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Wize University Chemistry Textbook > Equilibrium

Solving for K in Different Scenarios

The Equilibrium Constant (K)Previous Section
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Manipulating Equilibrium Constants

Now we are going to take a look at how the value for K changes in different scenarios (when we reverse the reaction, multiply a reaction by a coefficient, and add two reactions together).

First, let's write the K expression for the reaction below:

PCl3(g)+Cl2(g)⇌PCl5(g) PCl_3(g)+Cl_2(g)⇌PCl_5(g)

Kc=[PCl5][Cl2][PCl3]K_c=\frac{[PCl_5]}{\left[Cl_2\right]\left[PCl_3\right]}

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What happens to K when we reverse the reaction?

PCl5(g)⇌PCl3(g)+Cl2(g)PCl_5(g)⇌PCl_3(g)+Cl_2(g)


1Kc=[Cl2][PCl3][PCl5]\frac{1}{K_c}=\frac{\left[Cl_2\right]\left[PCl_3\right]}{[PCl_5]}


Wize Tip
If you reverse a reaction, take the inverse of K to find Knew!


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What happens to K when we multiply the reaction by a factor?

2PCl3(g)+2Cl2(g)⇌2PCl5(g)2PCl_3(g)+2Cl_2(g)⇌2PCl_5(g)


(Kc)2=([PCl5][PCl3][Cl2])2\left(K_c\right)^2=\left(\frac{\left[PCl_5\right]}{[PCl_3]\left[Cl_2\right]}\right)^{^2}



Wize Tip
When you multiply a reaction by a coefficient, take K to the power of that factor to solve for Knew!


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How do we solve for Koverall given K for reactions that are being added together?



2N2(g)+O2(g)⇌2N2O(g)] Kc,1+2N2O(g)+3O2(g)⇌4NO2(g) Kc,22N2(g)+4O2(g)⇌4NO2(g) Koverall\def\arraystretch{1.5}\begin{array}{cc}2N_2(g)+O_2(g)⇌2N_2O(g)]\ K_{c,1} \\ +2N_2O(g)+3O_2(g)⇌4NO_2(g)\ K_{c,2}\\ \hline 2N_2(g)+ 4O_2(g)⇌4NO_2(g) \ K_{overall}\end{array}








Koverall = (Kc,1)∗(Kc,2)K_{overall}\ =\ (K_{c,1})*(K_{c,2})

Wize Tip
When adding two reactions together, multiply their K values together to solve for Koverall!

Practice: Solving For K

Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_2{(g)} \hspace{20pt} K_c,1
2H2S2(g)⇌2H2(g)+S2(g)Kc,22H_2S_2{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_c,2
The equilibrium constant for the reaction is:
2HCl(g)+12S2(g)⇌H2S2(g)+Cl2(g)Kc,32HCl_{(g)} + \frac{1}{2} S_{2(g)} \rightleftharpoons H_2S_{2(g)}+Cl_{2(g)} \hspace{20pt} K_c,3
a)Kc3=Kc,1Kc,2K_c3 = \frac{K_c,1}{K_c,2}

