 # Mass-Action Expressions (Q) Tutorial

## Key Concepts

• Mass-action expression is also known as the reaction quotient, or as the concentration fraction.
• Mass-action expression (reaction quotient or concentration fraction) is given the symbol Q
• For a given reversible reaction:

aA + bB ⇋ cC + dD

the mass-action expression (Q) is defined as

 Q = [C]c[D]d[A]a[B]b

where the square brackets, [], refer to the concentration of that species in a certain phase.
• The mass-action expression (Q) can have any value.

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

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

 Q = numerator   denominator

By general agreement:

• the numerator of the mass-action expression (above the line) contains the product terms multiplied together
• the denominator of the mass-action expression (below the line) contains the reactant terms multiplied together

 general reaction: reaction equation: term for each species numerator term denominator term mass-action expression, Q = reactants ⇋ products aA + bB ⇋ cC + dD [A]a [B]b [C]c [D]d [C]c[D]d [A]a[B]b 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: reaction equation: reactants ⇋ products 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: reaction equation: terms for each species: reactants ⇋ products 2CO2(g) ⇋ 2CO(g) + 1O2(g) [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: reaction equation: terms for each species: numerator term reactants ⇋ products 2CO2(g) ⇋ 2CO(g) + 1O2(g) [CO2(g)]2 [CO(g)]2 [O2(g)]1 [CO(g)]2[O2(g)]

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

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

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

 general reaction: reaction equation: terms for each species: numerator term denominator term: reactants ⇋ products 2CO2(g) ⇋ 2CO(g) + 1O2(g) [CO2(g)]2 [CO(g)]2 [O2(g)]1 [CO(g)]2[O2(g)] [CO2(g)]2 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: reaction equation: reactants ⇋ products 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: reaction equation: individual terms: reactants ⇋ products 1Fe3+(aq) + 1SCN-(aq) ⇋ 1Fe(SCN)2+(aq) [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: reaction equation: individual terms: numerator term: reactants ⇋ products 1Fe3+(aq) + 1SCN-(aq) ⇋ 1Fe(SCN)2+(aq) [Fe3+(aq)]1 [SCN-(aq)]1 [Fe(SCN)2+(aq)]1 [Fe(SCN)2+(aq)]

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

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

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

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

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