The Hydroxide Ion Concentration Of An Aqueous Solution Of 0.382 M Acetic Acid Is Given By $\left[OH^{-}\right]=4.6 \times 10^{-2} \, \text{M}.$An Error Has Been Detected In Your Answer. Check For Typos, Miscalculations, Etc., Before Submitting
Introduction
In chemistry, the hydroxide ion concentration of an aqueous solution is a crucial parameter that determines the pH of the solution. The hydroxide ion concentration is given by the equation , where is the water dissociation constant and is the hydrogen ion concentration. In this article, we will analyze the hydroxide ion concentration of an aqueous solution of 0.382 M acetic acid and identify any errors in the calculation.
Theoretical Background
Acetic acid (CH3COOH) is a weak acid that dissociates in water to produce hydrogen ions (H+) and acetate ions (CH3COO-). The dissociation reaction is as follows:
CH3COOH (aq) ⇌ H+ (aq) + CH3COO- (aq)
The equilibrium constant for this reaction is given by the equation:
K = [H+][CH3COO-] / [CH3COOH]
The water dissociation constant (Kw) is given by the equation:
Kw = [H+][OH-] = 1.0 x 10^(-14) at 25°C
Calculation of Hydroxide Ion Concentration
Given that the hydroxide ion concentration of the aqueous solution of acetic acid is 4.6 x 10^(-2) M, we can calculate the hydrogen ion concentration using the equation:
[H+] = Kw / [OH-]
Substituting the values, we get:
[H+] = 1.0 x 10^(-14) / 4.6 x 10^(-2) = 2.17 x 10^(-13) M
Analysis of the Calculation
However, upon closer inspection, we notice that the hydrogen ion concentration calculated above is extremely low. This is unlikely to be the case, as acetic acid is a weak acid that dissociates only partially in water. A more plausible value for the hydrogen ion concentration would be in the range of 10^(-5) to 10^(-6) M.
Error Analysis
Upon further analysis, we realize that the error lies in the calculation of the hydrogen ion concentration. The correct calculation should be:
[H+] = Kw / [CH3COO-]
Since the dissociation reaction is:
CH3COOH (aq) ⇌ H+ (aq) + CH3COO- (aq)
The concentration of acetate ions (CH3COO-) is equal to the concentration of hydrogen ions (H+). Therefore, we can substitute [CH3COO-] = [H+] in the equation above.
Correct Calculation
Substituting the values, we get:
[H+] = Kw / [H+] = 1.0 x 10^(-14) / [H+]
However, we need to find the value of [H+]. To do this, we can use the equation:
K = [H+][CH3COO-] / [CH3COOH]
Since [CH3COO-] = [H+], we can substitute [CH3COO-] = [H+] in the equation above.
Solving for [H+]
K = [H+][H+] / [CH3COOH] = [H+]^2 / [CH3COOH]
Rearranging the equation, we get:
[H+]^2 = K[CH3COOH]
Substituting the values, we get:
[H+]^2 = (1.8 x 10^(-5))[CH3COOH] = (1.8 x 10^(-5))(0.382) = 6.89 x 10^(-6)
Taking the square root of both sides, we get:
[H+] = √(6.89 x 10^(-6)) = 2.62 x 10^(-3) M
Calculation of Hydroxide Ion Concentration
Now that we have the correct value of [H+], we can calculate the hydroxide ion concentration using the equation:
[OH-] = Kw / [H+]
Substituting the values, we get:
[OH-] = 1.0 x 10^(-14) / 2.62 x 10^(-3) = 3.81 x 10^(-12) M
Conclusion
In conclusion, the hydroxide ion concentration of an aqueous solution of 0.382 M acetic acid is 3.81 x 10^(-12) M, not 4.6 x 10^(-2) M as previously calculated. The error in the calculation was due to a miscalculation of the hydrogen ion concentration. By using the correct equation and substituting the correct values, we were able to obtain the correct value of the hydroxide ion concentration.
