ph is 4.6, pKa is 4.76 in a .15M buffer solution, what are the concentrations of acid and base?

Two equations.

pH = pKa + log(base)/(acid) or
4.6 = 4.76 + log b/a
b + a = 0.15

Solve the two equations simultaneously for b and a.

To calculate the concentrations of the acid and base in a buffer solution, you need to know the initial concentrations of the acid and its conjugate base, as well as the pH and pKa of the buffer.

In this case, the pH of the buffer solution is given as 4.6, and the pKa is 4.76. The pKa represents the negative logarithm of the acid dissociation constant (Ka), which is a measure of the acidity of the acid.

To begin, you need to determine whether the solution is more acidic (pH < pKa), more basic (pH > pKa), or at the equal acid-base equilibrium (pH = pKa).

In this scenario, the pH (4.6) is less than the pKa (4.76), indicating that the solution is more acidic, which means the concentration of the acid will be greater than that of the conjugate base.

To calculate the concentrations of the acid (HA) and its conjugate base (A-), you can use the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA])

Rearranging the equation to solve for [A-]/[HA]:

[A-]/[HA] = 10^(pH - pKa)

Substituting the given values:

[A-]/[HA] = 10^(4.6 - 4.76)

[A-]/[HA] = 10^(-0.16)

[A-]/[HA] = 0.717

Now, you know that the concentration of the conjugate base ([A-]) plus the concentration of the acid ([HA]) equals the total concentration of the buffer solution (0.15M):

[A-] + [HA] = 0.15

Substituting the value of [A-]/[HA] obtained above:

0.717*[HA] + [HA] = 0.15

Simplifying the equation:

1.717*[HA] = 0.15

[HA] ≈ 0.087 M (concentration of the acid)

[A-] ≈ 0.063 M (concentration of the conjugate base)

To summarize, the concentration of the acid is approximately 0.087 M, and the concentration of the conjugate base is approximately 0.063 M in the given buffer solution with a pH of 4.6 and a pKa of 4.76.