Given the balanced chemical equation of a reaction in equilibrium aU + bV <-> cY + dZ, we define as the forward reaction aU + bV -> cY + dZ with reactants U,V and products Y, Z and the reverse reaction as cY + dZ -> aU + bV with reactants Y, Z and products U, V. The coefficients a, b, c, d represent the relative amounts (in moles) of the substances U, V, Y, Z needed for the reaction. That is, a moles of U and b moles of V react to form c moles of Y and d moles of Z. [1 mole is a quantity (6.022 x 10^23) of things just like 1 dozen is a quantity (12) of things]
By definition, equilibrium is when the rate of the forward reaction equals the rate of the reverse reaction. So when a reaction is in equilibrium, the concentrations of the substances (reactants and products) remains constant even as the reactions continue happening.
If we add (or subtract) the amount of one (or more) of the substances, the reaction will no longer be in equilibrium. The reactions will continue at different rates until equilibrium is again reached at the same equilibrium concentrations as before.
For example, if we add substance U to the mixture the increase in the concentration of U will cause an increase in the rate of the forward reaction (more U-molecules reacting with the available V-molecules) tending to increase the product concentrations [Y] and [Z] while decreasing the reactant concentrations [U] and [V]. The product concentrations will increase until the reverse rate of reaction matches the forward rate. Note the forward rate will decrease as the concentrations of [U] and [V] decrease.
A reaction depends on the right molecules interacting with each other with the right kinetic energy to cause the necessary reaction-causing collisions to effect the redistribution of electrons amongst the constituent molecules. The ambient temperature is a measure of the average kinetic energy of the molecules and the actual molecules have a kinetic energy distribution which we can take as a probability density function about this average. Thus some molecules have higher than average KE and some lower. In particular, the higher the temperature the more higher energy collisions. At the same time, the concentrations of the constituent molecules is also directly related to the rate of reaction-causing collisions. The more molecules we have per volume, the more likely they will collide.
A mathematical description of the discussion above follows. The rate of a reaction
aU + bV -> cY + dZ is governed by the probability of getting effective collisions between reacting molecules. For example, in the forward reaction we need to get a molecules of U together with b molecules of V in a small enough volume dW and with sufficient kinetic energy to make effective collisions. Assuming for now that the temperature T allows some number of such collisions (the number then being proportional to the temperature) the other factor is the concentrations [U] and [V] of the reactants. The probability of getting a U molecule in a volume dW is directly proportional to [U] and the same for V molecules. Thus the probability of getting the required number of molecules in dW for a reaction to occur is proportional to [U]^a [V]^b. Let P(T) be the probability of a reaction occurring at temperature T given the molecules are within the reaction volume dW. Then the overall probability of a reaction is proportional to the product [U]^a [V]^b x P(T). Since P(T) is fixed for the reaction we have that the probability of an effective collision is directly proportional to [U]^a [V]^b. Thus the rate of the forward reaction is directly proportional to [U]^a [V]^b. Similarly, the rate of the reverse reaction is directly proportional to [Y]^c [Z]^d. Since at equilibrium these rates are equal, we know that the ratio [U]^a [V]^b/[Y]^c [Z]^d must be equal to some constant for a given temperature T. This equilibrium constant is a property of the chemical reaction aU + bV <-> cY + dZ and can be used to predict outcomes of experiments.
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