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Mass-Action Expressions (Q) Tutorial

Key Concepts

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Writing the Mass-Action Expression, Q

By agreement, reactants are defined as on the left of a chemical equation and products on the right:

reactants products
aA + bB cC + dD

Each term used in the mass-action expression, Q, is the concentration of the species raised to the power of its stoichiometric coefficient:

general reaction: reactants products
reaction equation: aA + bB cC + dD
term for each species [A]a   [B]b   [C]c   [D]d

The mass-action expression, Q, is written in the form:

Q =   numerator  
denominator

By general agreement:

general reaction: reactants products
reaction equation: aA + bB cC + dD
term for each species [A]a   [B]b   [C]c   [D]d
numerator term   [C]c[D]d
denominator term [A]a[B]b  
mass-action expression, Q =   numerator  
denominator
= [C]c[D]d
[A]a[B]b

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Worked Example: Reaction in Gas Phase

Question: Write the mass-action expression for the following reaction:

2CO2(g) ⇋ 2CO(g) + O2(g)

Step 1: Determine which are the products and which are reactants for this reaction:

general reaction: reactants products
reaction equation: 2CO2(g) 2CO(g) + 1O2(g)

Remember: if there is no number in front of the chemical formula for a particular species in the equation, then it is understood that the stoichiometric coefficient is in fact 1.

Step 2: Write a term for each species in the form of its concentration raised to the power of its stoichiometric coefficient:

general reaction: reactants products
reaction equation: 2CO2(g) 2CO(g) + 1O2(g)
terms for each species: [CO2(g)]2   [CO(g)]2   [O2(g)]1

Note: any number raised to the power of 1 is simply equal to that number, that is, 21 = 2, 10561 = 1056, etc
So, [O2(g)]1 = [O2(g)]

Step 3: Write the term for the numerator by multiplying together the terms for each product:

general reaction: reactants products
reaction equation: 2CO2(g) 2CO(g) + 1O2(g)
terms for each species: [CO2(g)]2   [CO(g)]2   [O2(g)]1
numerator term     [CO(g)]2[O2(g)]

Step 4: Write the term for the denominator by multiplying together the terms for each reactant:

general reaction: reactants products
reaction equation: 2CO2(g) 2CO(g) + 1O2(g)
terms for each species: [CO2(g)]2   [CO(g)]2   [O2(g)]1
numerator term     [CO(g)]2[O2(g)]
denominator term: [CO2(g)]2        

Step 5: Write the mass-action expression, Q, by dividing the numerator by the denominator:

general reaction: reactants products
reaction equation: 2CO2(g) 2CO(g) + 1O2(g)
terms for each species: [CO2(g)]2   [CO(g)]2   [O2(g)]1
numerator term     [CO(g)]2[O2(g)]
denominator term: [CO2(g)]2        
mass-action expression, Q =   numerator  
denominator
= [CO(g)]2[O2(g)] 
[CO2(g)]2

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Worked Example: Reaction in Aqueous Solution

Question: Write the mass-action expression for the following reaction:

Fe3+(aq) + SCN-(aq) ⇋ Fe(SCN)2+(aq)

Step 1: Determine which are the products and which are reactants for this reaction:

general reaction: reactants products
reaction equation: 1Fe3+(aq) + 1SCN-(aq) 1Fe(SCN)2+(aq)

Remember: if there is no number in front of the chemical formula for a particular species in the equation, then it is understood that the stoichiometric coefficient is in fact 1.

Step 2: Write a term for each species in the form of its concentration raised to the power of its stoichiometric coefficient:

general reaction: reactants products
reaction equation: 1Fe3+(aq) + 1SCN-(aq) 1Fe(SCN)2+(aq)
individual terms: [Fe3+(aq)]1   [SCN-(aq)]1   [Fe(SCN)2+(aq)]1

Note: any number raised to the power of 1 is simply equal to that number, that is, 21 = 2, 10561 = 1056, etc
So, [Fe3+(aq)]1 = [Fe3+(aq)]
and [SCN-(aq)]1 = [SCN-(aq)]
and [Fe(SCN)2+(aq)]1 = [Fe(SCN)2+(aq)]

Step 3: Write the term for the numerator by multiplying together the terms for each product:

general reaction: reactants products
reaction equation: 1Fe3+(aq) + 1SCN-(aq) 1Fe(SCN)2+(aq)
individual terms: [Fe3+(aq)]1   [SCN-(aq)]1   [Fe(SCN)2+(aq)]1
numerator term:     [Fe(SCN)2+(aq)]

Step 4: Write the term for the denominator by multiplying together the terms for each reactant:

general reaction: reactants products
reaction equation: 1Fe3+(aq) + 1SCN-(aq) 1Fe(SCN)2+(aq)
individual terms: [Fe3+(aq)]1   [SCN-(aq)]1   [Fe(SCN)2+(aq)]1
numerator term:     [Fe(SCN)2+(aq)]
denominator term: [Fe3+(aq)][SCN-(aq)]    

Step 5: Write the mass-action expression, Q, by dividing the numerator by the denominator:

general reaction: reactants products
reaction equation: 1Fe3+(aq) + 1SCN-(aq) 1Fe(SCN)2+(aq)
individual terms: [Fe3+(aq)]1 + [SCN-(aq)]1 [Fe(SCN)2+(aq)]1
numerator term:     [Fe(SCN)2+(aq)]
denominator term: [Fe3+(aq)][SCN-(aq)]    
mass-action expression, Q =   numerator  
denominator
= [Fe(SCN)2+(aq)] 
[Fe3+(aq)][SCN-(aq)]

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