Design a buffer that has a pH of 7.24 using one of the weak base/conjugate acid systems shown below. Weak Base Kb Conjugate Acid Ka pka CH3NH2 4.2 x 10-4 CH3NH3* 2.4 x 10-11 10.62 C6H1503N 5.9 x 10-7 C6H1503NH* 1.7 x 10-8 7.77 C5H5N 1.5 x 10-⁹ C5H5NH+ 6.7 x 10-6 5.17 How many grams of the bromide salt of the conjugate acid must be combined with how many grams of the weak base, to produce 1.00 L of a buffer that is 1.00 M in the weak base? grams bromide salt of conjugate acid = grams weak base =

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**Designing a Buffer with a pH of 7.24**

To create a buffer with a pH of 7.24 using one of the given weak base/conjugate acid systems, consider the following data:

| Weak Base       | \(K_b\)         | Conjugate Acid     | \(K_a\)          | \(pK_a\) |
|-----------------|-----------------|--------------------|------------------|----------|
| \(CH_3NH_2\)    | \(4.2 \times 10^{-4}\) | \(CH_3NH_3^+\)       | \(2.4 \times 10^{-11}\) | 10.62    |
| \(C_6H_{15}O_3N\)| \(5.9 \times 10^{-7}\) | \(C_6H_{15}O_3NH^+\)   | \(1.7 \times 10^{-8}\)  | 7.77     |
| \(C_5H_5N\)     | \(1.5 \times 10^{-9}\) | \(C_5H_5NH^+\)       | \(6.7 \times 10^{-6}\)  | 5.17     |

### Problem Statement:
Determine the number of grams of the bromide salt of the conjugate acid and the grams of the weak base required to produce 1.00 L of a buffer that has a concentration of 1.00 M in the weak base.

### Calculation Steps:
1. **Select the Buffer System:**
   - Choose a system where the \(pK_a\) is close to the desired pH of 7.24. In this case, \(C_6H_{15}O_3N\) / \(C_6H_{15}O_3NH^+\) is the most suitable with a \(pK_a\) of 7.77.

2. **Henderson-Hasselbalch Equation:**
   - \[ \text{pH} = pK_a + \log\left(\frac{[A^-]}{[HA]}\right) \]
   - Substitute the values: \[ 7.24 = 7.77 + \log\left(\frac{[C_6H_{15}O_3N
Transcribed Image Text:**Designing a Buffer with a pH of 7.24** To create a buffer with a pH of 7.24 using one of the given weak base/conjugate acid systems, consider the following data: | Weak Base | \(K_b\) | Conjugate Acid | \(K_a\) | \(pK_a\) | |-----------------|-----------------|--------------------|------------------|----------| | \(CH_3NH_2\) | \(4.2 \times 10^{-4}\) | \(CH_3NH_3^+\) | \(2.4 \times 10^{-11}\) | 10.62 | | \(C_6H_{15}O_3N\)| \(5.9 \times 10^{-7}\) | \(C_6H_{15}O_3NH^+\) | \(1.7 \times 10^{-8}\) | 7.77 | | \(C_5H_5N\) | \(1.5 \times 10^{-9}\) | \(C_5H_5NH^+\) | \(6.7 \times 10^{-6}\) | 5.17 | ### Problem Statement: Determine the number of grams of the bromide salt of the conjugate acid and the grams of the weak base required to produce 1.00 L of a buffer that has a concentration of 1.00 M in the weak base. ### Calculation Steps: 1. **Select the Buffer System:** - Choose a system where the \(pK_a\) is close to the desired pH of 7.24. In this case, \(C_6H_{15}O_3N\) / \(C_6H_{15}O_3NH^+\) is the most suitable with a \(pK_a\) of 7.77. 2. **Henderson-Hasselbalch Equation:** - \[ \text{pH} = pK_a + \log\left(\frac{[A^-]}{[HA]}\right) \] - Substitute the values: \[ 7.24 = 7.77 + \log\left(\frac{[C_6H_{15}O_3N
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