Download Fundamentals of Physical Chemistry

Fundamentals of Physical Chemistry
Dr. Jaroslava Miksovska
CP 328
[email protected]
Textbook
Lecture 1
Introduction
Aim of the lecture:
1) Physical state of matter
2) Properties of matter
3) Properties of gases (ideal gas)
• Physical chemistry
A) physical properties of matter (composition,
structure, energy)
B) basis for modern methods of analysis
Energy capture and storage
Ligand binding to proteins
Structure of proteins
• States of matter:
A) gas
B) liquid
Macroscopic
Random
Fill container movement
No strong
intermolecul
ar forces
Well defined
surface
C) solid
Microscopic
Particles are
in contact,
move in
Fixed volume restricted
manner
Well
Particles
defined
trapped in a
shape
single
Fixed
position and
volume
oscillate
Physical state and its characterization
- Properties of matter in terms of state (gas, liquid solid ),
volume, temperature, pressure and amount
Mass – measure of quantity ( 1 kg = 103 g)
Volume – amount of space the sample occupies (liters (L), cm3)
Temperature – property that determine the direction of flow of energy
(Kelvin, oC),
T/K = θ/oC + 273.15
Objects are in thermal equilibrium if there is no flow of energy between
them
ZERO LAW OF THERMODYNAMICS
if object A is in thermal equilibrium with object B, and object B is in
thermal equilibrium with object C, then object C is also in thermal
equilibrium with object A.
• Chemical amount ( # of moles) – amount of
substance (mol)
n = m/M (m- mass, M – molar mass)
n = N/NA ( N – number of particles,
NA – Avogadro constant; NA = 6.022x1023 mol-1
for H2O (M= 18 g mol-1) the mass of one mole is 18 g and the mass of one molecule
is (18 g)/(6.02 × 1023) ≈ 3 × 10−23 g.
The Avogadro constant NA is related to the Faraday constant. The Faraday constant F
is the absolute value of the charge on one mole of electrons. Therefore F = NAe, where
e is the absolute value of the charge on one electron.
Each year in America, from 6:02 AM to 6:02 PM on 10/23, the
mole is celebrated by chemists, mathematicians and
physicists.
• Concentration
Molar concentration [J] = cJ = nJ/VJ (mol/L, M)
(VJ – volume of solution = Vsolute + Vsolvent)
Molality bJ = nJ/msolvent (mol/kg)
Molar fraction: fJ= nJ/n
(unitless)
Force (F)
Mercury barometer
F = ma ( m= mass; a = acceleration); vector quantity
Units: 1 N = 1 kg ms-2
Pressure (p)
p = force per area; p = F/A (A – area)
Units: kg m-1 s-2
1 Pa = 1 Nm-2 = 1 kg m-1 s-2
1 bar = 105 Pa
1 atm = 101.325 kPa = 1.013 25 bar
760 Torr = 1 atm
1 Torr ~ Hg
Mercury barometer
p = gh (-density; h – height, g – acceleration of free fall – 9.81 ms-2)
• Energy – capacity to do work
1 J = kg m2 s-2
a) kinetic energy – energy of a body due to the motion
Ek = ½ mv2 (m – mass, v – speed)
b) potential energy – energy of a body due to its position;
depend on the forces acting on a body
in the gravitation field: Ep = mgh
for change particles
Ep = Q1Q2/(4or)
Q – charge;
o – vacuum permitivity (8.854 x 10-12 J-1C2m-1)
r- distance between particles
radiation energy E = Nh (h – Planc constant =
6.6252x10- 34Js; - frequency)
E = Ek + Ep (energy can be converted between
different form but total energy remind constant)
Energy conversion and energy exchange
Solar energy is:
absorbed by desert; water and converted to heat
absorbed by solar panels and converted to electric energy (use to do work)
absorbed by plants and converted to chemical energy (chemical bond)
Thermodynamics deal with
interchanges between different form of
energy
OPEN SYSTEM
Open systems can
exchange both matter and
energy with an outside
system.
CLOSE SYSTEM
Closed systems exchange
energy but not matter with
an outside system.
ISOLATED SYSTEM
Isolated systems can
exchange neither energy
nor matter with an outside
system.
