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Gas Laws & Solutions GAS LAWS & SOLUTIONS KINETIC MOLECULAR THEORY (KMT) (pp. 426-429) I. The kinetic molecular theory was developed to help predict the behavior of gases. It describes the behavior of gases at the molecular level. 2. This theory is based on assumptions about a theoretical gas known as an I1H;;)q L coAS 3. The assumptions are: a. Ideal gas particles are so small that the volume of the individual particles if they were at rest is essentially zero when compared with the total volume of the gas. b. Ideal gas particles are in constant, rapid, random motion, moving in straight lines in all directions until they collide with other particles. c. There are no attractive or repulsive forces between particles and collisions between particles are elastic. d. The average kinetic energy of the particles is directly proportional to the absolute temperature (measured in Kelvins). FOUR VARIABLES DESCRIBE A GAS Temperature I. The temperature of a gas determines the average kinetic energy of the particles. 2. While the average kinetic energy of a collection of gases at a given temperature will be same, the velocity at which they travel will not. This is because the mass values of the various gases are different. 3. Temperature is usually measured in either Celsius or Kelvin. Both are related to one another: Volume I. A derived unit: ~ X ~S X \1 2. Gas volumes are expressed four different ways: .3 fY\ Pressure I. The force that the gas particles exert over a unit area: FvR.C.G' fftr=ssu/(<= s: UNIT ~"'A 2. Pressure is a measure of the total force exerted by the moving particles of a gas as they collide with the walls of the container. 3. Atmospheric pressure is measured in terms of: cd-IVt. 10(,.3 J:{ Standard Temperature and Pressure (STP) 1. In order to study the effects of changing temperature and pressure on a gas, one must have a standard for comparison. 2. STP represents a pressure and temperature that are fairly easy to reproduce: T s: a 7.3 J( oCe A,.:JD /,00 a.t-~ 373K l!l,.:J o 10/, 3 ~p~ f .:= Iol-Wl a13~ A.v 0 l\oO~ CJ-13K -4..)0 7~O,O I11nA WJ d13 II: "\"-'D 7~(}. 0 .h.l\' r Particles I. Gases with equal volumes under the same conditions of pressure and temperature have equal numbers of particles. 2. This is Avo GA~ 's LA\,J and it holds true only for gases. 3. The amount of gas is measured in Wl 0 Ie 4. The volume of one mole of gas at STP is known as the MO LA l V()LlJ/VI~ I VV\~:- a.~.Lj L GAS LAWS (pp. 403-415) I. The gas laws are a series of mathematical relationships that relate the following variables: ~I - Tbl'V\P8Z,A 'NfL l;- V- vo t.vm E- f- Pt~s,ul-l? V\ - t'\10LE~ Charles' Law 1. Relates volume and temperature. 2. As the temperature decreases, the volume of a gas decreases. As temperature increases, the volume of a gas increases. 3. The volume of a gas at constant pressure is directly proportional to the absolute temperature. 4. Charles' Law helped prove the existence of absolute zero. 5. Mathematically this is: V, Yz.. TJ. ***** A sample of gas occupies 24.0m3 at IOO.OK. Determine its volume at 400.0K. V, 'V-z. s: - Tz.- Vz.... z t{Oo] ***** Gas in a balloon occupies 2.50L at 300.0K. At what temperature will the balloon expand to 7.50L? VI \[ L ( 3elO, 0) (1 ..r0 ) .=: Ia. :: T, T2.. 01·50 Q,S-O L 7, S-o l ::. 9(Jo. K 30G.OIL I~ OJ. 9,00 )((0 K Boyle's Law I. The volume of a gas at constant temperature is inversely proportional to the pressure. 2. Like Charles' Law, we can write: P,V. ~ P,- VL ***** The gas in a balloon has a volume of 4.00L at IOO.OkPa. The balloon is released into the atmosphere and the gas in it expands to a volume of 8.00L. Determine the pressure on the balloon at the new volume. PIV, =~ 1- (4.00)( 100.0) .: P'2. (6-.0d) ( ~•0 0) ( I00 .0] (8' ·00 J ***** Ifthe pressure of a 2.50m3 sample of gas is 1.50 atm, what volume will the gas occupy if the pressure is changed to 7.50 atm? ~ V I ~ P2. \f 2- ( I •50 ')( Ol ' S-O) z: ( 1.~o 1V d- (I. so) (0I.$1:J)_ 7. )"0 Gay-Lussac's Law I. The pressure of a given gas varies with the Kelvin temperature when the volume remains constant. 