 ## Chemistry (CH- Chemical Equilibrium)

2a-1

A 0.0200-mole sample of SO3 is placed in a 1.0-liter reaction vessel and allowed to decompose until equilibrium is established according to the reaction;  2 SO3(g) = 2 SO2(g) + O2(g).
At equilibrium 0.0029 mole of O2 is present.  What is the composition of the equilibrium mixture in terms of moles/liter of each substance present?

Ans:- [SO3] = 0.0142 [SO2] = 0.0058 [O2] = 0.0029

2a-2

A mixture of 0.296 mole NH3, 0.170 mole N2, and 0.095 mole H2, in a 1.0-liter vessel, is allowed to reach equilibrium according to the reaction;  2 NH3(g) = N2(g) + 3 H2(g).
At equilibrium, it is found that 0.268 mole NH3 is present.  What is the composition of the equilibrium mixture in terms of moles/liter of each substance present?

Solution:- [NH3] = 0.268 [N2] = 0.184 [H2] = 0.137

2a-3

Write the expression for the equilibrium constant for each of the following reactions.
(a) SO2(g)  + Cl2(g)  = SO2Cl2(g)
(b) 2 NO2(g)  = N2(g) +  2 O2(g)
(c) 2 SO3(g)  + CO2(g) =  CS2(g) + 4 O2(g)
(d) 4 H2(g)  + CS2(g)  = CH4(g) +  2 H2S(g)

Ans:- (a) Kc = [SO2Cl2]/[SO2][Cl2] (b) K2 = [N2][O2]2/[NO2]2
(c) Kc = [CS2][O2]4/[SO3]2[CO2] (d) Kc = [CH4][H2S]2/ [H2]4[CS2]

2a-4

The equilibrium constant expression for a gas-phase reaction is KC = [H2O]2[SO2]2/[H2S]2[O2]3. Write the balanced chemical equation form which this expression is obtained.

Ans:- 2H2S(g)+3O2(g)=2H2O(g)+2SO2(g)

Solution:-

2a-5

At a particular temperature, a hypothetical chemical system has the following equilibrium molar concentrations: A = 3.00,  B = 2.00, and C = 5.00. Calculate the value of the equilibrium constant for the system if the reaction occurring were each of the following.
(a) A(g)  = 2 B(g)  + C(g)
(b) A(g)  + 3 B(g)  = 2 C(g) (c) 2 B(g)  = A(g) + C(s)
(d) 4 C(g)  + B(g) = 3 A(g)

Ans:- (a) 6.67 (b) 1.04 (c) 0.750 (d) 0.0216

2a-6

A mixture of 5.000×10-3 mole H2  and 1.000×10-2 mole of I2 is placed in a 5.000-liter container at 448oC and allowed to come to equilibrium according to the following equation.  Analysis of the equilibrium mixture shows that the concentration of HI is 1.87×10-3M. Calculate Kc at 448oC for the reaction mixture.
H2(g)  + I2(g)  = 2HI(g)

Ans:- Kc = 51

Solution:-

2b-1

Write the expression for the equilibrium constant for each of the following reactions.
(a) 2Pb(NO3)2(s)  = 2PbO(s)  + 4NO2(g)  + O2(g)
(b) 2KClO3(s)  = 2KCl(s)  + 3O2(g)
(c) 2Ag(s)  + Cl2(g)  = 2AgCl(s)
(d) PCl5(s)  = PCl3(l)  + Cl2(g)

Ans:-(a) Kc = [NO2]4[O2] (b) Kc = [O2]3 (c) Kc = 1/[Cl2] (d) Kc = [Cl2]

2b-2

Which one of the substances (H2,  H2O, O2) when added to Fe3O4 in a closed container at high temperature, permits attainment of equilibrium in the reaction;  3Fe(s)+4H2O(g)= Fe3O4(s)+4H2(g)?