b)Kc3=Kc,2Kc,1K_c3 = \frac{K_c,2}{K_c,1}

c)Kc3=2Kc,1Kc,2K_c3 = \frac{2K_c,1}{K_c,2}

d) Kc3=Kc,1Kc,212K_c3 = \frac{K_c,1}{K_c,2^\frac{1}{2}}

e)Kc3=Kc,22Kc,1K_c3 = \frac{K_c,2^2}{K_c,1}

Extra Practice
Equilibrium
Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_2{(g)} \hspace{20pt} K_c,1
2H2S2(g)⇌2H2(g)+S2(g)Kc,22H_2S_2{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_c,2
Equilibrium
Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_2{(g)} \hspace{20pt} K_c,1
2H2S2(g)⇌2H2(g)+S2(g)Kc,22H_2S_2{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_c,2
Equilibrium
Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_2{(g)} \hspace{20pt} K_c,1
2H2S2(g)⇌2H2(g)+S2(g)Kc,22H_2S_2{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_c,2
Equilibrium
Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_2{(g)} \hspace{20pt} K_c,1
2H2S2(g)⇌2H2(g)+S2(g)Kc,22H_2S_2{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_c,2
Equilibrium
Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_2{(g)} \hspace{20pt} K_c,1
2H2S2(g)⇌2H2(g)+S2(g)Kc,22H_2S_2{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_c,2
Equilibrium
Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_2{(g)} \hspace{20pt} K_c,1
2H2S2(g)⇌2H2(g)+S2(g)Kc,22H_2S_2{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_c,2
Equilibrium
Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_2{(g)} \hspace{20pt} K_c,1
2H2S2(g)⇌2H2(g)+S2(g)Kc,22H_2S_2{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_c,2
Concept Clarifier
Consider the following reaction
2 SO2+O2⇌2 SO3\rm 2\ {SO_2} \quad+\quad {O_2}\quad \xrightleftharpoons{\hspace{1.5cm}}\quad 2\ {SO_3}
ΔH0=−180 kJ/mol\Delta H^0=-180\ kJ/mol
Equilibrium constant
The value of Kp for the reaction: NO (g) ⇌ ½ N2 (g) + ½ O2 (g) is 2.5x107. What is the Kp for the reaction: N2 (g) + O2 (g) ⇌ 2 NO (g)?
Equilibrium constant
The equilibrium constant for reaction #1 below is K. The equilibrium constant for reaction #2 is therefore ________.
(1) 2 SO3 (g) ⇌ 2 SO2 (g) + O2 (g)
(2) SO2 (g) + ½ O2 (g) ⇌ SO3 (g)
Equilibrium constant
Consider the following equilibrium: 2 HI (g) ⇌ H2 (g) + I2 (g)
If the equilibrium constant for this reaction at a certain temperature is Kc = 0.04, what is the equilibrium constant K’c for the following reaction at the same temperature:
½ H2 (g) + ½ I2 (g) = HI (g)
Equilibrium constant
For the following equilibria determine whether K>1K > 1, K<1K < 1 or K≈1K \approx 1. Enter your answers as "Greater", "Less", "1" respectively.
A)
B)
Equilibrium: Equilibrium constant
If the equilibrium constant for reaction 1 below is K, what is the equilibrium constant for reaction 2?
(1) SO2 (g) + ½ O2 (g) ⇌ SO3 (g)
(2) 2SO3 (g) ⇌ 2 SO2 (g) + O2 (g)
Equilibrium: Equilibrium constant
If Kc = 0.212 at 100oC for N2O4 (g) ⇌ 2 NO2 (g)
Determine the value of Kc at 100oC for 2 NO2 (g) ⇌ N2O4 (g)
Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_{2(g)} \hspace{20pt} K_{c,1}
2H2S(g)⇌2H2(g)+S2(g)Kc,22H_2S_{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_{c,2}
A reaction is found to have an equilibrium constant of 3.5 x 10-3 at standard temperature. If the enthalpy change of this process is +45.6 kJ/mol, what will be the value of the equilibrium constant at 455 K?
At 450 K, the equilibrium constant in terms of pressure,
