Calculating the Reaction Quotient, Q

The expression for the reaction quotient, Q, looks like that used to calculate an equilibrium constant but Q can be calculated for any set of conditions, not just for equilibrium.

Q can be used to determine which direction a reaction will shift to reach equilibrium. If K > Q, a reaction will proceed forward, converting reactants into products. If K < Q, the reaction will proceed in the reverse direction, converting products into reactants. If Q = K then the system is already at equilibrium.

In order to determine Q we need to know:

the equation for the reaction, including the physical states,
the quantities of each species (molarities and/or pressures), all measured at the same moment in time.

To calculate Q:

Write the expression for the reaction quotient.
Find the molar concentrations or partial pressures of each species involved.
Subsitute values into the expression and solve.

Example: 0.035 moles of SO₂, 0.500 moles of SO₂Cl₂, and 0.080 moles of Cl₂ are combined in an evacuated 5.00 L flask and heated to 100^oC. What is Q before the reaction begins? Which direction will the reaction proceed in order to establish equilibrium?

SO₂Cl₂(g) SO₂(g) + Cl₂(g) K_c = 0.078 at 100^oC

Write the expression to find the reaction quotient, Q.
Since K_c is given, the amounts must be expressed as moles per liter (molarity). The amounts are in moles so a conversion is required.

0.500 mole SO₂Cl₂/5.00 L = 0.100 M SO₂Cl₂

0.035 mole SO₂/5.00 L = 0.070 M SO₂

0.080 mole Cl₂/5.00 L = 0.016 M Cl₂
Substitute the values in to the expression and solve for Q.
Compare the answer to the value for the equilibrium constant and predict the shift.

0.078 (K) > 0.011 (Q)

Since K >Q, the reaction will proceed in the forward direction in order to increase the concentrations of both SO₂ and Cl₂ and decrease that of SO₂Cl₂ until Q = K.

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