Solution:- Only H2

2b-3

When the following reactions come to equilibrium, does the equilibrium mixture contain (1) mostly reactants,  (2) mostly products, or (3) appreciable concentrations of both reactants and products?
(a) H2(g)  + S(s)  = H2S(g) KC = 7.8105
(b) N2(g)  + 2 H2(g)  = N2H4(g) KC = 7.410-26
(c) Cl2(g)  + 2 NO2(g)  = 2 NO2Cl2(g) KC = 1.8
(d) H3PO4(aq)  = H+(aq) +  H2PO4-(aq) KC = 7.510-3

Ans:- (a)  2 (b) 1 (c) 3 (d) 3

2b-4

Methane (CH4) reacts with hydrogen sulfide (H2S) to yield H2 and carbon disulfide (CS2), a solvent used manufacturing rayon and cellophane;   CH4(g) + 2H2S(g) = CS2(g) + 4 H2(g).
What is the value of Kp at 1000K if the partial pressure in an equilibrium mixture at 1000K are 0.20atm of CH4, 0.25 atm of H2S, 0.52 atm of CS2, and 0.10 atm of H2.

Ans:- Kp = 4.210-3

2b-5

Nitric oxide reacts with oxygen to give nitrogen dioxide, an important reaction in the process for the industrial synthesis of nitric acid;  2 NO(g) + O2(g) = 2 NO2(g).
(a) If KC = 6.9x105 at 227oC, what is the value of Kp at this temperature?
(b) If Kp = 1.310-2 at 1000K, what is the value of KC at this temperature?

Ans:- (a) Kp = 1.7104 (b) KC = 1.1

2b-6

At 700oC, KC = 20.4 for the reaction;  SO2(g) + ½ O2(g) = SO3(g).
At the same temperature, calculate the following equilibrium constant values.
(a) KC for the reaction;  SO3(g) = SO2(g) + ½ O2(g)?
(b) KC for the reaction;  2 SO2(g) + O2(g) = 2 SO3(g)?
(c) Kp for the reaction;  2 SO2(g) + O2(g) = 2 SO3(g)?

Ans:- (a) KC = 0.0490 (b) KC = 416 (c) Kp = 5.21

2b-7

The equilibrium-constant expression for a reaction is KC = [NO2]4[O2]/[N2O5]2.  The value for the equilibrium constant at a certain temperature is 45.0. What is the value of the equilibrium constant for the reaction at the same temperature if the coefficients in the chemical reaction equation are halved and the equation is then reversed?

Ans:- K = 0.149

Solution:-

2b-8

Calculate the value of the equilibrium constant K3 from the values for K1 and K2.
1. CO(g)  + 3 H2(g)  = CH4(g) +  H2O(g) K1 = 3.92 2. CH4(g)  + 2 H2S(g)  = CS2(g) + 4 H2(g) K2 = 3.3×104 3. CO(g)  + 2 H2S(g)  = CS2(g) + H2O(g)  + H2(g) K3 = ?

Ans:- K3 = 1.3105

2c-1

At 100oC the equilibrium constant for the reaction;  COCl2(g)  = CO(g)  + Cl2(g)
has the value of KC = 2.1910-10.  Are the following mixtures of COCl2, CO, and Cl2 at equilibrium?  If not, indicate the direction that the reaction must proceed to achieve equilibrium.
(a) [COCl2] = 2.0010-3,  [CO] = 3.3110-6,  [Cl2] = 6.6210-6
(b) [COCl2] = 4.5010-2,  [CO] = 1.1010-7,  [Cl2] = 2.2510-6
(c) [COCl2] = 1.0010-2,  [CO] = 1.4810-6,  [Cl2] = 1.4810-6

Ans:- (a) QC > KC   The reaction will proceed to the left to attain equilibrium.
(b) QC < KC   The reaction will proceed to the right to attain equilibrium.
(c) QC = KC   The reaction mixture is at equilibrium.

