Kinetic Molecular Theory (KMT) Most of the vol of a gas is empty space (vol occupied by molecules is negligible) Molecules in gas move randomly and in straight path in all directions with various speeds (press is same in all directions) Recall: P is result of collisions with wall (# and force) Forces of attraction and repulsion between gas molecules are negligible except for when they collide; collisions are elastic EK is proportional to Temp (K)

Use KMT to explain Boyle’s Law Why is P proportional to 1/V (P1V1 = P2V2)?

Use KMT to explain Charles’s Law Why is V proportional to T (V1/T1 = V2/T2)?

Use KMT to explain Gay-Lussaic Why is P proportional to T (P1/T1 = P2/T2)?

Use KMT to explain Avogadro’s Law Why is V proportional to n?

Derived Gas Laws Combined and Ideal (see worksheet #2) Combined: P1V1 = P2V2 T1 T2 Ideal: PV= nRT MM = dRT/P all good cats cover their pee with dirt!

Stoichiometry with Gases Coefficients give mol ratio For gaseous reactions, give vol ratio 2A  3 B 2 mol A yields 3 mol B 2 L of A yields 3 L of B What vol of A is needed to produce 10 L of B at STP? (Ans: 6.67 L)

2 NaN3 (s)  3 N2 (g) + 2 Na (s) Air bags are filled with N2 when sodium azide pellets decompose How many grams of NaN3 must decompose to fill an air bag with 36 L of N2 @ 1.15 atm and 26oC?

Mix Unreactive Gases Together Studied by Dalton in 1801. He concluded that in a mix, each gas behaves independently Meaning, PA in mix = PA alone Ptotal is sum of individual partial pressures Ptotal = PA + PB + … partial press obey ideal gas law (next slide)

Dalton’s Law of Partial Pressure PA = nART PB = nBRT V V Ptotal = ntotalRT (where ntotal = nA + nB) V Partial press is a fraction () of total press

 is mole fraction (individual moles over total) () = 1; A + B + … = 1 PA = A (Ptotal)

Problem to Try A 10.0 L flask contains 1.031 g O2 and 0.572 g CO2 @ 18oC. What is partial pressure of each gas? total pressure in flask? mol fraction of each gas?

Concept Check A flask is equipped with a valve and contains 3.0 mol H2 (g). If 3.0 mol Ar (g) are introduced What happens to the PH2 after Ar is introduced? How does the PH2 compare to the PAr? How does total pressure relate to the individual partial pressures?

Collection of Gas Over Water In this case, Ptotal = Pgas + PH2O H2 (g) is collected over water at 18oC and 738 Torr. If the volume of the gas is 246 mL, what mass of wet H2 is collected? PH2O @ 18oC = 15.5 Torr 2 Al (s) + 6 HCl (aq)  2 AlCl3 (aq) + 3 H2 (g) If 1.50 g Al react, what is the volume of wet gas produced?

Movement of Gas Depends on Size/MM Lighter particles travel faster on avg than heavier ones As ↓MM, ↑ avg velocity and broaden the range of velocities possible (hence, broader curve)

Movement of Gas Depends on T (K) EK prop to T (K); ↑T, ↑EK

Effusion If you have a container filled with gas and poke a hole in the container, gas will escape through the hole (effusion) The rate at which particles effuse depends on 3 factors Size hole (↑size, ↑effusion) #molecules/volume (↑crowdedness, ↑effusion) avg molecular speed (↑speed, ↑effusion) What affects speed? Think MM

Why dip shape? Behavior is most ideal at Low Press and High Temp

van der Waal’s Equation P + n2a V – nb = nRT V2 Corrects for IM forces and volume n2a/V2 corrects P (up) a constant (expt determined) that relates to # e- which in turn relates to the complexity of a molecule and strength of IM forces (next unit) nb corrects V (down) b constant relates to molar volume

A 1.98L vessel contains 215 g dry ice (4.89 mol). P + n2a V – nb = nRT V2 A 1.98L vessel contains 215 g dry ice (4.89 mol). After standing at 26oC (299 K), the dry ice sublimes. The measured pressure is 44.8 atm. Compare Preal (44.8 atm) to the P from ideal gas law and van der Waals eqns. Pideal = 60.6 atm PVDW = 45.9 atm

Which gas would behave more ideally and Why? H2, O2, or N2 Nonpolar gas or a polar gas