CO(g)+H2O(g)→H2(g)+CO2(g)Kp=34.7CH4(g)+O2→CO2(g)+2 H2(g)Kp=119.2\begin{array}{cc} CO_{(g)}+H_2O_{(g)}\rightarrow H_{2(g)}+CO_{2(g)} & K_p=34.7 \\ CH_{4(g)}+O_{2}\rightarrow CO_{2(g)}+2\ H_2{(g)} & K_p=119.2 \end{array}
What is Kp for the following reactio at 450 K?
The equilibrium constant, Kc, for the following reaction below was measured at 7.7.
SO3(g)+NO(g)⇌NO2(g)+SO2(g)SO_{3}(g)+NO(g)\rightleftharpoons NO_{2}(g)+SO_{2}(g)
At the same temperature the measurement was taken, a mixture of 0.4 M SO3 and 0.4 M NO was generated. After allowing the system to reach equilibrium what is the concentration of SO2?
Equilibrium constant
At a certain temperature, the value of the equilibrium constant for the following reaction is
Kc = 100. N2 (g) + 2 O2 (g) ⇌ 2 NO2 (g)
What is the equilibrium constant for the following reaction?
Equilibrium: ICE Table
Cyclohexane (C6H12) undergoes an isomerization in the presence of the appropriate catalyst to form a compound called MCP.
C6H12 (g) ⇌ MCP (g) Kc = 0.143 at 25oC
The initial concentrations are [C6H12] = 0.800 M and [MCP] = 0.100 M. What are the equilibrium concentrations of these two compounds?
Equilibrium: Equilibrium Constant
For the equilibrium process 2 SO3 (g) ⇌ 2 SO2 (g) + O2 (g), determine the value of Kc when an equilibrium mixture contains 0.025 mol O2, 0.27 mol SO2, and 0.018 mol SO3 in a 5.00 liter container at 220oC.
A reaction mixture consisting of 0.400 mol H2 and 1.60 mol I2 was introduced into a 3.00 L flask and heated. At equilibrium 60% of the hydrogen gas had reacted. What is the equilibrium constant Kc for the reaction H2 (g) + I2 (g) ⇌ 2 HI (g)?
If the equilibrium constant for reaction 1 below is K, what is the equilibrium constant for reaction 2?
1. SO2(g) + ½ O2(g) ⇌ SO3(g)
2. 2 SO3(g) ⇌ 2 SO2(g) + O2(g)
If Kc = 0.212 at 100oC for N2O4(g) ⇌ 2 NO2(g)
Determine the value of Kc at 100oC for 2 NO2(g) ⇌ N2O4(g)
Equilibrium constant
At 550oC acetic acid (CH3COOH) is a gas. A sample of pure acetic acid vapour at 550oC decomposes into carbon dioxide (CO2) and methane (CH4) with an equilibrium constant of 3.40 X 104 measured in kPa. At equilibrium a near-IR spectrometer meassures the methane partial pressure to be 255 kPa. What are the equilibrium partial pressures for carbon dioxide and acetic acid?
Express your answer in units of kPa to three significant figures. do not include units in the answer field
Equilibrium Constant
A one liter vessel was filled with 0.398 mol of NOCl(g). Then the temperature of the system was increased to 245 °C to undergo the following reaction:
2NOCl(g)⇌2NO(g)+Cl2(g)2NOCl(g) \rightleftharpoons 2NO(g) +Cl_2(g)
When equilibrium was attained, the concentration of Cl2 was 0.0225 mol/liter. Calculate the value of Kc at 245 °C for the reaction.
Equilibrium
Consider the following equilibria:
2HCl(g)⇌H2(g)+Cl2(g)Kc,12HCl_{(g)} \rightleftharpoons H_{2(g)} +Cl_2{(g)} \hspace{20pt} K_c,1
2H2S2(g)⇌2H2(g)+S2(g)Kc,22H_2S_2{(g)} \rightleftharpoons 2H_{2(g)} +S_2{(g)} \hspace{20pt} K_c,2
Equilibrium: Equilibrium constant
For the equilibrium process NH4SH (s) ⇌ NH3 (g) + H2S (g), Kc = 1.2x10-4 at 218oC. What is the equilibrium concentration of NH3 if a sample of NH4SH is allowed to achieve equilibrium at 218oC in a sealed rigid vessel?
