chem 1201 chapter 10
kinetic-molecular theory of gases(cont)
- the P of a gas results from the collisions with the walls of the container -the magnitude of the P is determined by how often and how hard the molecules strike -the absolute T of a gas is a measure of the average kinetic energy. the motion of the molecules increases as T increases
mean free path
- the average distance traveled by a gas molecule between collisions -at sea level the mean free path for ir molecules is about 6x10^-6cm
relating ideal-gas equation and gas laws
-(P1V1/n1T1)=(P2V2/n2T2) -(P1V1/T1)=(P2V2/T2) -Boyles law: P1V1=P2V2 -Charles law: V1/T1=V2/T2 -Avogadros law:V1/n1=V2/n2
partial pressure
-Dalton observed: the total pressure of a mixture of gases equals the sum of the pressure that each would exert if present alone -partial pressure is the pressure exerted by a particular component of a gas mixture -Dalton's law of partial pressures: in a gas mixture the total pressure is given by the sum of partial pressures of each component -P(total)=P1+P2+P3....
collecting gas over water
-P(total)=P(gas)+P(water)
ideal-gas law
-PV=nRT -R = gas constant = 0.08206L*atm/mol*K -P=pressure in atm -V=volume in L -T= temp in Kelvin -n = gas quantity in moles -STP(standard temp and pressure)= 0c, 273.15 K, 1 atm
atmospheric pressure
-air 1 m^2 exerts a force of 1*10^5 N which = 1 bar -the pressure of 1m^2 column of air is 100kPa -atmospheric pressure at sea level is 100kPa or 1 bar
diffusion
-diffusion is the spread of one substance throughout a space of throughout a second substance -diffusion is slowed by collisions of gas molecules with one another -consider someone opening a perfume bottle: it takes awhile to detect the odor
molecular effusion and diffusion
-effusion is the escape of gas molecules through a tiny hole into an evacuated space -the rate of effusion depends directly on the rms speeds -the faster the speed(lower the MM) the higher the rate of effusion
gas properties
-gases are highly compressible and occupy the full volume of their containers -when a gas is subjected to pressure its volume decreases -gases always form homogeneous mixtures with other gases -gases only occupy a small fraction of the volume of their containers -as a result each molecule of gas behaves largely as though other molecules were absent
gas densities and molar mass
-n/V=P/RT -molesxmolarmass=mass (nxMM=m) -m/V=(PMM)/RT=density -density=PMM/RT -molar mass MM=(Density)RT/P
standard atmospheric pressure
-pressure required to support 760 mm of Hg in a column -1 atm = 760 mmHg = 760 torr = 1.013265x10^5 Pa = 101.325 kPa = 1.01325 bar
boyle's law
-pressure-volume (P-V) relationship -the volume of a fixed quantity of gas at constant temp is inversely proportional to pressure -V=constantx1/p -PV=constant
avogadro's law
-quantity-volume(n-V) relationship -the volume of gas at a given temp and pressure is directly proportional to the number of moles of gas -V=constantxn -V/n=constant -22.4L of any gas at 0C and 1 atm contains 6.02x10^23 gas molecules
charles's law
-temperature-volume (T-V) relationship -volume of a fixed quantity of gas at constant pressure is directly proportional ti its absolute temperature -V=constantxT -V/T=constant -T must be measured in K (add 273.15)
kinetic-molecular theory of gases
-the kinetic molecular theory of gases was developed to explain gas behavior -summary: 1. gases consist of a large number of molecules in constant random motion 2.the combined volume of all the molecules is negligible compared with the volume of the container 3. intermolecular forces(forces between gas molecules) are negligible
application of KMT to gas-laws
1. effect of an increase in V (at constant T): -as volume incr at constant T the average kinetic of the gas remains constant - if volume incr the gas molecules have to travel further to hit the walls of the container than P decreases 2.effect of an increase in T (at constant V): -as temp incr at constant V the average kinetic energy of the gas molecules incr - the change in momentum in each collision incr (molecules strike harder) then P incr
kinetic-molecular theory of gases (cont.)
4.energy can be transferred between molecules during collisions, but as long as temp remains constant, the average kinetic energy of the molecules does not change with time 5. the average kinetic energy of the gas molecules is proportional to the absolute temperature
distributions of molecular speed
- μ(rms)= (3RT/MM)^1/2 -the lower the MM the high the μrms for that gas at a constant T
distributions of molecular speed
- as kinetic energy increases, the velocity of the gas molecules increases -root-mean-square (urms) is the speed of a gas molecule having average kinetic energy -average kinetic energy (ε) is related to rms speed ε=(1/2)mu^2 m=mass of molecule
pressure
Pressure is the amount of force applied to an area P=F/A F is in Newtons(N) 1N=1kgm/s^2 P is in pascal (Pa) 1Pa= 1N/m^2
gas mixtures and partial pressures
combining equations: P1=(n1/nt)Pt=X1Pt -X1=(moles of compound 1)/(total moles)= n1/nt
graham's law of effusion
r1/r2=μrms1/μrms2=(3RT/MM1)^1/2/(3RT/MM2)^1/2=(MM2/MM1)^1/2