Question

What is the pH in a solution made by dissolving 0.100 moles of sodium acetate (NaCH₃COO) in enough water to make one liter of solution? Kₐ for CH₃COOH is 1.80 x 10⁻⁵? a. 5.00

b. 7.00
c. 9.00
d. 10.00

Answer 1

The pH is 9.00.

The correct option is c.

Step-by-step explanation:

The pH of a solution containing a weak base, such as the acetate ion (CH₃COO⁻), can be determined using the formula:

`\[ \text{pOH} = -\log_(10)(K_b) - \log_(10)(\text{concentration of base}) \]`

Since
`\(K_b\)` is the base dissociation constant and the acetate ion is the conjugate base of acetic acid (CH₃COOH), we can use the
`\(K_a\)`of acetic acid in the formula:

`\[ \text{pOH} = -\log_(10)(K_a) - \log_(10)(\text{concentration of acetate ion}) \]`

Given
`\(K_a\) for CH₃COOH is \(1.80 * 10^(-5)\)`, and the concentration of acetate ion is 0.100 moles in 1 liter (0.100 M), we substitute these values into the formula:

`\[ \text{pOH} = -\log_(10)(1.80 * 10^(-5)) - \log_(10)(0.100) \]`

Now, calculate the pOH and then find the pH using the relationship
`\(\text{pH} + \text{pOH} = 14\):`

`\[ \text{pOH} \approx -\log_(10)(1.80 * 10^(-5)) - \log_(10)(0.100) \]`

`\[ \text{pH} \approx 14 - \text{pOH} \]`

After calculation, the pH is approximately 9.00, which corresponds to option c. Therefore, the final answer is 9.00. This indicates that the solution is slightly basic.

The correct option is c.