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A buffer is prepared by mixing \(50.0 \mathrm{mL}\) of \(0.200 M \mathrm{NaOH}\) with \(100.0 \mathrm{mL}\) of \(0.175 M\) acetic acid. a. What is the pH of the buffer? b. What is the pH of the buffer after \(1.00 \mathrm{g} \mathrm{NaOH}\) is dissolved in it?

Short Answer

Expert verified
Answer: The initial pH of the buffer solution is 4.17 and its final pH after the addition of 1.00 g of NaOH is 12.70.

Step by step solution

01

Calculate initial amounts of NaOH and acetic acid

To determine the initial amount of NaOH and acetic acid in the buffer solution, we'll use the formula: Amount (in moles) = Molarity 脳 Volume (in L) Initial amount of NaOH: \(50.0 \mathrm{mL} * 0.200 M * \frac{1 L}{1000 \mathrm{mL}} = 0.0100 \, \text{moles}\) Initial amount of acetic acid: \(100.0 \mathrm{mL} * 0.175 M * \frac{1 L}{1000 \mathrm{mL}} = 0.0175 \, \text{moles}\)
02

Calculate the initial pH of the buffer

Using the Henderson-Hasselbalch equation: \(pH = pK_a + \log{\frac{ [\mathrm{A}^{-}]}{[\mathrm{HA}]}}\) We know that pK\(_a\) of acetic acid is 4.74. We also know that the initial molar concentrations of acetic acid and the acetate ion are: \([\mathrm{HA}]_0 = \frac{0.0175 \, \text{moles}}{0.150 \, \text{L}} = 0.1167 M\) \([\mathrm{A}^{-}]_0 = \frac{0.0100 \, \text{moles}}{0.150 \, \text{L}} = 0.0667 M\) Now, we can calculate the initial pH of the buffer: \(pH = 4.74 + \log{\frac{0.0667}{0.1167}} = 4.74 + (-0.567) = 4.17\) The initial pH of the buffer is 4.17.
03

Calculate the amount of NaOH and acetic acid after the addition of NaOH

We need to dissolve 1.00 g of NaOH in the buffer. To find the moles of NaOH added, use the formula: Moles = mass / molar mass (NaOH has a molar mass of 40.0 g/mol) Moles of NaOH added: \(\frac{1.00 \, \text{g}}{40.0 \, \text{g/mol}} = 0.0250 \, \text{moles}\) The amount of NaOH in the buffer after the addition of NaOH becomes: \(0.0100 \, \text{moles} + 0.0250 \, \text{moles} = 0.0350 \, \text{moles}\) The moles of acetic acid will decrease by the amount of NaOH added as they react, thus: Final amount of acetic acid: \(0.0175 \, \text{moles} - 0.0250 \, \text{moles} = -0.0075 \, \text{moles}\) As the negative moles of acetic acid are not possible, all the acetic acid has reacted with NaOH and there is still 0.0075 moles of NaOH left in the buffer.
04