2. This is expressed as: P, P-z.. - T, TL ***** The pressure of a gas in a tank is 324.24kPa at 295.0K. Determine the gas pressure if the temperature is raised to 333.0K. Pr P2- :: - T, /2.- {J-z... = 33.3 ***** A gas in a sealed container has a pressure of 125.0kPa at 30.0oC. Determine the temperature in the container ifthe pressure is increased to 201.0kPa. P, P; T _(z.ul)(303) --I .., ~ -, ILJ T, do 'leQ lol- 0 :: 303.0 -I~ Dalton's Law (pp. 420 - 425) I. The total pressure in a gas mixture is the sum of the partial pressures of the individual components. 2. The M~n '"' L P..'2k--:s.sUIZl.?' of a gas is the pressure of an individual gas in a gas mixture that contributes to the total pressure of the mixture. 3. This is expressed mathematically as: PrDTAL:: PT:: ~ of p~-f Ps -I •• , 4. Dalton's law is often used to determine the pressure of a gas collected over water. ***** Hydrogen gas is collected over water at a total pressure of 95.0kPa. The volume of gas collected is 28.0mL at 25.0oe. Determine the partial pressure of the hydrogen gas if the water vapor pressure is 3.17kPa. p·rt)"; ;! P,..j'L- + P;.fz.o q S .0 llc(. :: (J,-h + .3.' 1)c~ -Rf 2-:: q 1 ,If k Ib. ***** A gas is collected over water at 50.0De and a barometric pressure of I05.00kPa. Determine the pressure of the gas if the water vapor pressure is 12.34kPa. PruT ~ ~aJ ·f PI-h. 0 10 S. o0 .kPtIl " 10J-I I;), a if fjaS .: q;;J. & (p:: q ;). 7)c ~ COMBINED GAS LAW 1. The combined gas law states the relationship among pressure, volume and temperature of a fixed amount of gas: i~ V, 2. The combined gas law allows one to work out problems involving more variables that change. ***** A gas at 11O.0kPa and 30.0oe fills a flexible container with an initial volume of2.00L. Ifthe temperature is raised to so.o-c and the pressure increased to 440.0kPa, what is the new volume? T,!' e;l1,3.,. 3.0 :: .30 .3 T2'= Jli3+ 81J:- 3.53 (110) ( t.ooo') (Ifl(O) V l :: 3.5 3 :58';) L ***** At O.OOoCand 1.00 atm pressure, a sample of gas occupies 30.0mL. If the temperature is increased to 30.0oC and the entire gas sample is transferred to a 20.0mL container, what will be the gas pressure inside the container? T, ~ d-/3 -10 s: ';)'73 (( .;173 /2.. ~ ~ 7"3 -+ 30 s: :lO 3. J{. P,V, :: f2- v'z Tz- IDEAL GAS LAW (pp. 415-420) 1. The number of moles is the fourth variable that can be used along with pressure, volume and temperature to describe a gas. 2. The ideal gas law is: N;:: n f2... T p ~ N'-£SSlJe..(;-- T; nll1 Pt:--.eA7VR.-l::- \/: VO LU /l'\ (; {l : MVLE"j 3. Ifpressure is expressed in atmospheres, then: L'JYY\ wwl /( 4. If pressure is expressed in kPa, then: R.:: [,,3/4 ***** Determine the number of moles of gas in a 3.00L container at 300.0K and a pressure of 1.50 atm. Pv= fl Q./ py (1,.$)(3) (\: ~ ~T :: C. oill) ( 300) ***** Determine the Celsius temperature of2.49 moles of gas contained in a l.OOL container at a pressure of 143kPa. N= nQ.. T PV (P/3)(1' T :: .- :: flfL (~,l(q)( 4', 3/ LI) s: ~,q, K 0 il.:- Ci" 313 SOLUTIONS WHAT ARE SOLUTIONS? Characteristics of Solutions 1. Solutions are homogeneous mixtures containing two or more substances called the solute and the solvent. 2. The ,sOLUTF is the substance that dissolves. 3. The SoLV&.J T is the dissolving medium. 4. A solution may exist as a gas, liquid or solid depending on the state of its solvent. 5. Solutions can contain more than one solute. 6. Some combinations of substances can readily form solutions and others do not. 7. A substance that dissolves in a solvent is said to be SCJI..v&L/.;;' in that solvent. 8. A substance that does not dissolve in a solvent is said to be ,bJSuLlJ ,g, L/;; in that solvent. 9. Two liquids that are not soluble in each other are said to be rmfl1I'sC., &rL t: 10. Two liquids that are soluble in each other are said to be M J sc, 6 L(;;' Solvation in Aqueous Solutions 1. To form a solution, solute particles must separate from one another and the solute and solvent particles must mix. 2. Forces of attraction exist between the pure solute particles, between the pure solvent particles, and between the solute and solvent particles. 3. When a solid solute particle is placed in a solvent, the solvent particles completely surround the surface of the solid solute.
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