Study Guide - Gas Laws (Chapter 5)

Units …

Pressure Volume Temperature1 atm 1 liter K = oC + 27376 cm Hg 1000 ml760 mm Hg 1000 cc760 torr 1000 cm3

101.325 kPa STP = 1-atm and 0oC14.7 psi ideal gas @ STP: 1 mol = 22.4 L (molar volume)

Boyles Law … P x V = Constant

P1V1 = P2V2 n and T are constant P P

V 1/VCharles’ Law … V/T = Constant

V1/T1 = V2/T2 n and P are constant V

Gay-Lussaic’s Law … P/T = Constant

P1/T1 = P2/T2 n and V are constant T

Combined Gas Law … PV/T = Constant

Avogadro’s Law … V/n = Constant

V1/n1 = V2/n2 P and T are constant

Ideal Gas Law …PV = nRT R = .0821 liter.atm/mole.K

Density …

Molar Mass …

Deviation from Ideal Gas Law (van der Waals equation)…

a = correction for inter-molecular forces b = correction for volume of atoms

Stoichiometry …

Question: 36.0-gm of methane (CH4) burn in air. Determine the volume of gas produced at 25oC.Assume the products are gases collected at 1-atm.

Answer: 190. litersSolution:

CH4(g) + 2O2(g) CO2(g) + 2H2O(g)

(36-gm CH4) / (16-gm/mole) = 2.25-mol CH4(g)

Therefore; 2.25-mol of CO2 and 4.50-mol H20 Total moles of gas = 7.75-mol

PV = nRT V = nRT/P V = (7.75-mol)(.0821-liters.atm/mol.K)(298-K)/(1-atm)

Dalton’s Law of Partial Pressures … ‘the total pressure of a mixture of gases is the sum of the pressures that each gas would exert if it were present alone.’ (Do not forget about water vapor)

PTotal = PT = PA + PB + PC + …Pn (+ PH2O if gas is collected through water)

Mole Fraction … XA = mol component A / total moles

XA = nA / (nA + nB + nC + …) XB = nB / (nA + nB + nC + …) XC = nC / (nA + nB + nC + …)

PA = XAPT PB = XBPT PC = XCPT

XA = PA/PT XB = PB/PT XC = PC/PT

Kinetic Molecular Theory (KMT) …Assumptions: 1. Gases may be considered to be point masses. No volume, just mass.

2. Gas molecules move in random straight-line motion with ‘elastic’ collisions. Collisions with walls of container are cause of pressure exerted by the gas.

3. Gas molecules do not have any inter-molecular forces (IMF).4. Average kinetic energy of a collection of gas particles is directly proportional to Kelvin temperature.

Two gases at the same temperature have the same kinetic energy.

KE (Kinetic Energy) is proportional to T (Temperature)

Molecular Speed of a Gas …

R = 8.314 J/K.molM = molecular mass in kg/mol

Question: What is the RMS (root mean square) speed of O2 atoms in air? Assume T = 25oCAnswer: uavg = 481 m/s or 1735 km/hr or 1084 mi/hr

Solution:

Graham’s Law of Effusion…

Effusion: the passage of a gas through a tiny orifice into an evacuated chamberDiffusion: the gradual mixing of gases by virtue of their kinetic properties

* the lower the molecular weight of a gas, the faster it will effuse/diffuse* see figure 5.22 on p.220 and figure 5.24 on p.221

Barometers and Manometers

You need to know what these are, what they look like, what they measure, and how they operate. Occasionally the AP Exam will have pictures of such devices as part of a question.

*see figure 5.2 on p.191 and figure 5.3 on p.191

TIPS …1. Make sure that…

temperature is in Kelvingas laws applied to gases onlythe units cancelthe answer is reasonable (does the answer agree with the gas law?)

2. If volume, temperature, or pressure change, combined gas law most likely3. If moles of gas are involved, ideal gas law most likely4. If a mixture of gases, Dalton’s Law and/or mole fraction most likely5. If a gas is collected over/through water, do not forget to include the vapor pressure of water.

Pgas = Ptotal – PH2O

6. Diatomic molecules = H2 , N2 , O2 , F2 , Cl2 , Br2 , I2

7. Molar Volume is 22.4 L/mol for a gas at STP only. If at a different temperature:

8. Real Gases … (non-ideal gases)- are not ideal gases since they do not conform to the assumptions of the kinetic molecular theory- common reasons for deviation from ideal gas behavior: particles have IMF’s and volume- van der Waals equation accounts for non-ideal behavior