Equilibrium: Equilibrium Constant
For the equilibrium process 2 SO3 (g) ⇌ 2 SO2 (g) + O2 (g), determine the value of Kc when an equilibrium mixture contains 0.025 mol O2, 0.27 mol SO2, and 0.018 mol SO3 in a 5.00 liter container at 220oC.
Equilibrium: Equilibrium Constant
If Kc = 0.212 at 100oC for N2O4 (g) ⇌ 2 NO2 (g)
Determine the value of Kc at 100oC for 2 NO2 (g) ⇌ N2O4 (g)
Equilibrium constant
A 1.0 L flask was loaded and the system was allowed to reach equilibrium at 25 °C. The equilibrium mixture was found to contain: 1.5 mol Cr (S), 1.5 mol CCI4 (g), 2.3 mol CrCl3, (g), and 2.5 mol C (S). Determine the Kc value for this reaction at 25 °C.
Equilibrium Constant
Based on the reactions and equilibrium constants given below, determine the value of the equilibrium constant (Kf) for the formation of the soluble PbI42- complex:
𝑃𝑏𝐼2(𝑠)⇌𝑃𝑏2+(𝑎𝑞)+2𝐼−(𝑎𝑞)𝐾𝑠𝑝=7.9×10−9𝑃𝑏𝐼2(𝑠)+2𝐼−(𝑎𝑞)⇌𝑃𝑏𝐼42−(𝑎𝑞)𝐾=2.37×10−4𝑃𝑏2+(𝑎𝑞)+4𝐼−(𝑎𝑞)⇌𝑃𝑏𝐼42−(𝑎𝑞)𝐾𝑓=?\begin{alignedat}{} &𝑃𝑏𝐼_2 (𝑠) ⇌𝑃𝑏^{2+}(𝑎𝑞)+2 𝐼^− (𝑎𝑞) &&𝐾_{𝑠𝑝}=7.9×10^{−9}\\ &𝑃𝑏𝐼_2(𝑠)+2 𝐼^− (𝑎𝑞) ⇌𝑃𝑏𝐼_4^{2−} (𝑎𝑞) &&𝐾=2.37×10^{−4}\\ &𝑃𝑏^{2+} (𝑎𝑞)+4 𝐼^− (𝑎𝑞)⇌𝑃𝑏𝐼_4^{2−} (𝑎𝑞) &&𝐾_𝑓= ? \end{alignedat}
Which answer below correctly describes the calculation to find the equilibrium expression K4?
CH4(g)+H2O(g)⇌CO(g)+3H2(g)K1CH4(g)+2S2(g)⇌CS2(g)+2H2S(g)K2CO2(g)+H2(g)⇌CO(g)+H2O(g)K3CS2(g)+2H2S(g)+3CO2(g)⇌4CO(g)+2S2(g)+2H2O(g)K4\def\arraystretch{1.5} \begin{array}{c:c} CH_4 (g)+H_2 O(g)⇌CO(g)+3H_2 (g) & K_1 \\ CH_4 (g)+2S_2 (g)⇌CS_2 (g)+2H_2 S(g) & K_2\\ CO_2 (g)+H_2 (g)⇌CO(g)+H_2 O(g) & K_3\\ CS_2 (g)+2H_2 S(g)+3CO_2 (g)⇌4CO(g)+2S_2 (g)+2H_2 O(g) & K_4 \end{array}
Equilibrium Constant
Given the following information:
Ni(OH)2(s)⇌Ni2+(aq)+2OH−(aq)Ksp=6.0×10−16H2O(l)⇌H+(aq)+OH−(aq)Kw=1.0×10−14\def\arraystretch{1.5}\begin {array}{cc}Ni(OH)_2 (s) ⇌Ni^{2+} (aq)+2OH^- (aq)&&K_{sp}= 6.0 ×10^{-16}\\ H_2 O(l) ⇌H^+ (aq)+OH^- (aq) &&K_w= 1.0×10^{-14}\end{array}
What is the equilibrium constant for the reaction,
Equilibrium: Equilibrium constant
At 25 ˚C, KP = 5.2 × 10–2 for the following decomposition reaction:
NH4HS(s)⇌NH3(g)+H2S(g)NH_4HS(s)⇌NH_3(g)+H_2S(g)
Use the following scenario for the next two questions
The reaction for the reforming of methane from steam is given by:
CH4(g)+H2O(g)⇌CO(g)+3H2(g)CH_4 (g) + H_2 O (g) ⇌ CO (g) + 3 H_2 (g)
Given the following information at 298 K:
SnO2(s)+2H2(g)⇌Sn(s)+2H2O(g)K1=8.12H2(g)+CO2(g)⇌H2O(g)+CO(g)K2=0.771\def\arraystretch{1.5} \begin{array}{cc} SnO_2 (s) + 2 H_2 (g) ⇌ Sn (s) + 2 H_2 O (g) & K_1 = 8.12 \\ H_2 (g) + CO_2 (g) ⇌ H_2 O (g) + CO (g) &K_2 = 0.771 \end{array}
Determine the K for the overall reaction: SnO2(s)+2CO(g)⇌Sn(s)+2CO2(g).SnO_2 (s) + 2 CO (g) ⇌ Sn (s) + 2 CO_2 (g).
Equilibrium and Le Chatelier's Principle
At time = t0, 0.40 mol of Br2 (ℓ) and 0.40 mol of Cℓ2 (g) are placed in an empty, rigid 10.00 L flask and allowed to reach equilibrium.
After reaching equilibrium at time = t2, the flask is found to contain 0.20 mol of BrCℓ (g). The temperature is held constant throughout the reaction.
Equilibrium: Keq Values
Consider the following equilibria:
2HBr(g)⇌H2(g)+Br(g)Kc,12HBr_{(g)} \rightleftharpoons H_{2(g)} +Br_{(g)} \hspace{20pt} K_c,_1
2H2O(g)⇌2H2(g)+O(g)Kc,22H_2O_{(g)} \rightleftharpoons 2H_{2(g)} +O_{(g)} \hspace{20pt} K_c,_2