Reaction Equilibrium - Physical Chemistry

When the molar amount of acid equals the molar amount of base, the solution has reached what is known as the equivalence point. When a strong acid is titrated with a strong base, such as in this example, the two agents will neutralize each other completely. Because the conjugate base for the acid is incredibly weak, it will not manipulate the pH. As a result, the pH at this equivalence point is 7.00.

Since hydrofluoric acid is a weak acid, we need to consider how much of the conjugate base is created when the base neutralizes the acid. We can start by determining how many moles of acid are present initially.

Using the same equation, we find that only 0.004 moles of base have been added.

After the acid and base cancel each other out, we are left with 0.006 moles of acid and 0.004 moles of the conjugate base. This is based on the neutralization equation:

(For simplicity, the bystander sodium ion has been omitted, although it is present).

Now that we know the amount of acid and conjugate base, we can solve for the pH using the Henderson-Hasselbalch equation.

This question is not as easy as just assuming that the pH is 7 because there are equal amounts of acid and base. The reason is because although the acid and base have neutralized each other, there is still the issue of the fluoride ion acting as a conjugate base. The equation for this reaction is:

(The sodium ion has been omitted, as it is simply a spectator ion).

By converting each amount of acid and base to moles, we can find that 0.01 moles of each has been added, neutralizing each other in the process. According to the equation, that will leave us with 0.01 moles of fluoride ions. In order to find the concentration, we simply divide this by the new volume after all of the base has been added:

Next, we can determine the base dissociation constant for the fluoride ion by using the equation

Finally, we use an ICE table in order to determine the hydroxide concentration in the solution.

The fluoride ion concentration will decrease by , and both the hydroxide and hydrofluoric acid concentrations will increase by . This leaves us with the equilibrium expression:

Using the pH equation, we determine the new pH of the system to be 8.07.

Since there is now more strong base than weak acid in the solution, the remaining amount of strong base alone will dictate the pH.

By converting concentration to moles, we can determine that we started with 0.01 moles of weak acid.

Using the same equation, we can determine that 0.012 moles of base was added.

After neutralization, that leaves us with 0.002 moles of strong base. This strong base is the only value we will use to determine the pH. Since the final volume is 110mL, the concentration of remaining sodium hydroxide is calculated as

Finally, we can solve for the pH by first finding the pOH, then subtracting from 14.

A generic acid-base reaction involves the production of salt and water. The amount of products depends on the strength of the reactants. Recall that a strong acid completely dissociates into hydrogen ions and conjugate base in water. Similarly, a strong base completely dissociates into conjugate acid and hydroxide ions in water. A salt (like ) is formed from the conjugate base ( from ) and conjugate acid ( from ); therefore, to get the highest yield of salt we need complete dissociation of acid and base into their respective conjugates. Since they completely dissociate and form conjugates, strong acid and strong base will yield the highest concentration of salt (in this question solution A).

Solution B will also form salt; however, since acetic acid is a weak acid only few molecules of conjugate base (acetate) will be produced, thereby decreasing the amount of salt produced.

The pH is a measure of the concentration of hydrogen ions in solution. An increase in pH corresponds to lower hydrogen ion concentration whereas a decrease in pH corresponds to higher hydrogen ion concentration. Recall that a strong base dissociates completely into conjugate acid and hydroxide ions whereas a weak acid doesn’t dissociate completely into conjugate base and hydrogen ions. Since there is an excess of hydroxide ions in a weak acid/strong base solution, the hydroxide ions will react with and consume the hydrogen ions from weak acid. This will decrease the hydrogen ion concentration and, subsequently, increase the pH. On the other hand, a weak base doesn’t produce as many hydroxide ions; therefore, not as much hydrogen ions will be consumed (pH will be decreased).

The pKa is a measure of the strength of an acid. The lower the pKa the stronger the acid. The extent of dissociation of acid into hydrogen ions and conjugate base depends on the strength; therefore, pKa determines how much hydrogen ion will be produced.

A strong acid and strong base will completely dissociate into their respective conjugates. This means that if equal amounts of strong acid and strong base are added, equal amounts of hydrogen ions and hydroxide ions are produced. Since there are equal amounts of them, hydrogen ions and hydroxide ions will react with each other and form water. Recall that water has a pH of 7; therefore, a strong acid/strong base solution will always have a pH of 7 (if equal amounts of strong acid and strong base are added). The definition of pH is:

If we solve for hydrogen ion concentration:

Therefore, the hydrogen ion concentration in a strong acid/strong base solution is:

The relationship between hydrogen ion concentration and hydroxide ion concentration is:

If we solve for :

The buffer region occurs when the pH of the solution equals the pKa of the acid. This means that the pKa of the acid is 4; therefore, this acid is a weak acid. Recall that buffer regions occur during titration when a weak component (acid or base) is added to a strong component (acid or base). For example, buffer regions can be seen when a weak acid is added to a strong base. Since we already determined that the acid is weak, the other component in the solution must be a strong base. Note that titration with two strong agents (strong acid and strong base) does not produce a buffer region.

