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Now that we have a symbol to designate reversible reactions, we will need a way to express mathematically how the amounts of reactants and products affect the equilibrium of the system. A general equation for a reversible reaction may be written as follows:
We can write the reaction quotient ( Q ) for this equation. When evaluated using concentrations, it is called Q c . We use brackets to indicate molar concentrations of reactants and products.
The reaction quotient is equal to the molar concentrations of the products of the chemical equation (multiplied together) over the reactants (also multiplied together), with each concentration raised to the power of the coefficient of that substance in the balanced chemical equation. For example, the reaction quotient for the reversible reaction is given by this expression:
(a)
(b)
(c)
(b)
(c)
(a)
(b)
(c)
(a) (b) (c)
The numeric value of Q c for a given reaction varies; it depends on the concentrations of products and reactants present at the time when Q c is determined. When pure reactants are mixed, Q c is initially zero because there are no products present at that point. As the reaction proceeds, the value of Q c increases as the concentrations of the products increase and the concentrations of the reactants simultaneously decrease ( [link] ). When the reaction reaches equilibrium, the value of the reaction quotient no longer changes because the concentrations no longer change.
![Three graphs are shown and labeled, “a,” “b,” and “c.” All three graphs have a vertical dotted line running through the middle labeled, “Equilibrium is reached.” The y-axis on graph a is labeled, “Concentration,” and the x-axis is labeled, “Time.” Three curves are plotted on graph a. The first is labeled, “[ S O subscript 2 ];” this line starts high on the y-axis, ends midway down the y-axis, has a steep initial slope and a more gradual slope as it approaches the far right on the x-axis. The second curve on this graph is labeled, “[ O subscript 2 ];” this line mimics the first except that it starts and ends about fifty percent lower on the y-axis. The third curve is the inverse of the first in shape and is labeled, “[ S O subscript 3 ].” The y-axis on graph b is labeled, “Concentration,” and the x-axis is labeled, “Time.” Three curves are plotted on graph b. The first is labeled, “[ S O subscript 2 ];” this line starts low on the y-axis, ends midway up the y-axis, has a steep initial slope and a more gradual slope as it approaches the far right on the x-axis. The second curve on this graph is labeled, “[ O subscript 2 ];” this line mimics the first except that it ends about fifty percent lower on the y-axis. The third curve is the inverse of the first in shape and is labeled, “[ S O subscript 3 ].” The y-axis on graph c is labeled, “Reaction Quotient,” and the x-axis is labeled, “Time.” A single curve is plotted on graph c. This curve begins at the bottom of the y-axis and rises steeply up near the top of the y-axis, then levels off into a horizontal line. The top point of this line is labeled, “k.”](/ocw/mirror/col11830_1.13_complete/m51109/CNX_Chem_13_02_quotient.jpg)
When a mixture of reactants and products of a reaction reaches equilibrium at a given temperature, its reaction quotient always has the same value. This value is called the equilibrium constant ( K ) of the reaction at that temperature. As for the reaction quotient, when evaluated in terms of concentrations, it is noted as K c .
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