Recommendations
Based on the analysis above, we recommend the following:
- Always check for typos and miscalculations before submitting an answer.
- Use the correct equation and substitute the correct values to obtain the correct answer.
- Be careful when calculating the hydrogen ion concentration, as it can have a significant impact on the final answer.
Future Work
In the future, we plan to investigate the effect of temperature on the hydroxide ion concentration of an aqueous solution of acetic acid. We also plan to explore the use of different methods to calculate the hydroxide ion concentration, such as the use of pH meters or spectrophotometry.
Q: What is the hydroxide ion concentration of an aqueous solution of acetic acid?
A: The hydroxide ion concentration of an aqueous solution of acetic acid is 3.81 x 10^(-12) M, not 4.6 x 10^(-2) M as previously calculated.
Q: What is the error in the previous calculation?
A: The error in the previous calculation was due to a miscalculation of the hydrogen ion concentration. The correct calculation should have used the equation [H+] = Kw / [CH3COO-], where [CH3COO-] = [H+].
Q: How do I calculate the hydroxide ion concentration of an aqueous solution of acetic acid?
A: To calculate the hydroxide ion concentration of an aqueous solution of acetic acid, you need to use the equation [OH-] = Kw / [H+], where [H+] is the hydrogen ion concentration. You can calculate [H+] using the equation [H+] = √(K[CH3COOH]), where K is the dissociation constant of acetic acid and [CH3COOH] is the concentration of acetic acid.
Q: What is the dissociation constant of acetic acid?
A: The dissociation constant of acetic acid is 1.8 x 10^(-5).
Q: How do I calculate the hydrogen ion concentration of an aqueous solution of acetic acid?
A: To calculate the hydrogen ion concentration of an aqueous solution of acetic acid, you need to use the equation [H+] = √(K[CH3COOH]), where K is the dissociation constant of acetic acid and [CH3COOH] is the concentration of acetic acid.
Q: What is the effect of temperature on the hydroxide ion concentration of an aqueous solution of acetic acid?
A: The effect of temperature on the hydroxide ion concentration of an aqueous solution of acetic acid is not well understood and requires further investigation.
Q: How do I measure the hydroxide ion concentration of an aqueous solution of acetic acid?
A: You can measure the hydroxide ion concentration of an aqueous solution of acetic acid using a pH meter or spectrophotometry.
Q: What are the applications of the hydroxide ion concentration of an aqueous solution of acetic acid?
A: The hydroxide ion concentration of an aqueous solution of acetic acid has applications in various fields, including chemistry, biology, and environmental science.
Q: Can I use the hydroxide ion concentration of an aqueous solution of acetic acid to predict the pH of a solution?
A: Yes, you can use the hydroxide ion concentration of an aqueous solution of acetic acid to predict the pH of a solution. The pH of a solution is related to the hydroxide ion concentration by the equation pH = -log[OH-].
Q: What are the limitations of the hydroxide ion concentration of an aqueous solution of acetic acid?
A: The hydroxide ion concentration of an aqueous solution of acetic acid has limitations, including the assumption that the dissociation constant of acetic acid is constant and the neglect of other factors that may affect the hydroxide ion concentration.
Q: How do I troubleshoot common errors in calculating the hydroxide ion concentration of an aqueous solution of acetic acid?
A: To troubleshoot common errors in calculating the hydroxide ion concentration of an aqueous solution of acetic acid, you need to check for typos and miscalculations, use the correct equation and substitute the correct values, and be careful when calculating the hydrogen ion concentration.
Q: What are the future directions for research on the hydroxide ion concentration of an aqueous solution of acetic acid?
A: The future directions for research on the hydroxide ion concentration of an aqueous solution of acetic acid include investigating the effect of temperature on the hydroxide ion concentration, exploring the use of different methods to calculate the hydroxide ion concentration, and applying the hydroxide ion concentration to real-world problems.