Equivalence point is the point at which the amount of acid or base added is equal to the amount of its counterpart. In a strong acid-strong base titration, the equivalence point occurs when the pH is equal to 7. In a weak acid-strong base titration, the equivalence point occurs at a higher pH. This is because at equivalence point all of weak acid is converted to conjugate base, increasing the concentration of hydroxide ions. Endpoint is the end of titration. This typically occurs at the equivalence point; therefore, strong acid-strong base titration has a lower pH at endpoint.

To solve this question we need to use the definition of equilibrium constant. The equilibrium constant, , for this reaction is

For a given value, the concentration of C and D would be the same. The stoichiometric coefficients of C and D are both 1; therefore, the amount of C and D produced would be the same and would depend on the limiting reagent. We do not know what the limiting reagent is (it could be A or B) and cannot determine the absolute concentrations of C and D; however, we can determine the relative concentrations. The concentration of C and D are the same and the ratio is 1:1.

The reaction quotient, , is calculated the same way as equilibrium constant; however, the concentrations used are derived from a nonequilbrium state. Consider the reaction below.

If this reaction is NOT in equilibrium, then the reaction quotient is defined as

If it’s at equilibrium then equilibrium constant is defined as

Note that reaction quotient cannot be calculated when reaction is in equilibrium.

The question states that the reaction quotient is twice as much as the equilibrium constant. Since we can calculate reaction quotient, this reaction is not in equilbrium. The numerator for is higher than the numerator of (because reaction quotient is higher). There are more products created than reactants in the current nonequilbrium state and, therefore, the forward reaction is happening faster than the reverse reaction.

Chemical equilibrium is the state during which the rate of forward reaction equals the rate of reverse reaction. Equilibrium properties of a reaction determine how much products is produced. It’s important to remember that enzymes alter the rate of a reaction; however, they DO NOT alter the equilibrium. This means that enzymes speed up a reaction; however, they do not increase the amount of products produced.

ONLY increasing or decreasing temperature will alter equilibrium constant. Other factors such as concentration, volume, and pressure do not change it. Changing these other factors might shift the reaction left or right to bring the reaction back to equilibrium; however, it does not change the equilibrium constant. This means that these other factors can change the individual concentration of reactants and products at equilibrium, but they will not change the ratio of products to reactants.

As mentioned, at equilibrium the rates of forward and reverse reactions are equal. This means that new products and reactants are constantly being produced; however, there is no net production of these molecules.

Le Chatelier’s principle states that a chemical system will respond to changes in the environment and maintain equilibrium by changing the direction of reaction. A reaction will shift to the right if the ratio of concentration of products to reactants goes down and will shift to the left if the ratio goes up. Reaction quotient, , characterizes the state of a reaction in a nonequilbrium state. It is calculated the same way as equilibrium constant.

The question is asking about a shift to the right. Reaction shifts to the right (and approaches equilbrium) when the nonequilbrium reaction has more reactants than products. This occurs when the ratio of products to reactants () is lower than the ratio of products to reactants at equilibrium ().

Hess's Law allows us to combine the two given equation to create the equation that we need. Hess's Law also tells us that when combining equilibrium constants, the value is the product of K1 and K2.

Remark: a common misconception in this type of problem is to find the sum of the values. This use of Hess's Law is only valid for thermodynamic values.

Adding contributes ions into the solution, driving the reaction to the left, and decreasing the solubility of the calcium hydroxide. This is known as the common-ion effect. The remains unchanged. This is due to the fact that only a change in temperature can bring about a change in an equilibrium constant.

When a system is at equilibrium, it is possible to predict how a system will respond to sudden changes using Le Chatelier's principle. In this scenario, ammonia has been removed from the system. This will cause the reaction to produce more ammonia, and proceed to the right in order to reestablish equilibrium.

According to Le Chatelier's principle, a change in pressure will cause a shift in order to counteract the pressure change. When the pressure of a vessel is increased, the side of the reaction with fewer gas molecules will be preferred in order to minimize contact between gas molecules. For this reaction, there are four gas molecules on the left side and two gas molecules on the right side. As a result, the products side will be preferred and more ammonia will be created.

High pressure will favor the side of the reaction with fewer moles of gas, which in this case is the product side.

The reaction is exothermic, meaning that it generates heat. By removing heat from the reaction, we are constantly stressing the system towards the product side.

Finally, the reaction should occur under a lamp. This is due to the hv symbol above the double arrows, which signifies that light promotes the reaction. Note: had the hv symbol been below the double arrows, the reaction should have occurred in the dark.