Solution:-

Q = [Cl2][CO]/[COCl2]

1. Q = 1.09 x 10^-8
since Q > Kc,
c. The reaction will proceed left to attain equilibrium.

2. Q = 5.5 x 10^-12
since Q<Kc,
b. The reaction will proceed right to attain equilibrium.

3. Q = 2.19 x 10^-10
since, Q = Kc,
a. The reaction is at equilibrium.

2c-2

A mixture of SO2,  SO3, and O2 gases is maintained in a 10.0 liter flask at a temperature at which the equilibrium constant for the reaction;  2 SO2(g) + O2(g) = 2 SO3(g), is KC = 1.00102.
(a) If the number of moles of SO2 and SO3 in the flask are equal, how many moles of O2 are present?
(b) If the number of moles of SO3 in the flask is twice the number of moles of SO2, how many moles of O2 are present?

Ans:- (a) 0.100 mole O2 (b) 0.400 mole O2

2c-3

A 1.00-liter vessel contains an unknown amount of PCl5 and 0.020 mole each of PCl3 and Cl2 at equilibrium at 250oC.  The equilibrium reaction is;  PCl5(g)  = PCl3(g)  + Cl2(g).
How many moles of PCl5 are in the vessel if KC for this reaction is 0.0415 at 250oC?

Ans:- [PCl5] = 0.0096

Solution:-

PCl5 (g) → PCl3 (g) + Cl2(g)
1. [PCl3]equ = 0.020 mol / 1.00L
= 0.020 M
[Cl 2] = 0.020 mol / 1.00L
= 0.020 M
Setting up the ICE table,
PCl5 (g) → PCl3(g) + Cl2(g)
Initial: x                  0 0
Change: – 0.020 M     + 0.020M + 0.020 M
Equilibrium: x – 0.020       0.020  0.020
Kc = [PCl3][Cl2] /[PCl5]
0.0415 =(0.020)2 / (x – 0.020)
x = 0.0296 M
[PCl 5]initially = 0.0296 M
[PCl 5]equilibrium = x -0.020 =  0.0296 – 0.020
=0.0096 M

2c-4

In an equilibrium mixture of the gases N2, H2, and NH3 at 500oC, the partial pressure of H2 is 0.928 atm and that of N2 is 0.432 atm.  The equilibrium reaction is; N2(g) + 3 H2(g) = 2 NH3(g).
What is the partial pressure of NH3 of the equilibrium mixture if Kp for this reaction is 1.4510-5 at 500oC?

Solution:- 2.2410-3 atm

2c-5

At 750 oC, KC = 0.771 for the reaction;  H2(g)+CO2(g)=CO(g)+H2O(g) If 1.00 mole of H2 and 1.00 mole of CO2 are placed in a 5.00 liter container and allowed to react, what will be the molar equilibrium concentrations of all species?
Ans :-  [H2] = [CO2] = 0.106 [CO] = [H2O] = 0.0937

Solution:-

Equilibrium: H2(g)  + CO2(g)  = CO(g)  + H2O(g) Equilibrium Constant KC = 0.534

Change in the number of moles of gases, n = n productsn reactants = 2 – 2 = 0

Equilibrium constant in terms of  partial pressure, Kp = KC(RT)Δn = KC(RT)0 = KC

Equilibrium: H2(g)  +   CO2(g)   =   CO(g)   +   H2O(g)

Initial (mol): 0 0 1.00 1.00

Change(mol): +x +x -x -x

Equilibrium (mol) x x 1.00-x 1.00-x

Equilibrium constant, Kc = [CO][H2O][CO2][H2] , (1.00-x)(1.00-x)(x)(x)= 0.534 x = 0.034

2c-6

Solid NH4HS is introduced into an evacuated flask at 24oC and reacts as; NH4HS(s)=NH3(g)+ H2S(g). At equilibrium the total pressure (NH3 plus H2S) is 0.614 atm.  What is Kp for this equilibrium mixture?

