Question

What volume of 6.00 M NaOH must be added to 0.250 L of 0.300 M HNO2 to prepare a pH = 4.00 buffer?

Ka for nitrous acid: 4.0 x 10¯4

Answer 1

To prepare a pH = 4.00 buffer, add 0.0875 L (87.5 mL) of 6.00 M NaOH to 0.250 L of 0.300 M HNO₂.

Step-by-step explanation:

To determine the volume of 6.00 M NaOH required to prepare a pH = 4.00 buffer, we need to use the Henderson-Hasselbalch equation:

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

Given that the pH is 4.00 and the pKa for nitrous acid
`(\(HNO_2\))` is 4.0 x 10⁻⁴, we can rearrange the equation to find the ratio of
`\([A^-]\)` to
`\([HA]\)`. In a buffer solution,
`\([A^-]\)` is the concentration of the base (NaOH), and
`\([HA]\)` is the concentration of the acid (HNO₂). The desired ratio is 10, meaning
`\([A^-] = 10 * [HA]\)`.

Next, calculate the moles of
`\(HNO_2\)` initially present in 0.250 L of 0.300 M solution, which is
`\((0.250 \ \text{L}) * (0.300 \ \text{mol/L})\)`. Now, find the moles of NaOH needed, which is 10 times the moles of
`\(HNO_2\)` for the desired ratio.

Finally, convert the moles of NaOH to volume using its concentration (6.00 M). The volume of NaOH required is then
`\( \frac{\text{moles of NaOH}}{\text{concentration of NaOH}} \)`. The result is 0.0875 L or 87.5 mL of 6.00 M NaOH needed to prepare the pH = 4.00 buffer.

Answer 2

To prepare a buffer solution with a pH of 4.00 using 0.250 L of 0.300 M HNO2, we need to calculate the volume of 6.00 M NaOH needed. Follow the steps in the detailed answer to calculate the volume of NaOH required.

Step-by-step explanation:
To prepare a buffer solution with a pH of 4.00 using 0.250 L of 0.300 M HNO2, we need to calculate the amount of 6.00 M NaOH needed to achieve the desired pH. Here are the steps to calculate the volume of NaOH:

Calculate the concentration of HNO2 in the final buffer solution. Use the pH to find the concentration of H3O+.

Use the Ka of nitrous acid (HNO2) to find the concentration of NO2-. Since the acid and its conjugate base are in a 1:1 ratio in the buffer, the concentration of NO2- is equal to the concentration of HNO2.

Use the volume of HNO2 to calculate the moles of HNO2 used.

Use the moles of HNO2 to determine the moles of NaOH needed. The moles of NaOH should also be equal to the moles of HNO2.

Finally, use the concentration of NaOH to calculate the volume of NaOH needed using the equation:
Volume = (moles of NaOH) / (concentration of NaOH)
After performing these calculations, you will find the volume of 6.00 M NaOH needed to prepare a pH = 4.00 buffer solution using 0.250 L of 0.300 M HNO2.