Calculate the final pH after the addition of NaOH

After the addition of NaOH, the final molar concentrations of the acetic acid, acetate ion, and hydroxide ion (OH鈦) are: \([\mathrm{HA}]_f = 0\) \([\mathrm{A}^{-}]_f = 0.0350 \, \text{moles} / 0.150 \, \text{L} = 0.2333 M\) \([\mathrm{OH}^{-}]_f = 0.0075 \, \text{moles} / 0.150 \, \text{L} = 0.0500 M\) Now we can calculate the pOH using the formula: \(pOH = -\log{[\mathrm{OH}^{-}]}\) \(pOH = -\log(0.0500) = 1.30\) Finally, we can determine the final pH using the relationship between pH and pOH: pH + pOH = 14.00 \(pH = 14.00 - 1.30 = 12.70\) The final pH of the buffer after the addition of NaOH is 12.70. a. The initial pH of the buffer is 4.17. b. The pH of the buffer after dissolving 1.00 g of NaOH is 12.70.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Henderson-Hasselbalch equation
The Henderson-Hasselbalch equation is a useful formula in chemistry for calculating the pH of a buffer solution. It is written as: \[ pH = pK_a + \log{\frac{ [\mathrm{A}^{-}]}{[\mathrm{HA}]}} \]In this equation:
  • \(pH\) represents the acidity or basicity of the solution.
  • \(pK_a\) is the negative logarithm of the acid dissociation constant, \(K_a\), which reflects the strength of the acid.
  • \([\mathrm{A}^{-}]\) is the concentration of the base form of the buffer, often an anion like acetate.
  • \([\mathrm{HA}]\) is the concentration of the acid form, such as acetic acid.
This equation is based on the principle that most buffers are formed by a weak acid and its conjugate base. It allows for the approximation of pH by considering the ratio of the base to the acid, alongside the acid's strength. Typically, it works best in conditions where the concentrations of acid and base are similar.
acetic acid
Acetic acid is a simple carboxylic acid with the formula \( \mathrm{CH}_3\mathrm{COOH} \). It's widely known as the main ingredient in vinegar, giving it a sour taste and strong, distinct smell. In the context of buffer solutions, acetic acid acts as a weak acid. This means it doesn鈥檛 completely dissociate in solution, establishing an equilibrium between the acid and its conjugate base, acetate ion (\( \mathrm{CH}_3\mathrm{COO}^{-} \)).

The acetic acid buffer is a popular choice in chemistry because:
  • Its \( pK_a \) is about 4.74, making it suitable for making buffer solutions in the mildly acidic range.
  • It exhibits resistance to changes in pH upon addition of small amounts of strong acid or base.
  • It provides both an acid (\( \mathrm{CH}_3\mathrm{COOH}\)) and a friendly base (\( \mathrm{CH}_3\mathrm{COO}^{-} \)), ideal for maintaining a stable pH.
The buffering capability depends on maintaining a significant concentration of both the acetic acid and its conjugate base.
pH calculation
pH calculation is essential in determining how acidic or basic a solution is. It is represented on a scale usually ranging from 0 (most acidic) to 14 (most basic), with 7 being neutral. The pH is calculated using the equation:\[ pH = -\log{[\text{H}^+]} \]Where \([\text{H}^+]\) is the concentration of hydrogen ions in the solution. Buffer solutions suppress significant changes in pH by reacting with added acids or bases.

In the given exercise, the Henderson-Hasselbalch equation was employed to calculate the initial pH of the buffer, considering the concentrations of the acetic acid and its conjugate base. Subsequent changes in pH, such as by adding \( \mathrm{NaOH} \), involve further calculations. These changes can be predicted by recalculating new concentrations and applying these to the appropriate formula (such as the relation \(pH + pOH = 14.00\) when dealing with hydroxide ions).
Remember: precise calculations rely on exact concentrations, and understanding the relationship between pH and \([\text{H}^+]\) is fundamental.
sodium hydroxide
Sodium hydroxide (\( \mathrm{NaOH} \)) is a strong base often used in chemical reactions to adjust pH. When dissolved in water, it dissociates completely into \( \mathrm{Na}^+ \) and \( \mathrm{OH}^- \) ions, increasing the solution's pH markedly. This property makes \( \mathrm{NaOH} \) effective for pH adjustments in buffer solutions.

For instance, the addition of extra \( \mathrm{NaOH} \) can shift the balance in a buffer, reacting with available \( \mathrm{HA} \) (acetic acid) to form more \( \mathrm{A}^- \) \( (\mathrm{CH}_3\mathrm{COO}^- ) \) and water. Thus:
  • The buffer responds by consuming \( \mathrm{OH}^- \), moderating changes in solution pH.
  • In cases where all the acid reacts, excess \( \mathrm{OH}^- \) directly affects the pH, creating a more basic solution.
  • This is apparent in the exercise as acetic acid is exhausted, leaving extra \( \mathrm{NaOH} \) to increase pH.
Managing \( \mathrm{NaOH} \) in buffer systems is pivotal for maintaining intended pH levels, making it an indispensable tool in both instructional and practical chemistry settings.

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