When The Newly Discovered Gracious Acid \[$\left(k_a=8.83 \times 10^{-5}\right)\$\] Is Dissolved In Water To A Concentration Of 0.84 M, What Is The Equilibrium PH?
When a weak acid is dissolved in water, it partially dissociates into its conjugate base and hydrogen ions. The degree of dissociation depends on the acid's dissociation constant (Ka). In this problem, we are given a newly discovered weak acid, gracious acid, with a dissociation constant (Ka) of 8.83 × 10^(-5). We need to find the equilibrium pH when the acid is dissolved in water to a concentration of 0.84 M.
Weak Acid Dissociation Reaction
The dissociation reaction of a weak acid (HA) in water can be represented as:
HA (aq) ⇌ H+ (aq) + A- (aq)
where HA is the weak acid, H+ is the hydrogen ion, and A- is the conjugate base.
Acid Dissociation Constant (Ka)
The acid dissociation constant (Ka) is a measure of the strength of the acid. It is defined as the ratio of the concentration of the hydrogen ion (H+) to the concentration of the conjugate base (A-) to the concentration of the undissociated acid (HA):
Ka = [H+][A-] / [HA]
Given Values
- Ka = 8.83 × 10^(-5)
- Initial concentration of HA = 0.84 M
Equilibrium Concentration of HA
Since the acid is weak, we can assume that the initial concentration of HA is approximately equal to the equilibrium concentration of HA. Therefore, the equilibrium concentration of HA is also 0.84 M.
Equilibrium Concentration of H+ and A-
Let x be the equilibrium concentration of H+ and A-. Since the acid is weak, we can assume that the equilibrium concentration of H+ and A- is much smaller than the equilibrium concentration of HA. Therefore, we can write:
[H+] = x [A-] = x [HA] = 0.84 - x
Ka Expression
Substituting the equilibrium concentrations into the Ka expression, we get:
Ka = [H+][A-] / [HA] = x × x / (0.84 - x) = x^2 / (0.84 - x)
Solving for x
Since Ka is given, we can set up an equation using the Ka expression:
8.83 × 10^(-5) = x^2 / (0.84 - x)
To solve for x, we can rearrange the equation to get:
x^2 = 8.83 × 10^(-5) × (0.84 - x)
Expanding the right-hand side, we get:
x^2 = 7.44 × 10^(-5) - 8.83 × 10^(-5) × x
Rearranging the equation to get a quadratic equation in x, we get:
x^2 + 8.83 × 10^(-5) × x - 7.44 × 10^(-5) = 0
Quadratic Formula
To solve the quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = 8.83 × 10^(-5), and c = -7.44 × 10^(-5).
Substituting the values into the quadratic formula, we get:
x = (-(8.83 × 10^(-5)) ± √((8.83 × 10(-5))2 - 4(1)(-7.44 × 10^(-5)))) / 2(1)
Simplifying the expression, we get:
x = (-8.83 × 10^(-5) ± √(7.84 × 10^(-9) + 2.976 × 10^(-4))) / 2
x = (-8.83 × 10^(-5) ± √(2.998 × 10^(-4))) / 2
x = (-8.83 × 10^(-5) ± 0.0173) / 2
Since x represents the equilibrium concentration of H+, it must be a positive value. Therefore, we take the positive root:
x = (-8.83 × 10^(-5) + 0.0173) / 2
x ≈ 0.0087
Equilibrium pH
The equilibrium pH is given by:
pH = -log[H+]
Substituting the value of x into the expression, we get:
pH = -log(0.0087)
pH ≈ 2.06
Therefore, the equilibrium pH when the gracious acid is dissolved in water to a concentration of 0.84 M is approximately 2.06.
Conclusion
In the previous article, we discussed the dissociation of a weak acid (gracious acid) in water and found the equilibrium pH. Here, we will answer some frequently asked questions related to weak acid dissociation in water.
Q: What is the difference between a strong acid and a weak acid?
A: A strong acid is an acid that completely dissociates in water, producing a high concentration of hydrogen ions (H+). Examples of strong acids include hydrochloric acid (HCl) and sulfuric acid (H2SO4). A weak acid, on the other hand, only partially dissociates in water, producing a low concentration of hydrogen ions. Examples of weak acids include acetic acid (CH3COOH) and carbonic acid (H2CO3).
Q: What is the acid dissociation constant (Ka)?
A: The acid dissociation constant (Ka) is a measure of the strength of an acid. It is defined as the ratio of the concentration of the hydrogen ion (H+) to the concentration of the conjugate base (A-) to the concentration of the undissociated acid (HA). The Ka value is a characteristic property of each acid and is used to predict the degree of dissociation in water.
Q: How do I calculate the equilibrium pH of a weak acid in water?
A: To calculate the equilibrium pH of a weak acid in water, you need to know the acid dissociation constant (Ka) and the initial concentration of the acid. You can use the Ka expression to set up an equation and solve for the equilibrium concentration of H+. Then, you can use the equilibrium concentration of H+ to find the equilibrium pH.
Q: What is the relationship between the Ka value and the pH of a weak acid?
A: The Ka value and the pH of a weak acid are inversely related. As the Ka value increases, the pH of the solution decreases. This is because a higher Ka value indicates a stronger acid, which will produce a higher concentration of H+ ions and a lower pH.
Q: Can I use the Ka value to predict the pH of a strong acid in water?
A: No, you cannot use the Ka value to predict the pH of a strong acid in water. Strong acids completely dissociate in water, producing a high concentration of H+ ions. The Ka value is only useful for predicting the pH of weak acids, which only partially dissociate in water.
Q: How do I determine the Ka value of a weak acid?
A: The Ka value of a weak acid can be determined experimentally by measuring the concentration of H+ ions and the concentration of the conjugate base (A-) at equilibrium. The Ka value can also be calculated from the equilibrium concentrations using the Ka expression.
Q: What is the significance of the pH of a weak acid in water?
A: The pH of a weak acid in water is significant because it determines the acidity of the solution. A low pH indicates a high concentration of H+ ions and a strong acid, while a high pH indicates a low concentration of H+ ions and a weak acid.
Q: Can I use the pH of a weak acid to predict the pH of a strong acid in water?
A: No, you cannot use the pH of a weak acid to predict the pH of a strong acid in water. The pH of a strong acid is determined by its complete dissociation in water, producing a high concentration of H+ ions. The pH of a weak acid, on the other hand, is determined by its partial dissociation in water, producing a low concentration of H+ ions.
Conclusion
In this Q&A article, we discussed some frequently asked questions related to weak acid dissociation in water. We covered topics such as the difference between strong and weak acids, the acid dissociation constant (Ka), and the relationship between the Ka value and the pH of a weak acid. We also discussed the significance of the pH of a weak acid in water and how it can be used to predict the acidity of a solution.