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P Chem test 1

gases assume the ____ and ____ of their containers volume and shape
when pressure is applied to a gas, its volume decreases; gases are highly compressible
gases form what type of mixtures homogeneous
A gas's density is what compared to liquids and solids lower
characteristic properties of gases arise because individual molecules are relatively far apart (don't feel inter molecular attractions as much)
pressure equals force/area = mass*acceleration/(length*width) = kgm/s^2m^2 therefore 1 N/m^2 = 1 Pa = kg/ms^2
atmospheric pressure equation P = h(density)g
standard atmospheric pressure 1 atm; the pressure that supports a column of mercury exactly 760 mm high at 0 degrees Celsius at sea level
how can a measure of volume be a measure of pressure? P=h(density)g = 760 X10^-3 m*(1.36X10^4 kg/m^3)*9.81 m/s^2 = 1.01X10^5 Pa because density mercury = 13.6 cm^-3
perfect gas equation of state PV=nRT
perfect gas the absence of molecular interactions
ideal gas mixtures in which all the molecular interactions are the same but not necessarily zero
Boyle's law PV = constant; P proportional to 1/V
isotherm constant temperature
isobar constant pressure
Charles's Law V proportional to T
absolute zero 0 K; -273.15 degrees Celsius; theoretically lowest attainable temperature
why does some ideal gas data have to be extrapolated gas-liquid phase change
Avogadro's Law V proportional to n
density and the ideal gas equation PV = nRT; d = M/V ; d= PM/RT
One of the most variable constituents of air is water vapor, and the humidity it causes. The presence of water vapor results in a lower density of air at a given temperature and pressure. Why? P,V,n,T; P & T constant; n increase; % of H2O Molar Mass in air decrease (lighter than other constitutes of air); d = PM/RT; RTP constants therefore M decreases
Dalton's law of partial pressure the total pressure of a mixture of gases = the sum of the pressure that each would exert if it were present alone; Pt = Pa + Pb +...
The pressure exerted by a particular component of a mixture of gases is called the partial pressure of that gas
Pj = xjP is what partial pressure of a gas equation where xj = nj/ntotal
How is the pressure exerted by N2 gas affected when some O2 is introduced into a container if the temperature and volume remain constant? pressure of N2 won't change but the total pressure will
Kinetic Molecular Theory assumptions 1 & 2 1. gases consist of large # of molecules in continuous, random motion; 2. combination of volumes of all the molecules of the gas is negligible relative to the Vtotal in which the gas is contained (molecules can be considered as 'points'
Kinetic Molecular Theory assumptions 3-5 3. intermolecular forces are negligible; 4. collisions are perfectly elastic (PE = 0 b/c of #3); 5. average kinetic energy is proportional to the absolute temperature
pressure of a gas is caused by collisions of the molecules with the walls of the container; container in different areas has varying levels of pressure but if you take the average it feels constant; magnitude determined by how often & how forcefully they hit the wall
explanation of temeprature absolute T of a gas is a measure of average KE of its molecules; 2 different gases are at the same T their molecules have the same average KE; if the absolute T doubles, the average KE doubles
Consider three samples of gas: HCl (at 298K), H2 (at 298K), and O2 (at 350K). Compare the average KE of the molecules in the three samples. HCl and H2 will have the same average KE, O2's will be higher
Kinetic model pressure volume equation pV = (nMc^2)/3
root mean square speed c= <v^2>^0.5
Maxwell Distribution of Speeds we can't determine an exact speed of a molecule we need a Gaussian Distribution
Normal Gaussian Distribution equation e^(-ax^2)
Why is the Maxwell distribution of speed a shifted Gaussian curve v^2 term
do all molecules travel at the same speed nope that's why we have a distribution
Maxwell distribution of speeds f(v) = 4pi (M/2piRT)^3/2 v^2 *e^(-Mv^2/2RT)
Interpretations of Maxwell Distribution M & T are the only 2 things that can change; v is just your placement n x-axis
At high temperatures, a __________ fraction of the molecules can be expected to have high speeds than at low temperatures so the scewed Gaussian shifts right higher
will heavy molecules be likely to be found at very high speeds not really; light molecules are more likely to move faster than heavy molecules; the fraction of heavy molecules will move slwer than the fraction moving @ a faster speed
how do you use Maxwell's distribution of speed? calculate the fraction in a range of speeds that is too wide to be treated as infinitesimal; fraction range v1 to v2 use an integral
mean speed c = v1 + v2+.../N ; sqr(8RT/piM)
