Calculate the change in Gibbs free energy $($

$$

$$

$$G$)$ for the reaction

$2$

SO

$2$

$($

$$

$)$

$+$

O

$2$

$($

$$

$)$

$$

$2$

SO

$3$

$($

$$

$)$

$2$SO

$2$

$($g$)+$O

$2$

$($g$)2$SO

$3$

$($g$)$ at $298$ K$,$ given the following standard free energies of formation:

$$

$$

$$

$$

$($

SO

$2$

$($

$$

$)$

$)$

$=$

$$

$300\mathrm{.}4$

$$

kJ$/$mol

$$G

f

$$

$($SO

$2$

$($g$))=300\mathrm{.}4$kJ$/$mol$,$

$$

$$

$$

$$

$($

O

$2$

$($

$$

$)$

$)$

$=$

$0$

$$

kJ$/$mol

$$G

f

$$

$($O

$2$

$($g$))=0$kJ$/$mol$,$ and

$$

$$

$$

$$

$($

SO

$3$

$($

$$

$)$

$)$

$=$

$$

$370\mathrm{.}4$

$$

kJ$/$mol

$$G

f

$$

$($SO

$3$

$($g$))=370\mathrm{.}4$kJ$/$mol$.$

The decomposition of hydrogen peroxide is a first$-$order reaction with a rate constant of

$1\mathrm{.}06$

$$

$1$

$0$

$$

$3$

$$

min

$$

$1$

$1\mathrm{.}0610$

$3$

min

$1$

at $25$C$.$ Calculate the time required for the concentration of hydrogen peroxide to decrease from $0\mathrm{.}5$ M to $0\mathrm{.}1$ M$.$

Calculate the standard cell potential $($

$$

$$

E

$$

$)$ for the cell reaction

Zn

$($

$$

$)$

$+$

Cu

$2$

$+$

$($

$$

$$

$)$

$$

Zn

$2$

$+$

$($

$$

$$

$)$

$+$

Cu

$($

$$

$)$

Zn$($s$)+$Cu

$2+$

$($aq$)$Zn

$2+$

$($aq$)+$Cu$($s$),$ given the standard reduction potentials:

$$

$$

$($

Zn

$2$

$+$

$/$

Zn

$)$

$=$

$$

$0\mathrm{.}76$

$$

V

E

$$

$($Zn

$2+$

$/$Zn$)=0\mathrm{.}76$V and

$$

$$

$($

Cu

$2$

$+$

$/$

Cu

$)$

$=$

$+$

$0\mathrm{.}34$

$$

V

E

$$

$($Cu

$2+$

$/$Cu$)=+0\mathrm{.}34$V$.$

For the reaction

N

$2$

$($

$$

$)$

$+$

$3$

H

$2$

$($

$$

$)$

$$

$2$

NH

$3$

$($

$$

$)$

N

$2$

$($g$)+3$H

$2$

$($g$)2$NH

$3$

$($g$),$ the equilibrium constant

$$

$$

K

c

at $500$ K is $6\mathrm{.}0.$ Calculate the concentrations of all species at equilibrium if the initial concentrations are

$[$

N

$2$

$]$

$=$

$1\mathrm{.}0$

$$

M

$[$N

$2$

$]=1\mathrm{.}0$M$,$

$[$

H

$2$

$]$

$=$

$1\mathrm{.}5$

$$

M

$[$H

$2$

$]=1\mathrm{.}5$M$,$ and

$[$

NH

$3$

$]$

$=$

$0$

$$

M

$[$NH

$3$

$]=0$M$.$

Calculate the pH of a $0\mathrm{.}1$ M acetic acid solution. The

$$

$$

K

a

of acetic acid is

$1\mathrm{.}8$

$$

$1$

$0$

$$

$5$

$1\mathrm{.}810$

$5$

$.$

Calculate the amount of heat released when $5\mathrm{.}00$ grams of propane $($

C

$3$

H

$8$

C

$3$

H

$8$

$)$ is burned in excess oxygen, given the standard enthalpies of formation:

$$

$$

$$

$$

$($

C

$3$

H

$8$

$($

$$

$)$

$)$

$=$

$$

$104\mathrm{.}7$

$$

kJ$/$mol

$$H

f

$$

$($C

$3$

H

$8$

$($g$))=104\mathrm{.}7$kJ$/$mol$,$

$$

$$

$$

$$

$($

CO

$2$

$($

$$

$)$

$)$

$=$

$$

$393\mathrm{.}5$

$$

kJ$/$mol

$$H

f

$$

$($CO

$2$

$($g$))=393\mathrm{.}5$kJ$/$mol$,$ and

$$

$$

$$

$$

$($

H

$2$

O

$($

$$

$)$

$)$

$=$

$$

$285\mathrm{.}8$

$$

kJ$/$mol

$$H

f

$$

$($H

$2$

O$($l$))=285\mathrm{.}8$kJ$/$mol$.$

Calculate the wavelength of the photon emitted when an electron in a hydrogen atom transitions from the

$$

$=$

$3$

n$=3$ level to the

$$

$=$

$2$

n$=2$ level. Use the Rydberg constant

$$

$$

$=$

$1\mathrm{.}097$

$$

$1$

$0$

$7$

$$

m

$$

$1$

R

H

$=1\mathrm{.}09710$

$7$

m

$1$

$.$

Calculate the number of possible stereoisomers for a compound with the molecular formula

C

$6$

H

$12$

O

$4$

C

$6$

H

$12$

O

$4$

that contains two chiral centers.

Calculate the mass of

KClO

$3$

KClO

$3$

needed to produce $5\mathrm{.}0$ grams of oxygen gas by decomposition. The reaction is

$2$

KClO

$3$

$($

$$

$)$

$$

$2$

KCl

$($

$$

$)$

$+$

$3$

O

$2$

$($

$$

$)$

$2$KClO

$3$

$($s$)2$KCl$($s$)+3$O

$2$

$($g$).$

Calculate the freezing point depression of a solution containing $0\mathrm{.}5$ moles of glucose $($

C

$6$

H

$12$

O

$6$

C

$6$

H

$12$