours. he partial pressure of water vapor is 0.0725 atm in air exhaled at 310.K. Assume ideal gas behavior, and calculate the mass of water vapor (in g) exhaled per hour by one student
41.0 g/hr
What is the unit of b? p = nRT/Vactual = nRT/V - nb a) dm3/ mol b) dm3 mol c) dm6/mol2 d) atm dm3/mol e) atm dm6/mol2
A
Calculate the amount of heat (in kJ) necessary to raise the temperature of 47.8 g benzene by 57.0 C. The specific heat capacity of benzene is 1.05 J/g*K
2.86 kJ
100.0 g of liquid He evaporate inside an NMR. Calculate the number of Joules of heat that is absorbed. ∆Hvap (He) = 82.0 J mol-1
2050
How much heat in J is required to raise the temp of 1.0 kg of H2O by 60C? Cp,m (H2O) = 75.29 J mol^-1K^-1. Molar Mass (H2O) = 18.015 gmol^-1
250,715.7 J
C Value
C = Cv,m / R
Heat Capacity @ constant volume
Cv = (∂U/∂T) or dU = Cvdt
What is the possible unit of thermal expansion coefficient α? α = 1/V*(∂V/∂T) a) L^-1*K^-1 b)L^-1*atm*K^-1 c)L^-1*atm*K^-1 d) K^-1
D
Closed System
only energy (work and heat) can flow in and out of system
Partial Pressure of a Perfect Gas
pj = njRT/V
Standard State
pure form of a substance @ specified T, P = 1 bar
Calorimeter Constant C (formula)
q = CΔT
Heat at Constant Pressure (qp)
qp = Cp*ΔT
Small Heat Capacity
small supply of heat, large ΔT
Isothermal Reversible Expansion
system is in contact with constant thermal surroundings (bath or heating element)
Boyle Temperature
temperature at which B' is 0 - real gas behaves ideally
How does a calorimeter work?
1. Rxn conducted in constant volume bomb 2. Bomb placed in stirred water bath, forms calorimeter 3. Calorimeter placed in second water bath, temp is continuously adjusted to temp of bomb bath = adiabatic system 4. Rxn either releases or absorbs heat = ΔT of calorimeter
How can the internal energy of a system be changed?
1. Doing work to the system (w) 2. Energy transferred (heat) to the system (q)
When 229 J of energy is supplied as heat to a gas at constant volume, the temperature of the gas increases by 2.55 C. Calculate Cv ar constant volume.
90 J/K
Enthalpy Formula
H = U + PV ΔH = Δq
0th Law of Thermodynamics
If system A and B are in thermal equilibrium with system C, then A and B are in thermal equilibrium with one another
Infinite Heat Capacity
at a phase transition, energy changes phases
ΔT Adiabatic Expansion
Tf = Ti(Vi/Vf)^1/c
Charles's Law
V1/T1=V2/T2 - V = constant * T @ constant n & P - p = constant *T @ constant n @ V
Work Adiabatic Expansion
Wad = Cv*ΔT
Compression Factor Z
Z = Vm / V0m Vm = molar volume of real gas V0m = molar volume if gas were ideal also: Z = pVm/ RT
Ideal Gas Definition & Characteristics
a hypothetical gas, or collection of molecules and atoms, which undergo continuous random motion. - particle speed increases with temperature -molecules far apart, only interactions are infrequent elastic collisions with walls of container & particles -NO intermolecular forcews (dipole-dipole, disperson) -particles are point masses, no volume
The constant-pressure heat capacity of a sample of an perfect gas, 1 mol, was found to vary with temperature according to the expression Cp /(J K−1) = 20.17 + 0.4001(T/K). Calculate q, w, ΔU, and ΔH when the temperature is raised from 0°C to 100°C (a) at constant pressure, (b) at constant volume.
a) q = ΔH = 14.9 x 10^3 J, w = -831 J, ΔU = 14.1 kJ b) ΔH = 14.9 kJ, ΔU = 14.1 kJ, w = 0, q = +14.1 kJ
Real Gas
actual gas that does not obey the gas law exactly bc of molecular interactions deviations occur @ high pressure and low temperature
Diathermic Boundary
allows the flow of energy between two contacting objects resulting in a change of state to occur
Work required to move and object over distance dz (formula)
dw = -Fdz ** negative sign, system moves against opposing force = decrease in U - find integral
Work done against external pressure (formula)
dw = -pex*dV
Avogadro's Principle
equal volumes of gases at the same temperature and pressure contain equal numbers of particles V = constant * n @ constant p & T
Pressure
force applied per unit area -pressure exerted by a gas is caused by the collisions within the walls of a container. more collisions = greater pressure
Endothermic Process
heat absorbed
Exothermic Process
heat released
Large Heat Capacity
large supply of heat, small ΔT
Isobars
lines of constant pressure
Isotherms
lines of constant temperature
Isochores
lines of constant volume
Expansion Work System
massless, frictionless, rigid, perfectly fitting piston of area A
Open System
matter and energy can flow in and out of system
Compressibility
measure of the nonideality of real gases due to presence of molecular interactions -expressed by compression factor Z
Isolated System
nothing can flow in and out of system
Internal Energy
total energy of a system at any given time - total kinetic and potential energy of the molecules in a system - state function: only depends on current state, not preparation of state -extensive property: dependent on matter delta U = q + w
Isotherm R. Expansion Work Formula
w = -nRT* ln(Vf/Vi)
