A chemistry graduate student is given 500. mL of a 1.50M trimethylamine ((CH3)¸N) solution. Trimethylamine is a weak base with K,=7.4 × 10 *. what mass of (CH) NHBR should the student dissolve in the (CH,) N solution to turn it into a 3 buffer with pH =10.62? You may assume that the volume of the solution doesn't change when the (CH,) NHB is dissolved in it. Be sure your /3 answer has a unit symbol, and round it to 2 significant digits.

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### Buffer Preparation Problem

A chemistry graduate student is given **500. mL** of a **1.50 M trimethylamine ((CH₃)₃N)** solution. Trimethylamine is a weak base with \( K_b = 7.4 \times 10^{-4} \). What mass of **(CH₃)₃NHBr** should the student dissolve in the **(CH₃)₃N** solution to turn it into a buffer with \( pH = 10.62 \)?

You may assume that the volume of the solution doesn't change when the **(CH₃)₃NHBr** is dissolved in it. Be sure your answer has a unit symbol, and round it to 2 significant digits.

#### Important Information:

- 500 mL of 1.50 M trimethylamine ((CH₃)₃N)
- \( K_b \) of trimethylamine: \( 7.4 \times 10^{-4} \)
- Target pH: 10.62

#### Steps to Solve:

1. **Calculate the \( pOH \) from \( pH \)**:
   \[
   pOH = 14 - pH
   \]

2. **Find the \( [OH^-] \) concentration**:
   \[
   [OH^-] = 10^{-pOH}
   \]

3. **Use the Henderson-Hasselbalch equation to find the necessary amount of conjugate acid**:
   \[
   pH = pK_b + \log\left(\frac{[Base]}{[Acid]}\right)
   \]

4. **Calculate the molar amounts of trimethylamine ((CH₃)₃N) and its conjugate acid ((CH₃)₃NHBr)** based on the given volume and concentration.

#### Answer Format:

- Ensure the final mass is expressed in grams (g).
- Round the answer to 2 significant digits.

#### Note:

It is important for students to understand the relevance of the buffer solution in maintaining pH stability in various chemical and biological processes. The solution process involving \( pH, pOH, \) and the Henderson-Hasselbalch equation should reinforce fundamental concepts in analytical chemistry.
Transcribed Image Text:### Buffer Preparation Problem A chemistry graduate student is given **500. mL** of a **1.50 M trimethylamine ((CH₃)₃N)** solution. Trimethylamine is a weak base with \( K_b = 7.4 \times 10^{-4} \). What mass of **(CH₃)₃NHBr** should the student dissolve in the **(CH₃)₃N** solution to turn it into a buffer with \( pH = 10.62 \)? You may assume that the volume of the solution doesn't change when the **(CH₃)₃NHBr** is dissolved in it. Be sure your answer has a unit symbol, and round it to 2 significant digits. #### Important Information: - 500 mL of 1.50 M trimethylamine ((CH₃)₃N) - \( K_b \) of trimethylamine: \( 7.4 \times 10^{-4} \) - Target pH: 10.62 #### Steps to Solve: 1. **Calculate the \( pOH \) from \( pH \)**: \[ pOH = 14 - pH \] 2. **Find the \( [OH^-] \) concentration**: \[ [OH^-] = 10^{-pOH} \] 3. **Use the Henderson-Hasselbalch equation to find the necessary amount of conjugate acid**: \[ pH = pK_b + \log\left(\frac{[Base]}{[Acid]}\right) \] 4. **Calculate the molar amounts of trimethylamine ((CH₃)₃N) and its conjugate acid ((CH₃)₃NHBr)** based on the given volume and concentration. #### Answer Format: - Ensure the final mass is expressed in grams (g). - Round the answer to 2 significant digits. #### Note: It is important for students to understand the relevance of the buffer solution in maintaining pH stability in various chemical and biological processes. The solution process involving \( pH, pOH, \) and the Henderson-Hasselbalch equation should reinforce fundamental concepts in analytical chemistry.
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