most probable speed sqr(2RT/M) ; speed for which f(v) is a maximum (peak of a curve)
Diffusion the spread of a gas throughout open space; the process by which the molecules of different substances mingle with each other
solids and diffusion the atoms of two solids diffuse into each other when the two solids are in contact, but the process is very slow
liquids and diffusion the diffusion of a solid through a liquid solvent is much faster but mixing normally needs to be encouraged by stirring or shaking the solid in the liquid (the process is then no longer pure diffusion)
gases and diffusion gaseous diffusion is much faster; it accounts for the largely uniform composition of the atmosphere
effusion the escape of a gas through a small hole, as in a puncture in an inflated balloon or tire
Graham's Law of Effusion at a given T and p, the rate of effusion of a gas is inversely proportional to the square root of its molar mass
rate of effusion is proportional 1/M^0.5
Graham's Law r1/r2 = sqr(M2/M1) at constant temperature and ressure in containers with identical pinholes
Graham's Law explained the only way for a molecule to escape from its container is for it to 'hit' the pinhole. The faster the molecules are moving, the greater is the likelihood that a molecule will hit the pinhole and effuse
which will effuse first He or N2 He has smaller M, therefore effuses faster than N2
Diffusion and Mean Free Path open a vial of perfume at one end of a room. a few minutes elapse before the scent is detected at the other end of the room. this is because of mean free path
which to dyou smell first ammonium and HCl HCl is heavier than NH4, but HCl is moving faster than the NH4 particles
RMS Speed sqr(3RT/M)
Molecular Collisionsnm kintetic thery can be used to determine the collisional frequency between gaseous particles. Understanding the frequency of olecular collisions is important in describing chemical phenomena like rates of chemical reactions
mean free path average distance traveled by a molecule between collisions. Varries with pressure; V is constant, P is changing, n can change, T is usually held constant; ex. shopping mall @ Christmas? on a Tuesday?
z-collision frequency the average rate of collisions made by one molecule in a given time interval divided by the length of the interval; ex 10 collisions per second, z = 10 s^-1
time of flght 1/z; average time that a molecule spends in flight between collisions
assumpion made for collision frequency and time of flight hard spheres with radius d and two molecules will hit another molecule
collision cross-section sigma=pid^2 =pi(r1 + r2)^2
mean free path lambda = (RT)/(2^0.5 NasigmaP
collision frequency for one type of particle (1/2^0.5)(P1Na/RT)^2sigma(8RT/piM1)^0.5
effect on the mean free path of the gas molecules in a sample of gas: a. increasing pressure; b. increasing T a. mean free decreases; change b/c T/P = constant and V & n are constant and T and P are changing proportionally
Real Gases rel gases show deviations from the erfect gas law because molecules ineract with one another and actually have volume; thereefore they have some PE
Real Gases: at intermediate separations, where the PE is negative, the attractive interactions dominate
Real Gases: at large separations the PE is 0 and there is no interaction between the molecules
For a perfect gas PV/RT is wat at all pressure if n =1 1 b/c other terms will change to balance it out
Real Gases: at high pressures, deviation from ideal behavior is large and is different for each gas
at low pressure and high temperature real gases follow ideal gas laws
Would you expect He gas to deviate from ideal behavior at low temp and hight pressure
Understanding Deviations from ideal behavior V of the gas particles has an effect on the V of the gas; interactions between gas particles have an effect on the P of the gas (there is PE); real gases are not t masses; they have V
Effect of Volume n&Tconstant; real molecules have V; at high p, the combined V iof the gas molecules is a larger fraction of the containerV; the non-0 V of molecules themselves makes the V available for the molecules to move in less than V
effect of interaction between gas particles p depends on z w/ walls & force of each collision; attractive forces from nearby molecules; interactions lessen impact w/ molecules hit the wall therefore pressure appears > than it is; attractive forces and volume effects are more dominant under high p
effects oof temperature T decreases,KE decrease; intermolecular attractions reamin constant; cooling a gas deprives the molecules of energy; more KE means molecules have more energy to break away from intermolecular forces & hit the wall as opposed to being pulled back
van der Waals coefficients a and b; characteristic of each gas but independent of the temperature
why is pressure term added in van der Waals equation attractive forces reduce the pressure
