Reaction Graphs
Chemical reactions occur either in closed or in open systems. Closed systems are those that are separate from their surroundings, no matter can enter or leave the system. Evidence from many chemical reactions occurring in a closed system has shown that even after the reactions appear to have stopped, there is still a mixture of reactants and products present. This indicates that closed systems are in a dynamic equilibrium where the forward reaction and the reverse reaction are both occurring simultaneously and at the same rate. A Forward reaction depicts the formation of products from reactants, and the reverse reaction depicts the formation of reactants from the products.
In summary, Equilibrium is, therefore, a state in which there are no observable changes as time goes by. A chemical equilibrium is achieved when the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products remain constant.
An illustration of chemical equilibrium with A representing reactants and B representing products. (Source: Wikipedia-CC BY-SA 3.0)
Physical equilibrium: Occurs when there is a change, such as state without an actual chemical reaction. For example:
H2O(l) ⇆ H2O(g).
Chemical equilibrium: Occurs when there is an actual chemical reaction, with or without other changes in physical properties. For example:
N2O4(g) ⇆ NO2(g)
Phase equilibrium: Occurs when the only change is in the state/phase of the reactants. For example:
H2O(l) ⇆ H2O(g)
Solubility equilibrium: Occurs when there is a change in solubility of either the reactant or the product. For example:
CuSO4(s) ⇆ Cu2+(aq) + SO4 2-(aq)
There are three possible scenarios in chemical reactions.
The rate of the forward reaction decreases as the number of reactant molecules decreases resulting in fewer collisions. While the rate of the reverse reaction increases as the number of product molecules increases allowing more collisions.
In previous studies, such as in stoichiometry, we have assumed that all the reactants molecules form products resulting in the maximum possible yield. These reactions can be called quantitative reactions. Some reactions however do not react to the point of using up all the reactants. Percent Yield provides a way to refer to the chemicals present in equilibrium systems. For example:
H2 (g) + I2 (g) ⇆ 2HI (g) at t= 448oC
The percent yield is easily calculated as (Yield at equilibrium / Maximum possible yield) * 100.
| Reaction | Concentration at equilibrium | Maximum possible concentration | Percent Yield (%) | Classification |
|---|---|---|---|---|
| 1 | 7.80 | 10.0 | 78.0 | Products favored |
| 2 | 0.30 | 8.20 | 0.04 | No apparent reaction (non-spontaneous) |
| 3 | 3.80 | 10.0 | 38.0 | Reactants favored |
| 4 | 4.95 | 5.0 | 99.0 | Quantitative |
The table above shows the concept of percent yield, that different reactions will have result in different concentrations of products. The percent yield values can also be used to determine whether a reaction will be spontaneous (or not) and whether it will move in the forward direction (favor products) or reverse direction (favor reactants). Reactions with percent yield less than 50% favor reactants and move in the reverse direction. Reactions with percent yield >50% favor products and move in the forward direction. Reactions with near 0 percent yield will not occur spontaneously.
ICE tables are used for quantitative calculations involving chemical equilibrium systems that are not quantitative (i.e. less than 99.9% yield). I- Initial, C - Change and E - Equilibrium.
Consider the reaction example provided before - H2 (g) + I2 (g) ⇆ 2HI (g) at t= 448oC. The ICE table below shows the concentration of reactants and products, and the change.
| Reaction | H2 (g) | I2 (g) | 2HI (g) |
|---|---|---|---|
| Initial | 1 | 1 | 0 |
| Change | - 0.78 | - 0.78 | +1.6 |
| Equilibrium | 0.22 | 0.22 | 1.6 |
When there are more than one mole of substances in the reaction, for example, 2X(g) ⇆ 3Y (g) + 4Z (g)
| Reaction | 2X | 3Y | 4Z |
|---|---|---|---|
| Initial | 0.5 | 0 | 0 |
| Change | -0.15 | +0.225 | +0.30 |
| Equilibrium | 0.350 | 0.225 | 0.30 |
Change in amount = Equilibrium amount - Initial amount.
Consider the following generic reaction equation for a system at equilibrium:
aA + bB ⇆ cC + dD
The equilibrium law expression can be used to calculate the value of the equilibrium constant, Kc.
Equilibrium law expressions do not have to include solids or liquids because their concentrations are fixed – the chemical amount (number of moles) per unit volume is a constant value. The greater the value of the equilibrium constant, the more the products are favored at equilibrium. If Kc > 1, then the products are favored at equilibrium. If Kc is less than 1, then the reactants are favored at equilibrium. The equilibrium constant for water does not change so does not need to be included in calculations. The Kc for solids is also considered constant and should not be included.
Examples:
6HCl (aq) + 1Fe2O 3 (s) ⇆ 2FeCl3 (aq) + 3H2O (l)
In this example, exclude water and solids
Kc = [FeCl3]2 ⁄ [HCl]6
The ICE table can be extended to include Ratio, making it the RICE table. Ration in this case depicts the molar ratios of each component of the reaction in a balanced chemical equation. For example, in the reaction below, if K = 64, and [I2] = 0.020 moles, what will be concentrations at Equilibrium.
