# Find the pH of 0.1M H3PO4 solution.

The pH of a solution is a measure of the molar concentration of hydrogen `(H^+)` , or hydronium `(H_3O^+)` ions of the solution. If a solution has a hydronium ion concentration of `[H^+]` , the pH of the solution is equal to `-1*log_10[H^+]` .

The pH of pure water at STP is equal to 7. Acids have a pH less 7.

When phosphoric acid `H_3PO_4` is diluted with water it dissociates as follows:

1) `H_3PO_4 -> H^+ + H_2PO_4^-`

2) `H_2PO_4^(-) -> H^+ + HPO_4^(2-)`

3) `HPO_4^(2-) -> H^+ + PO_4^(3-)`

The acid dissociation constants of (1), (2), and (3) are equal to 7.1*10^-3, 6.3*10^-8 and 4.5*10^-13 resp.

To determine the pH of a 0.1 M solution of phosphoric acid, the concentration of H^+ in the solution has to be determined. The first deprotonation step leads to the formation of 0.1 M of hydrogen ions.

The second and third deprotonation steps can be ignored for acid concentrations greater 0.001 M as the [H^+] due to these is negligible.

Now Ka1 = `([H^(+)]*[H_2PO_4^(-)])/[H_3PO_4]`

If we express `[H^+]` as X.

Ka1 = `(X*X)/(.1 - X)`

The value of Ka1 is `7.1*10^-3` .

Solving `7.1*10^-3 = (X*X)/(.1 - X)` for X gives 0.0233 as the positive solution of X.

The pH of the solution is `-1*log_10 0.0233` = 1.63

The pH of a 0.1 M solution of phosphoric acid is 1.63.

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The pH scale is a scale from 0 to 14 that indicates the acidity of a substance.  The number 7 is in the middle and represents neutrality, in terms of qualifying a substance as an acid or a base.  Substances that are lower than 7 are classified as acids, meaning they have increasing numbers of hydrogen ions (H+) when dissolved with water.  Substances that are higher than 7 are classified as bases, meaning they have less hydrogen ions and more hydroxide ions (OH-) when dissolved with water.

To find the pH of a .1 M sample of H3PO4, understand the .1 M is the same as 1 x 10-1.  If we take the logarithm of 1 x 10-1, that would be expressed as  - (-1), which would be 1.  The pH of this solution would be 1, which would qualify it as a very strong acid, providing many hydrogen ions upon dissolution with water.  Th pH scale is very useful in indicating the acidity or basicity of substances.

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its a tripotic acid with three different Ka values they are Ka1, Ka2 and Ka3.

Ka1 = H3PO4 = 7.5 * 10^-3

Ka2 = H2PO4^- = 6.2 * 10^-8

Ka3 = HPO4^2- = 4.8 * 10^-13

Ka1>>Ka2 and Ka3.

which says that majority of Hydronium is produced during step one so we can ignore step 2 and 3.

Since H3PO4 is weak acid it will not dissociate completely and we have to write the ICE table

H3PO4 + H2O ↔ H3O^+ + H2PO4^-

I         0.10M               0               0

C           -x                  +x              +x

E           0.10-x             x                x

Ka1 = ([H3O^+][H2PO4^-])/[H3PO4]

7.5*10^-3 = ([x][x])/[0.10-x]

Find x usind qudratic equation...

x = 0.024M

[H3O^+] = x = 0.024M

PH = -log[H3O^+]

PH = -log[0.024]

Ph = 1.619

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