why is volume term subtracted in van der Waals equation particles actually have volume
van der Waals equation can only predict above critical temperature
Redlich-Kwong euation state's a and b are ________________ van der Waal's equation different from
compression factor Z= PVm/RT =Vm/Vm perfect; the ratio of a gas of its measured Vm to Vm of a perfect gas at the same pressure and temperature; deviation from Z is a measure of departure from perfect behavior
at high pressures Z Z>1 therefore Vm > Vm perfect gas
at intermediate pressures Z Z< 1 Vm <Vm perfect attractive forces reducing molar volume relative to that of perfect gas; lots of attractive forces compress the gases (force the molecules to be closer together)
PV = ZnRT is true for a real gas
critical temperature the T at and above which vapor of the substance cannot be liquefied, nomatter how much pressure is applied; at and above Tc the sample has a single phase that occupies the entire V of the container; such a phase is a gas; lq hase doesn't form above the Tc
unphysical region van der Waal's flaws; the region where both P & V are increasing which can't happen due to Boyle's Law
Supercritical Fluid T>Tc and P>Pc ; density is more of that of a liquid; fluid nt strictly a liquid b/c it never possesses a surface that sepparates it from a vapor phase; too dense to be a gas; used as solvents; commercially used for decaffeinated coffee
Tc of CO2 (31 degrees Celcius ) is only a few degrees above room T. Therefore, it can be used to treat organic compounds with little danger of thermal degraton. CO2 is an excellent solvent for nonpolar compounds but not as good for polar compounds
Pr P/Pc
Vr Vm/Vc
Tr T/Tc
reduced state basically proportionizing them; pretty good approximation all gases show the same P-Vm-T behavior
Law of Corresonding States an approximation; it works best for gases compoed of sppherical molecules, fails sometimes badly whenthe molecules are non-pherical or polar
Law of Corresponding States graph P-V-T data for gases within a few %, excet for compounds with large dipole moments
thermodynamics the study of the transformations of energy and, in particular, the transformation of heat into work and vice versa; originally formulated by physicists and engineers interested in the efficiency of steam engines
thermodynamics of steam engines water is heated and boils and the expanding steam does work to ropel the locomotive. example of a practical benefit of termodynamics
why we care about thermodynamics reactions reach equilibrium; composition at equilibrium, and how reactions in electrochemical (and biological) cells can be used to generate electricity
Classical thermodynamics `provides useful relations between observable properties of bulk matter
statistical thermodynamics theory of the connection between atomic and bulk thermodynamic properties
work done to achieve motion against an opposing force; energy used to cause an object with mass to move
energy capacity to do work
heat energy used to raise temperature of an object
thermodynamic system could be a reaction vessel, an engine, an electrochemical cell, a biological cell, etc; ex. popping popcorn
thermodynamic process a prcess where there are changes in state of a thermodynamic system
surroundings region outside the system and are where we make our measurements; so huge it either has constant volume or constant pressure regardless of any changes that take place to the system; remain effectively the same size
open system exchange both energy and matter with its surroundings
closed system exchange energy but not matter with its surroundings
isolated system can exchange neither matter nor energy with its surroundings
universe system and surroundings
flask that is not stoppered and to which various substances can be added is an example of an open system
stoppered flask, energy can be exchanged with the contents of the flask b/c the walls may be able to conduct heat is an example of a closed system
insulated thermos containing hot coffee is an imperfect example of an isolated system
diathermic walls that permit heating as a mode of transfer of energy; e.g. metal container
adiabatic walls that don't permit heating even though there is a difference in temperature; e.g. double walls of a vacuum flask (approximate)
exothermic a process in a system that releases energy as heat; e.g. combustion of coal; qp = -
endothermic a process n a system that absorbs energy as heat. e.g. endothermic dissollution of ammonium nitrate in water in instant cold-packs that are included in sme first-aid kits; qp = +
expansion work many chemical reactions produce gas. Work is done when a system expands against an opposing pressure. Let us find out the work done when a system expands through a volume (deltaV) against a consntant Pex.