H2 (g) + I2 (g) ⇆ 2HI (g)
K = [HI]2 ⁄ [H2] [I2] = 64
Because [I2] = 0.02, and they are same ratio as [H2], then [H2] is also 0.020 moles.
[HI]2 = 64 X [0.02] [0.02] = 0.160. You can now use this value to fill in the RICE table below, in bold letters
| Reaction | H2 (g) | I2 (g) | 2HI (g) |
|---|---|---|---|
| Ratio | 1 | 1 | 2 |
| Initial | 0.1 | 0.1 | 0 |
| Change | -0.08 | -0.08 | +0.16 |
| Equilibrium | 0.02 | 0.02 | 0.16 |
Changes in the physical properties of a reaction system (including Temperature, Pressure, volume and concentration or reactants or products, presence of a catalyst) could disturb the equilibrium of the reaction. This theory was described through the Le Chatelier's principle developed by Henri Louis Le Chatelier. The Le Chatelier's Principle or Law states that The Equilibrium of a system acts in a way that opposes any change applied to that system. The Le Chatelier's Principle, therefore, provides a method of predicting the response of a chem. system to an imposed change.
Changing the concentration of a chemical will shift the equilibrium to the side that would reduce that change in concentration. The addition of a reactant to a system at equilibrium produces an equilibrium shift forward (to the right). The forward reaction produces more product molecules to oppose the change introduced.
Consider the reaction, CCl4 (l) + 2HF (g) ⇆ CCl2F2 (g) + 2HCL (g), when equilibrium has been achieved, then HF is added, there will be an increase in reactants, and therefore an increase in HCL and CCl2F2. The equilibrium shift to the right is indicated by the gradual decrease in concentration of the reactant and the gradual increase in concentration of the products.
Effects of increasing the concentration of the reactants
The removal of a product will also shift the equilibrium forward, producing more product molecules to oppose the change introduced. The equilibrium shift to the right is again indicated by the gradual decrease in concentration of the reactant and the gradual increase in concentration of the products.
Effects of decreasing the concentration of the products
However, it should be noted that changing concentration of either the reactants or the products has no effect on the value of the equilibrium constant, Kc. Increasing the concentration of reactants or products results in increased collisions between molecules therefore increasing the reaction rate again, until a new equilibrium is established. However, the ratio of concentration of products and reactants remains the same, thus the Kc remains constant.
The effect of temperature on a reaction depends, firstly, on whether the reaction was exothermic or endothermic. Remember, endothermic reactions absorb energy from the surrounding, therefore increasing the temperature will favor endothermic reactions. Exothermic reactions release energy to the surrounding in form of heat, therefore increasing the temperature will slow down the reaction. You can look at energy (temperature) as one of the reactants (in endothermic reactions) or as one of the products (in exothermic reactions). in exothermic reactions, increasing the temperature shifts the equilibrium to the left, while cooling shifts the equilibrium to the right. Remember, shifting equilibrium to the right, means there are more products being formed, and vise versa. Cooling, which shifts the equilibrium to the products increases the value of the equilibrium constant, Kc. Heating an exothermic reaction will therefore reduce the Kc.
In a closed system, changes in volume also affect the pressure of the system. The pressure is inversely proportional to the volume such that an increase in pressure results in reduced volume.
An increase in volume (decreasing pressure) will cause a shift toward the side with the larger number of moles of gaseous entities. An decrease in volume (increasing pressure) will cause a shift toward the side with the smaller number of moles of gaseous entities. Therefore, a system with equal amount of gas on each side is not affected by a change in volume. Also, liquids or solids are not affected by changes in volume/pressure.
Consider the reaction 2SO2 (g) + O2 (g) ⇆ 2SO3(g) + 198kJ. A volume (pressure) change will produce a 'spike' in concentrations of all gaseous entities, followed by a gradual equilibrium shift. Despite the equilibrium shift, changing volume (pressure) has no effect on the equilibrium constant, Kc.
Effects of increasing the volume/pressure causing an immediate spike in all gases in the reaction.
| Property | Change | Effect on reaction |
|---|---|---|
| Concentration | Increase | Reaction moves in the direction that ensures to use up the added reactant or product |
| Concentration | Decrease | The reaction shifts so as to replace the removed reactant or product |
| Temperature | Increase | Shifts to the right, if reaction is endothermic, and to the left, if reaction is exothermic. Changes Kc. |
| Temperature | Decrease | Shifts to the right if reaction is exothermic, and to the left if reaction is endothermic. Changes Kc. |
| Volume/Pressure | Increase volume / reduced pressure | Affects gases only. Shifts towards the side with the larger number of moles of the gaseous entities |
| Volume/Pressure | Decreased volume / Increased pressure | Affects gases only. Shifts to the side with the smaller number of moles of gaseous entities. |