Equation of state
State of matter is characterized by:
Volume, Temperature, Pressure and amount of substance (n)
These parameters are NOT independent
p = f(V, n, p, T)
Equation of state - equation that describes the state of matter
Perfect gas law:
pV = nRT
R – gas constant
R = 0.08206 atm L K-1 mol-1
R = 8.314 J K-1 mol-1
Boyles law V  1/P (at constant T)
Charles and Gay-Lussac law V  1/T (at constant p)
Avogadro’s law V  n (at constant P and T)
p1V1/T1 = p2V2/T2
Combined gas equation
Perfect gas:
consisting of identical particles
Particles: occupy negligible volume
undergo perfect elastic collision with
each other
no intermolecular forces
no intramolecular storage of energy
energy consist of kinetic energy
t = -273.15 oC = 0 K
Charles law
V
p1
Absolute
zero
The lowest
p3 attainable
temperature
p2
SATP – standard ambient p & T
p = 1 barr and T = 298 K
STP - standard p & T
p = 1 atm
T = 273 K
Extensive properties:
properties whose values
depend on amount of
substance
Intensive properties: values
does not depend on the
amount of substance
Molar volume (Vm)
Vm = V/n = RT/p
t
θ (oC)
• Dalton law of partial pressure
Total pressure of a system composed of two or more gases the total pressure
correspond to the sum of individual pressures each gas would exert if it occupies
the same volume
pT = p1+p2+p3+... =  pi
Partial pressure of i-th component can be expressed as:
p i = x i pT
See the derivation
• Real gases
Perfect gas law – holds for real gases at low p (p<10 atm) and high T
At high pressure – deviation from ideal behavior
For a perfect gas: pVm = RT and thus pVm/RT = 1
Real gases:
Compressibility factor Z
Z  1 Z = pVm/RT = Vm/Vm with Vom = molar volume of perfect gas
Z > 1 Vm of gas is larger than Vm of perfect gas due to the repulsion between molecules
Z < 1 attractive forces are dominant
• Equation of state for real gas
Z = 1 + B/Vm + C/Vm2 + ….
B – second virial coefficient
C- third virial coefficient
(Virial: comes from that Latin word
vis, viris, meaning force)
Determined experimentally from
the plot of p V T plots for real gases
pVm/RT = 1 + B/Vm + C/Vm2 +…
p= RT/Vm (1 + B/Vm + C/Vm2 +…)
p = nRT/V (1 + B/Vm + C/Vm2 +…)
B/Vm >> C/V2m
Virial equation of state
• Van der Waal equation of state
p= nRT/(V-nb) – a(n/V)2
Gas
a (Pa m3) b(m3/mol)
nb term - is the very small approximate volume
occupied by
the molecules themselves
Helium
3.46 x 10-3 23.71 x 10-6
Neon
2.12 x 10-2 17.10 x 10-6
a(n/V)2 term - a is a positive proportionality
constant, taking into account that the pressure
is reduced due to the attractive forces
Hydrogen 2.45 x 10-2 26.61 x 10-6
(p + a(n/V)2)(V-nb) ) = nRT
Van der Waals equation is valid over
the wider range of volume and
pressure
Provides molecular interpretation of
equation of state
Carbon
dioxide
Water
vapor
3.96 x 10-1 42.69 x 10-6
5.47 x 10-1 30.52 x 10-6
Value of a parameter correlates
with boiling point
• Homework
1. At STP 0.28 L of a gas weights 0.400 g. Calculate the molar mass of the gas.
2. Dissolving 3.00 g of an impure sample of CaCO3 in an excess of HCl produces 0.656 L
of CO2 (measured at 20 oC and 792 mm Hg). Calculate the percent by mass of CaCO3 in
the sample.
3. Nitrogen forms several gaseous oxides. One of them has a density of 1.27 g L-1
measured at 764 mm Hg and 150 oC. Write the formula of the compound.
4. Nitrogen dioxide can not be obtained in a pure form in the gas phase because it
exists as a mixture of NO2 and N2O4. At 25 oC and 0.98 atm, the density of this gas
mixture is 2.7 gL-1. What is the partial pressure of each gas.
5. Two bulbs of volumes Va and Vb are connected by a stopcock. The number of mole
of gases are na and nb, and initially the gases are at the same pressure, P, and
temperature, T. Show that the final pressure of the system, after the stopcock has been
open is equal P. Assume idea-gas behavior.
6. A flask contains a mixture of two ideal gases, A and B. Show graphically how the
total pressure of the system depends on the amount of A present; that is plot the
total pressure versus the mole fraction of A. Do the same for B on the same graph.
The total number of moles of A and B is constant.
7. Problems from the textbook: 1.3 (not included); 1.6 (1.10); 1.8 (1.12); 1.30; (1.35)
1.31 (1.36);.32 (1.37), 1.33 (1.39)