Solution:- Kp = 0.0943

2c-7

A sample of nitrosyl bromide, NOBr, decomposes according to the reaction;  2 NOBr(g) = 2 NO(g) + Br2(g).
An equilibrium mixture in a 5.00-liter vessel at 100oC contains 3.22 g of NOBr, 3.08 g of NO, and 4.19 g of Br2.  (a) Calculate KC for the reaction.
(b) Calculate Kp for the reaction.
(c) What is the total pressure exerted by the mixture?

Ans:- (a) Kc = 6.4410-2 (b) Kp = 1.97 (c) PTotal = 0.968 atm

2d-1

Consider the following chemical reaction at equilibrium;  CO(g) + 3 H2(g) = CH4(g) + H2O(g).
For each of the following adjustments in conditions, indicate the effect on the position of equilibrium as shifts left, shifts right, or no effect.

Answer: -(a) shifts right (b) shifts left (c) shifts left (d) shifts right

(a) increase in CO concentration
(b) increase in CH4 concentration
(c) decrease in H2 concentration
(d) decrease in H2O concentration

2d-2

Consider following chemical system at equilibrium; 2C2H2(g)+5O2(g)= 4CO2(g)+2H2O(g)+ heat.
For each of the following adjustments of conditions, indicate the effect on the position of equilibrium as shifts left, shifts right, or no effect.
(a) increasing the C2H2 concentration
(b) decreasing the O2 concentration
(c) increasing the temperature
(d) increasing the pressure by decreasing the volume of the container.

Ans:- (a) shifts right (b) shifts left (c) shifts left (d) shifts right

Solution:-

2d-3

Consider the following chemical reaction at equilibrium;  2H2O(g)+2Cl2(g)+heat=4HCl(g)+O2(g).
For each of the following adjustments in conditions, indicate the effect on the position of equilibrium as shifts left, shifts right, or no effect.
(a) heating the equilibrium mixture
(b) increasing the size of the mixture’s container
(c) increasing the pressure on the equilibrium mixture by adding unreactive He gas
(d) adding a catalyst to the equilibrium mixture

Ans:-(a) shifts right (b) shifts right (c) no effect (d) no effect

Solution:-

2d-4

Consider the following chemical reaction at equilibrium; N2(g)  + 3 H2(g) = 2 NH3(g).
KC = 5.81 at 350oC.  For an equilibrium mixture composition [N2] = 0.885,  [H2] = 0.665, and [NH3] = 1.230, indicate how each of the following adjustments in conditions will affect the position of the equilibrium using shifts left, shifts right, or no effect.
(a) [N2] is increased by 0.200
(b) [NH3] is decreased by 0.200
(c) [N2] is increased by 0.300 and [H2] is increased by 0.200
(d) [N2] is decreased by 0.300 and [H2] is increased by 0.300

Ans:- (a) shifts right (b) shifts right (c).  shifts right (d) QC < KC; shifts right

2d-5

In a 10.0-liter mixture of H2, I2, and HI at equilibrium at 425oC there are 0.100 mole of H2, 0.100 mole of I2, and 0.740 mole of HI.  The equilibrium reaction is; H2(g) + I2(g) = 2 HI(g).

If 0.50 mole of HI is added to this system, what will be the molar concentrations of all the species once equilibrium is reestablished?

Solution:- [H2] = [I2] = 0.0153 [HI] = 0.1134

2d-6

An equilibrium mixture,  CO2(g) + H2(g) = CO(g)  + H2O(g)
was found to contain 0.20 mole of H2, 0.80 mole of CO2, 0.10 mole of CO, and 0.40 mole of H2O in a 1.0-liter vessel.  How many moles of CO2 would have to be added to the equilibrium mixture at constant temperature and volume to increase the amount of CO to 0.20 mole?

Ans:- 3.3 moles/liter

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