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Chem 113A Homework # 6
Solutions
- If the reaction ๐น๐๐
2
3
comes to equilibrium at
a total pressure of 1 atm, analysis of the gas shows that at 700 K and 800 K,
๐
๐๐ป 3
๐
๐ป 2
= 2. 165 and 1. 083 , respectively, if only ๐ป
2
(๐) was initially present in the
gas phase and ๐น๐๐(๐ ) was in excess.
a) Calculate ๐พ
๐
at 700 K and 800 K.
b) Calculate โ๐ป
๐
ยฐ
and โ๐
๐
ยฐ
at 700 K and 800 K (assuming they are both
independent of temperature).
c) Calculate โ๐บ
๐
ยฐ
for this reaction at 298 K.
- Consider the Daniell cell, for which the overall cell reaction is ๐๐(๐ ) +
2 +
2 +
. The concentrations of CuSO 4
and ZnSO 4
are
2.50 and 1.10 ร 10
m, respectively.
a) Calculate E setting the activities of the ionic species equal to their molalities
b) Calculate ๐พ
ยฑ
for each of the halfโcell solutions using the DebyeโHuckel
limiting law.
c) Calculate E using the mean ionic activity coefficients determined in part (b).
- Consider the gas phase reaction H 2
+ I
2
= 2HI at equilibrium at T= 870 K and p =
1 bar. If ๏Gห (870K, 1 bar) = - 48.96 kJ, determine K, ฮพ and the equilibrium
amounts of H 2
, I
2
and HI (in mol) if the intial composition was nห(H 2
mol, nห(I 2
) = 0.400 mol, and nห(HI) = 0.200 mol.
ln ๐พ
๐
ยฐ
48. 96 ร 10
3
J/mol
๐
- 768
This equilibrium constant was calculated in the pressure standard state (since we
use the table value for ๏ Gยฐ). We convert to the mole fraction standard state to
calculate the equilibrium composition.
๐ฅ
๐
ยฐ
โ๐
๐
ยฐ
Let the extent of reaction at equilibrium be denoted ๐. The number of moles at
equilibrium and the mole fractions for each reactant and product are:
๐ป
2
๐ป 2
ยฐ
๐ผ
2
๐ผ 2
ยฐ
๐ป๐ผ
๐ป๐ผ
ยฐ
๐ป
2
๐ ๐ป
2
๐
3 โ๐
9
๐ผ
2
๐ ๐ผ
2
๐
4 โ๐
9
๐ป๐ผ
๐
๐ป๐ผ
๐
2 + 2 ๐
9
๐ฅ
๐ป๐ผ
2
๐ป
2
๐ผ
2
2
2
2
2
The roots of the equation are ๐ = 0. 411 ๐๐๐ and ๐ = 0. 293 ๐๐๐. Since a value
for the extent of reaction at equilibrium ๐ = 0. 411 ๐๐๐ is unphysical (it leads to
negative moles for H 2
and I 2
at equilibrium), the extent of reaction at equilibrium
is:
Finally, the equilibrium compositions are:
๐ป
2
๐ผ
2
๐ป๐ผ
- Calculate the equilibrium constant of the reaction ๐ถ๐(๐) + ๐ป
2
2
Given that, for the production of liquid formaldehyde from the same reactants,
๐
0
๐พ๐ฝ
๐๐๐
at 298 K and that the vapor pressure of formaldehyde is
1500 Torr at that temperature.
- The principal ions of human blood plasma and their molar concentrations are
mNa
= 0.14 m, mCl
= 0.10 m, mHCO 3
โ = 0.025 m. Calculate the ionic strength
of blood plasma.
[
2
2
2
)] = 0. 1325
- Consider the water gas shift equilibrium ๐ถ๐(๐) + ๐ป
2
2
2
At 1000 K, the equilibrium composition of the reaction mixture is
Substance ๐ถ๐
2
2
2
Mole % 27.1 27.1 22.9 22.
Calculate ๐พ
๐
and โ๐บ
๐
ยฐ
at 1000 K.
๐ฅ
๐
ยฐ
) ( 1000 ๐พ) ln( 0. 714 ) = 2. 80 ร 10
3
- Consider the Daniell cell, for which the overall cell reaction is ๐๐
2 +
2 +
. The concentrations of CuSO 4
and ZnSO 4
are 2.50 and 1.10 ร 1 0
3
m, respectively.
a) Calculate E setting the activities of the ionic species equal to their molalities.
b) Calculate ๐พ
ยฑ
for each of the halfโcell solutions using the DebyeโHuckel
limiting law.
c) Calculate E using the mean ionic activity coefficients determined in part (b).
- In this problem, you calculate the error in assuming that โ๐ป ๐
ยฐ
is independent of T for a
specific reaction. The following data are given at 25ยบC:
a) From Equation 6.64, โซ
๐ ln ๐พ
๐
๐พ ๐
(๐
๐
)
๐พ
๐
(๐
0
)
1
๐
โ๐ป
๐
ยฐ
๐
2
๐
๐
๐
0
๐๐. To a good
approximation we can assume that the heat capacities are independent of
๐
๐
2
ยฐ
= 9. 48 ร 10
โ 4
๐
2
= 9. 48 ร 10
โ 4
c) What value would you obtain if you assume that โ๐ป ๐
ยฐ
is independent of temperature
in the range 298.15 K to 1350 K?
๐
ln ๐พ
๐
๐ 2
= 1. 66 ร 10
โ 3
