A buffer is prepared by dissolving .0250 mol of sodium nitrite, NaNO2, in 250.0 mL of .0410 M nitrous acid, HNO2. Assume no volume change after HNO2 is dissolved. Calculate the pH of this buffer.

My book does a poor job of explaining buffers and I'm really lost on the concept. Any directions and explanations would be appreciated.

Use the Henderson-Hasselbalch equation.
pH = pKa + log [(base)/(acid)]/

[HNO2] = .0410 M

[NaNO2] = .0250 mol / .250 L = .100 M
[H+] = Ka x [HA (weak acid)] / [A- (conj. base)]
Ka = 6.0 x 10^-4 (a given constant)
[H+] = (6.0 x 10^-4) x [.041]/[.100]
= 2.5 x 10^-4 M.
pH = -Log[H+] -- pH = -log[2.5 x 10^-4]
pH = 3.61

To calculate the pH of the buffer solution, we need to understand the concept of a buffer and the Henderson-Hasselbalch equation.

A buffer solution is a solution that resists changes in pH when small amounts of acid or base are added to it. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid).

The Henderson-Hasselbalch equation is given by:

pH = pKa + log[(base)/(acid)]

where pH is the logarithmic measure of hydrogen ion concentration in the solution, pKa is the negative logarithm of the acid dissociation constant (Ka) of the weak acid, and (base)/(acid) represents the ratio of the concentration of the conjugate base to the concentration of the weak acid in the buffer solution.

In this problem, we are given that the buffer solution is prepared by dissolving 0.0250 mol of sodium nitrite (NaNO2) in 250.0 mL of 0.0410 M nitrous acid (HNO2). We can assume that the volume doesn't change after HNO2 is dissolved.

To solve the problem, we need to follow these steps:

Step 1: Calculate the concentration of the weak acid (HNO2) and conjugate base (NO2-) in the buffer solution.

The concentration of the weak acid (HNO2) is given as 0.0410 M. Since the weak acid is fully dissociated into its ions in water, the concentration of HNO2 is equal to its initial concentration.

The concentration of the conjugate base (NO2-) can be calculated using the stoichiometry of the reaction:

NaNO2 → Na+ + NO2-

Since 0.0250 mol of NaNO2 is dissolved in 250.0 mL of solution, the concentration of NO2- can be calculated as follows:

Concentration of NO2- = (0.0250 mol)/(0.250 L) = 0.100 M

Step 2: Calculate the pKa of nitrous acid (HNO2).

The pKa value can be found in a table or obtained from the acid dissociation constant (Ka) of HNO2.

The Ka value of nitrous acid (HNO2) is given by:

Ka = [H+][NO2-]/[HNO2]

From this equation, we can see that when [NO2-] = [HNO2] (concentration of weak acid is equal to the concentration of its conjugate base), the pH of the solution will be equal to the pKa of HNO2. This point is known as the half-equivalence point of the buffer solution.

To find the pKa, we can rearrange the equation and solve for pKa:

pKa = -log(Ka) = -log([H+][NO2-]/[HNO2])

Step 3: Calculate the pH using the Henderson-Hasselbalch equation.

Now that we have determined the pKa value and the concentrations of the weak acid (HNO2) and conjugate base (NO2-), we can substitute these values into the Henderson-Hasselbalch equation:

pH = pKa + log[(base)/(acid)] = pKa + log[(0.100 M)/(0.0410 M)]

By plugging in the values, we can calculate the pH of the buffer solution.

To calculate the pH of a buffer solution, you can use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation relates the pH of a buffer solution to the pKa of its acidic component (HNO2) and the ratio of the concentration of the conjugate base (NO2-) to the concentration of the acidic component.

The Henderson-Hasselbalch equation is as follows:
pH = pKa + log [(base)/(acid)]

In this case, the acidic component is HNO2, and the conjugate base is NO2-.

To calculate the pH of the buffer, you need to determine three key pieces of information:
1. The pKa value of HNO2
2. The concentration of HNO2 (acid)
3. The concentration of NO2- (base)

1. The pKa value of HNO2:
The pKa value can be found in the literature or provided in the problem. In this case, it is not given, so if you don't have access to a pKa table, you can use the Ka value. The Ka value of HNO2 is the acid dissociation constant and can be found in the literature or provided in the problem. The pKa is calculated by taking the negative logarithm of the Ka value: pKa = -log(Ka).

2. The concentration of HNO2 (acid):
The problem states that you have prepared the buffer by dissolving 0.0250 mol of sodium nitrite, NaNO2, in 250.0 mL of 0.0410 M nitrous acid, HNO2. The concentration of HNO2 can be calculated by using the formula: concentration (mol/L) = moles/volume (L).

For HNO2:
Concentration = moles/volume = 0.0410 M (given)

3. The concentration of NO2- (base):
Since NaNO2 is a sodium salt of HNO2, it completely dissociates in water to give one HNO2 molecule and one NO2- ion. Therefore, the concentration of NO2- will be equal to the concentration of the initial NaNO2.

For NO2-:
Concentration = moles/volume = 0.0250 mol / (250.0 mL * 0.001 L/mL)

Now that you have all the required information, let's plug the values into the Henderson-Hasselbalch equation:

pH = pKa + log [(base)/(acid)]
= pKa + log [(0.0250 mol / (250.0 mL * 0.001 L/mL)) / 0.0410 M]

Once you have the calculated values of pKa and the concentration ratio (base/acid), simply substitute them back into the equation to find the value for pH.