Question #167645

Calculate the pH of buffers that contain the acid and conjugate base in following concentrations:

(a) [HPO42-] = 0.33 M, [PO43-] = 0.52 M

(b) [CH3COOH] = 0.40 M, [CH3COO-] = 0.25

What ratio of concentrations of NaH2PO4 and Na2HPO4 in solution would give a buffer with pH = 7.65?

1.00 mol of ammonium chloride is added to 2.00 L of 1.00 mol.L-1 NH3(aq) (Kb = 1.8 x 10-5 mol.L-1) . Calculate the pH of the solution.

Expert's answer

**Q167645**

Calculate the pH of buffers that contain the acid and conjugate base in following concentrations:

(a) [HPO42-] = 0.33 M, [PO43-] = 0.52 M

(b) [CH3COOH] = 0.40 M, [CH3COO-] = 0.25

What ratio of concentrations of NaH2PO4 and Na2HPO4 in solution would give a buffer with pH = 7.65?

1.00 mol of ammonium chloride is added to 2.00 L of 1.00 mol.L-1 NH3(aq) (Kb = 1.8 x 10-5 mol.L-1).

**Solution: **

a) H_{3}PO_{4} is a tri-protic acid with pKa values.

H_{3}PO_{4}(aq) <==> H_{2}PO_{4}^{- }(aq) + H^{+} (aq) , pKa _{1} = 2.12

H_{2}PO_{4}^{-} (aq) <==> HPO_{4}^{2- } (aq) + H^{+} (aq) pKa_{2} = 7.21

** HPO**_{4}^{2-}** (aq) <==> PO**_{4}^{3- }** (aq) + H**^{+}** (aq) pKa**_{3}** = 12.3 **

in the question, we are provided the concentration of HPO_{4}^{2-} and PO_{4}^{3-}.

So we are interested in 3rd dissociation of H_{3}PO_{4}.

We will use the Henderson-Hasselbalch equation for finding the pH of the given buffer.

** HPO**_{4}^{2-}** **will be the** acid**, and** PO**_{4}^{3- } will be its **conjugate base. **

"pH = pKa + log \\frac{[A^-]}{[HA]} = pKa + log \\frac{[Base]}{[Acid]}"

"pH = pKa + log \\frac{[PO_4^{3-}]}{[HPO_4^ {2-}]}"

plug, pKa = 12.3, [HPO_{4}^{2-}]= 0.33M and [PO_{4}^{3-}] = 0.52 M , we have

"pH = 12.3 + log \\frac{0.52M}{0.33M} = 12.3 + log[1.576 ] = 12.3 + 0.1975\n\npH = 12.497 ;"

"pH = 12.497 ;"

In 2 decimal place, the answer is 12.50

**Hence the pH of the HPO**_{4}^{2-}**/PO**_{4}^{3-}**. buffer is 12.50.**

----------------------------------------x-------------------------------------------------------x-------------------------------------------------------

**(b) [CH**_{3}**COOH] = 0.40 M, [CH**_{3}**COO-] = 0.25.**

This problem would be solved in a similar way.

Acetic acid is a monoprotic acid with pKa = 4.745, Sometimes instead of pKa, you may be given Ka.

Ka of tactic acid is 1.8 * 10^{-5}.

If you are provided the Ka then use the formula

pKa = - log [Ka] and find the pKa first

pKa = - log [ 1.8 * 10^{-5} ] = 4.745 ;

**CH**_{3}**COOH** is the** acid **and** CH**_{3}**COO-**is its** conjugate base. **

"pH = pKa + log \\frac{[A^-]}{[HA]} = pKa + log \\frac{[Base]}{[Acid]}"

"pH = pKa + log \\frac{[CH_3COO^-]}{[CH_3COOH]}"

plug, pKa = 4.745 , [CH_{3}COOH]= 0.40M and [CH_{3}COO^{-} ] = 0.25 M , we have

"pH = 4.745 + log \\frac{0.25}{0.40M} = 4.745 + log[0.625 ] = 4.745 - 0.2041"

"pH = 4.541 ;"

In 1 decimal place, the answer is 4.54

**Hence the pH of the CH**_{3}**COOH**/** CH**_{3}**COO- buffer is 4.54.**

**------------------------------x-------------------------------------------x-------------------------------------**

**What ratio of concentrations of NaH2PO4 and Na2HPO4 in solution would give a buffer with pH = 7.65?**

**Solution: **

H_{2}PO_{4}^{-} / HPO_{4}^{2-} would be our buffer system.

In problem a, we say the reaction.

H_{2}PO_{4}^{-} (aq) <==> HPO_{4}^{2- } (aq) + H^{+} (aq) pKa_{2} = 7.21

**H**_{2}**PO**_{4}^{-}** ** will the **acid,** and ** HPO**_{4}^{2- } will be its **conjugate base.**

We are now given the pH of buffer = 7.65,

and asked to find the ratio of H_{2}PO_{4}^{-} / HPO_{4}^{2-} required for having pH = 7.65.

We will put pKa2 = 7.21, and pH = 7.65 , and find the ratio

"pH = pKa + log \\frac{[A^-]}{[HA]} = pKa + log \\frac{[Base]}{[Acid]}"

"pH = pKa + log \\frac{[HPO_4^{2-}]}{[H_2PO_4^ {-}]}"

"7.65 = 7.21 + log \\frac{[HPO_4^{2-}]}{[H_2PO_4^ {-}]}"

subtract 7.21 from both the side we have

"0.44 = log \\frac{[HPO_4^{2-}]}{[H_2PO_4^ {-}]}"

taking 10^ on both the side we have

"10^{0.44} = 10^{ log \\frac{[HPO_4^{2-}]}{[H_2PO_4^ {-}]}}"

"\\frac{2.754 }{1} = \\frac{[HPO_4^{2-}]}{[H_2PO_4^ {-}]}"

** in the question, we are asked the ratio of concentrations of NaH2PO4 and Na2HPO4.**

**which means we are asked the ratio H2PO4^- / HPO4^2- **

hence we will invert both sides of the equation.

flipping both sides of the equation we have

"\\frac{1 }{2.754} = \\frac{[H_2PO_4^ {-}]}{[HPO_4^{2-}]}"

"0.3631 = \\frac{[H_2PO_4^ {-}]}{[HPO_4^{2-}]}"

**Hence the ratio of concentrations of NaH2PO4 and Na2HPO4 should be 0.3631/ 1 **

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