We will abbreviate malonic acid, CH2(CO2H)2, as H2M. Find the pH and concentrations of

Chapter 9, Problem 9-5

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QUESTION:

We will abbreviate malonic acid, \(\mathrm{CH}_{2}\left(\mathrm{CO}_{2} \mathrm{H}\right)_{2}\), as \(\mathrm{H}_{2} \mathrm{M}\). Find the \(\mathrm{pH}\) and concentrations of \(\mathrm{H}_{2} \mathrm{M}, \mathrm{HM}^{-}\), and \(\mathrm{M}^{2-}\) in

(a) \(0.100 \ \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{M}\);

(b) \(0.100 \ \mathrm{M} \ \mathrm{NaHM}\);

(c) \(0.100 \ \mathrm{M} \ \mathrm{Na}_{2} \mathrm{M}\).

Questions & Answers

QUESTION:

We will abbreviate malonic acid, \(\mathrm{CH}_{2}\left(\mathrm{CO}_{2} \mathrm{H}\right)_{2}\), as \(\mathrm{H}_{2} \mathrm{M}\). Find the \(\mathrm{pH}\) and concentrations of \(\mathrm{H}_{2} \mathrm{M}, \mathrm{HM}^{-}\), and \(\mathrm{M}^{2-}\) in

(a) \(0.100 \ \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{M}\);

(b) \(0.100 \ \mathrm{M} \ \mathrm{NaHM}\);

(c) \(0.100 \ \mathrm{M} \ \mathrm{Na}_{2} \mathrm{M}\).

ANSWER:

Step 1 of 3

(a)

The equilibrium reaction of the malonic acid is as follows.

                                 ..............(1)

                                 .............(2)

 is small,  is a weak acid and  is also weaker acid because  is very small.

For this reason, assume that a solution of  behaves as a monoprotic acid.

                                       

Let’s write the equilibrium expression for the given reaction as follows.

                                                      …………………..(3)

Assume that,

 is equal to “x” and   is also equal to “x”.

And  is equal to 0.100 -x.

Substitute these values in expression (3)

                                                   

                                   


Let’s calculate the concentration of hydronium ion.

                                                   
                                                             

Let’s calculate the pH of the solution.

                                                     
                                                           

                                               
                                                             

                                                 
                                                             


Let’s write the equilibrium reaction for the equation (2).

 .............................(4)

Let’s rearrange the equation (4)

                                                   …………………..(5)

Substitute the given values.

                                           

                                                             

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