pH= 7.44

What is the ratio of [H2PO4^-]/[HPO4^2-]

What does the pH become if 25% of the hydrogen phosphate ions are converted to the dihydrogen phosphate ion?

What does the pH become if 15% of the dihydrogen phosphate ions are converted to hydrogen phisphate ions?

answered below.

To determine the ratio of [H2PO4^-]/[HPO4^2-], we need to use the Henderson-Hasselbalch equation, which relates the pH and pKa of an acid-base system:

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

In this case, H2PO4^- is the conjugate acid (HA) and HPO4^2- is the conjugate base (A-). The pKa for the H2PO4^-/HPO4^2- system is usually assumed to be around 7.21.

So, using the Henderson-Hasselbalch equation:

7.44 = 7.21 + log([HPO4^2-]/[H2PO4^-])

Rearranging the equation, we can solve for the ratio [HPO4^2-]/[H2PO4^-]:

log([HPO4^2-]/[H2PO4^-]) = 7.44 - 7.21
log([HPO4^2-]/[H2PO4^-]) = 0.23

Now, we need to convert this logarithmic equation into an exponential form to determine the actual ratio. We can use the fact that log(base 10)x = y is equivalent to 10^y = x.

[HPO4^2-]/[H2PO4^-] = 10^(0.23)
[HPO4^2-]/[H2PO4^-] ≈ 1.71

Therefore, the ratio of [H2PO4^-]/[HPO4^2-] is approximately 1.71.

To determine the new pH when 25% of the hydrogen phosphate ions are converted to the dihydrogen phosphate ion, we can use the Henderson-Hasselbalch equation again.

Let HPO4^2- be x and H2PO4^- be y. Initially, the ratio of [H2PO4^-]/[HPO4^2-] is 1.71. Since 25% of the HPO4^2- ions are converted to H2PO4^-, the new ratio becomes:

(x-0.25x) / (y+0.25x) = 1.71

Simplifying the equation:

0.75x / (1.25x) = 1.71

0.75x / 1.25x = 1.71

0.6 = 1.71

x = 0.6/1.71

This means that the new ratio of [H2PO4^-]/[HPO4^2-] is approximately 0.35.

To find the new pH, we substitute this updated ratio into the Henderson-Hasselbalch equation:

pH = pKa + log([HPO4^2-]/[H2PO4^-])

Since the pKa remains the same, we can directly calculate the new pH using the updated ratio:

pH = 7.21 + log(0.35)

After substituting the values, we can calculate the new pH.

Regarding the second question, the same approach can be used by updating the ratios with the given percentage.