physical chemistry

CHEM%3512%Winter%2015:%Physical%Chemistry% Problem%Set%5%

Due%date:%Fri%March%13% ! Directions:!Complete!all!problems!and!show!all!work!for!full!credit.! ! 1.! Which!of!the!following!molecules!can!show!a!pure!rotational!microwave!absorption! spectrum?!

a.! Methane,!CH4!

b.! Hydrogen!chloride,!HCl!

c.! Dichloromethane,!CH2Cl2!

d.! Carbon!dioxide,!CO2!

e.! Acetylene,!C2H2!

f.! Hydrogen!cyanide,!HCN!

g.! Benzene,!C6H6! ! 2.! Consider!a!linear!triatomic!molecule!with!the!structure!A–B–C.!See!the!figure!in!Table! 12B.1!of!Atkins!and!de!Paula.!There!is!a!typo!in!the!expression!for!the!moment!of!inertia!in! Table!12B.1;!here,!we!will!derive!the!correct!expression.!

a.! Assume!that!the!molecule!is!oriented!along!the!xPaxis!with!atom!B!at!the!origin.!Let! mA,!mB,!mC!denote!the!masses!of!atoms!A,!B,!C,!respectively;!let!xCM!denote!the!center!of! mass!of!the!molecule.!Write!the!moment!of!inertia!in!terms!of!masses!mA,!mB,!mC,!the! coordinate!xCM,!and!the!bond!lengths!R,!R´.!

b.! In!general,!the!center!of!mass!vector!RCM!is!defined!as!a!massPweighted!sum!of!indiP vidual!positions:!

RCM = 1 M

miri i ∑ !

where!mi,!ri!are!the!mass!and!position!vector!for!atom!i,!respectively,!and!M!is!the!sum! of!all!masses.!Write!xCM!in!terms!of!the!masses!mA,!mB,!mC!and!the!bond!lengths!R,!R´.!

c.! Substitute!your!result!in!part!(b)!into!part!(a)!to!obtain!an!expression!for!the!moP ment!of!inertia.!Identify!the!typo!in!the!expression!given!in!Table!12B.1.!

! 3.! Atkins!and!de!Paula,!Problem!12C.5.! !