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1 TA David Shudy

Name: ___________________________ Section: KEY _______________________

Chemistry 204 Quiz 1 Tuesday 2/1/

Use the following equations (if needed) to answer the 4 questions on both sides of this quiz.













−

∆

=

1 1 2

ln 2 1 1 R T T

H

P

P ovap R

S

RT

H

P

o (^) vap ∆ ovap

∆

ln =− ( V nb ) nRT

V

n P a  − = 









2

PV = nRT

1. Calculate the pressure exerted by 1.00 mol C 2 H6(g) behaving as both an ideal gas and a Van der Waals gas when it is heated to 1,000.0 K in a 0.100 L vessel. (4pts)

Van der Waals parameters for C 2 H 6 : a = 5.507 L^2 atmmol-2; b = 6.51 x 10-2^ L*mol- Ideal Gas

( ) ( )

atm L

K

mol K

L atm mol

V

nRT PV nRT P 820. 6

1. 100

1 0. 08206 1 , 000

=













⋅

⋅

= ⇒ = =

Van der Waals Gas (ie. real gas)

( ) ( )

( )

( )

( )

atm L

mol mol

L atm

mol

L

L mol

K

mol K

L atm mol

V

n a V nb

nRT P 1 , 801

1. 100

0. 100 1 0. 0651

1 0. 08206 1 , 000

2

2 2

2 2

2

⋅

−













−













⋅

⋅

− =

−

=

2. Octane (C 8 H 18 ) is a major component in gasoline. It has a vapor pressure of 13.95 Torr at 25˚C and 144.78 Torr at 75˚C, and a standard enthalpy of vaporization (∆H°vap) of 40.3kJ/mol. Determine the following: a. What intermolecular forces would you expect to occur in a solution of octane? (1pt) b. Standard entropy of vaporization (∆S˚vap) (2pts) c. Standard Gibbs free energy of vaporization (∆G°vap) (2pts) d. Normal boiling point of octane (remember: gasoline is a liquid at the pump!) (1pt)

a) London dispersion (also known as induced dipole – induced dipole) forces only

b)

( )( ) mol K

J

S

J mol K

S

J mol K K

J mol torr

torr

R

S

RT

H

P

o vap

ovap

ovap ovap

⋅

⇒∆ =

⋅

∆

+

⋅

×

=−











⇒

∆

+

∆

=−

8. 314 298 8. 314

ln

ln

3

c) ∆ G o^ vap =∆ Hovap − T ∆ Sovap = 40. 3 kJ mol ⋅ K −( 298 K )( 0. 102 kJ mol ⋅ K ) = 9. 9 kJ mol

d) ∆ G = 0 =∆ Ho^ vap − T ∆ Sovap ⇒ T =∆ Hovap ∆ Sovap = 40. 3 kJ mol 0. 102 kJ mol ⋅ K = 395 K

H 3 C^ C

H (^2) C H 2

C

H 2 C H 2

C

H (^2) C H (^2)

C H 3

Octane

58°C 69°C 89°C 101°C 198°C

H 3 C^ C

H 2

C

H 2

C

H 2

C

H 2

C H 3

C

O

H O H

H 3 C

C

H

C H 3

C

H C H 3

C H 3

3. Match each compound ( A - E ) with its boiling point by writing the compound’s letter designation under the listed boiling point. (5pts)

Compound: _ D __ _ A __ _ C __ _ E ___ _ B ___

4. We say that the hydrocarbon butane (CH 3 CH 2 CH 2 CH 3 ) is “insoluble” in water at 298K and 1 atm.

a) What does this imply about the sign of the standard Gibbs free energy of mixing (∆Gmix)? (2 pts) ∆Gmix is positive (+); positive ∆G means the process in non-spontaneous

b) Using the equation that relates ∆G to enthalpy and entropy, explain why butane does not spontaneously dissolve in water, despite the fact that the mixing of butane in water is slightly exothermic at standard conditions. A simple figure may help! ( Hint: don’t worry about absolute numbers. The equation and figure should guide your reasoning descriptively ) (3 pts) = ordered H 2 O cage

Triethylamine C Polar

Hexane A Nonpolar (Linear)

N

C H 2

C H 3

C H 2 H 3 C

C

H 2

C H^3 C

H 2

C

H 2

O H

H O

Ethylene Glycol B 2x H-bond

Formic Acid E 1x H-bond

2,3-dimethylbutane D Nonpolar (“Ball” like)

Polar water forms ordered cage around nonpolar butane molecule (hydrophobic effect). This leads to an increase of order and a non-favorable negative value of ∆S , which leads to an overall positive (non-spontaneous) value of ∆G. ∆G = ∆H - T∆S (+) (-) (-)