work done equation at constant pessure w=-Pex(deltaV)
free expansion expansion against 0 opposing force (Pex=0 therefore w=0) occurs in a vacuum when gas expands
work = max when a reversableprocess
reversible change a process that can be reversed by an infinitesimal change in a variable (pressure); Pex = Pgas equilibrium after each change we have to wait for them to reach equilibrium before moving on (mechanical equilibrium)
max work is obtained when the expernal pressure is only infinitesimally less than the pressure of the gas in the system
for isothermal, reversible expansion of an ideal gas work = w= -nRT ln(Vf/Vi)
irreversible work boom and done
an irriversible process is an idealized process in real life
Internal energy sum of KE + sum of PE of all particles; canot measure total energy but we can measure then change in
internal energy equation deltaU = q + w
the system is blind to the mode employed in internal energy
First Law of Thermodynamics if a system is isolated from its surroundings, then no change in internal energy takes place; q=0 w=0
+q system gains heat
-q system loses heat
+w work done on system
-w work done by system
+delta U net gain of energy by the system
-delta U net loss of energy by the system
intensive property does not depend on the amount oof sample being examined;; ex. T, mp, density
extensive properties depend on quantity of sample; ex. mass, vollume, internal energy
state function doesn't care how yyou got there, just cares about being there; ex. internal energy; depends on initial and final
heat and work _______ state functions aren't
atmosphere conditions constant pressure
enthalpy H = U + PV (if only PV work); state function; a nonsense thermo term that has no physical meaning; temperature dependent
enthaply at constant pressure and PV work only deltaH = qp
molar enthalpy Hm = H/n =Um + RT
enthalpy is more useful that internal energy b/c qp is easily measured or calculated b/c many physical and chemical changes of inerest occur at constant pressure
for most reactions the difference between delta H and delta U is small because PdeltaV is small especially in solid or liquid phase
under constant V delta U = qv
specific heat the amount of heat that must be added to one gram of a substance to raise its temperature by 1K or 1 degree Celcius; property of a material; intensive; difference between K and degrees Celcius is the same; s=q/(mdeltaT)
heat capacity C=ms=q/deltaT the amount of heat required to raise its temperature by 1K or 1 degree Celcius
calculate the work done when 50g of iron reacts with HCl to produce FeCl2 (aq) and H in a closed vessel of fixed volume 0 b/c volume is constant w=-PdeltaV
calculate the work done when 50 g of iron reacts with HCl acid to produce FeCl2 (aq) and H in an open beaker at 25 degree Celcius w=-PVf = -nRT = (50g/55.85g)*8.314 J/mol*K *298.15K = -2.2 kJ
calorimetry the study of heat transfer during physical and chemical processes
calorimeter a device for measuring energy transferred as heat; heat capacity must be known
to ensure adiabaticity, the calorimeter is immersed in a water bath w/ T continuously readjusted to that of the calorimeter at each stage of the combustion; makes them in equilibrium; feedback loop
heat capacity of the calorimeter is determined by combustion a sample that releases a known quantity of heat and measuring the temperature change; C may be determined by burning a known mass of substance (usually benzoic acid) that has a known heat output
constant pressure calorimetry atmosphere is not changing; qsoln=-qrxn ; acid-base neutralization; heat of solution
ex. of constant pressure calorimetry T of solution is rising b/c acid-base rxn is exothermic & you're left w/ aq soln since all you have in the cup is the solution the heat given off is absorbed by the solution the reaction is happening in
enthalpies of reaction deltaH=Hf-Hi (can't actually measure); enthalpy change that accompanies a reaction is called the deltaHrxn under constant pressure
what effect does reversing a reaction have on deltaH for a reaction change the sign of deltaH
what effect does multiplying coefficients by 2 have on deltaH for a reaction deltaH doubles
Hess's Law if a reaction is carried out in a series of steps, deltaH for the overall reaction will equal the sum of the enthalpy changes for the individual steps; state function
standard enthalpy of formation deltaH(nod)f; enthalpy change that results when one mole of a compound is formed from its elements at a pressure of 1 atm (1 bar); usually reported at 298 K
standard enthalpy of formation is most stable for any element when it equals zero
enthalpy of reaction deltaH(nod)rxn = sum of n*deltaH(nod products - sum of m*deltaH(nod)reactants (n & m are coefficients)
bond dissociation energy the enthalpy change required to break a particular bond in one mole of gaseous molecules
all bond enthalpies are_______charged. Why? positively; takes energy to break a bond so you have to put energy into it
chart values for bond dissociation energy are bad. Why? they don't take into account the chemical environment and their geometric shape (ex. equatorial vs. axial)
computer-aided molecular modelling estimates standard enthalpies of formation but it also has to make assumptions
most reliable method for determining enthalpies of formation calorimetry
Can you develop a solution of anions or cations alone? no; the charge has to be neutralized
which ion is defined to have a zero standard enthalpy of formation at all temperatures H+ (aq)
Created by: 530848841



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