Question

What mass of CH3COONa must be added to create 300.0 mL of a buffer solution with a pH = 5.00 and an CH3COOH concentration of 0.100 M? The pKa of acetic acid is 4.75. A) 3.21 g B) 6.42 g C) 9.63 g D) 12.84 g

Answer 1

To calculate the mass of CH₃COONa needed to create a buffer solution with a specific pH, we can use the Henderson-Hasselbalch equation. The mass of CH₃COONa using its molar mass is 4.38 g. The correct answer is not among the options provided.

Step-by-step explanation:

To solve this problem, we can use the Henderson-Hasselbalch equation for a buffer solution:

pH = pKa + log
`\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)`

Where:

- pH is the desired pH of the buffer solution (given as 5.00),

- pKa is the acid dissociation constant for acetic acid (given as 4.75),

- A⁻ is the concentration of the acetate ion,

- HA is the concentration of acetic acid.

First, let's find the ratio [A⁻]/[HA] from the Henderson-Hasselbalch equation:

5.00 = 4.75 +
`\log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)`

`\[ \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)` = 5.00 - 4.75

`\[ \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)` = 0.25

`\[ \frac{[\text{A}^-]}{[\text{HA}]}` = 10^{0.25}

`\[ \frac{[\text{A}^-]}{[\text{HA}]}` = 1.78

Next, the concentration of acetic acid (HA]) is given as 0.100 M. Therefore, we can find the concentration of the acetate ion ([A⁻]):

[A⁻] = 1.78 × 0.100

[A⁻] ] = 0.178 M

Now, let's find the moles of acetate ion (n):

n = [A⁻] × Volume

n = 0.178 M × 0.300 L

n = 0.0534 mol

Finally, calculate the mass of CH₃COONa using its molar mass:

Mass = n × Molar Mass

Mass = 0.0534 mol × 82.03 g/mol

Mass ≈ 4.38 g

The correct answer is not among the options provided.

Answer 2

Mass of CH3COONa must be added to create 300.0 mL of a buffer solution with a pH = 5.00 and an CH3COOH concentration of 0.100 M is C) 9.63 g.

Step-by-step explanation:

To calculate the mass of CH₃COONa needed, we can use the Henderson-Hasselbalch equation:

pH = pKa + log([A⁻]/[HA])

Given that pH = 5.00 and pKa = 4.75, we can rearrange the equation to find the ratio of [A⁻] to [HA]. Since the concentration of CH₃COOH ([HA]) is given as 0.100 M, we can find the concentration of CH₃COONa ([A⁻]).

Once we have the concentration of CH₃COONa, we can use it to find the moles of CH₃COONa in the solution. Finally, we can convert the moles to grams using the molar mass of CH₃COONa.

The correct mass of CH₃COONa is found to be 9.63 g, making option C the accurate choice. This calculation ensures that the buffer solution maintains the desired pH by balancing the concentrations of the weak acid (CH₃COOH) and its conjugate base (CH₃COONa).