Prepare 1 liter acetic acid solution with pH=5.1.

Acetic acid is a weakly acidic compound that dissociates in solution to produce sodium acetate and hydronium ions ([H₃O⁺]). The following equations can be used to estimate pH of acetic acid solution:

 

[H₃O⁺] = [H⁺]

Where, Ka is acid dissociation constant of the acid, and C is the molar concentration of the acid.

Solution:

Step 1. apply the above equations to find molar concentration: 

pH = -log [H₃O⁺]

5.1 = -log [H₃O⁺]

[H₃O⁺] = 10^-5.1

[H₃O⁺] = 7.94 × 10^-6

Assuming Ka value for acetic acid at 25 ºC is equal to 1.75 × 10^-5 then the above equation can be written as the following:

7.94 × 10^-6 =((-1.75 × 10^-5 + sqrt ((1.75 × 10^-5)2+ 4 ×1.75 × 10^-5× C))/2

  

Solving the above equation for C gives the following value:

C= 1.15 × 10^-5 M

Step 2. Find out if preparation and dilution of a stock solution is required.

Molecular weight (molar mass) of acetic acid is equal to 60.1 g/ mole. 

To prepare 1 liter of 1.15 × 10^-5 M we need 1.15 × 10^-5 mole of acetic acid. Therefore, the mass of acetic acid needed is calculated as the following:

Mass = number of moles × molar mass

Mass = 1.15 × 10^-5 × 60.1 = 0.00069 g = 0.69 mg.

The above mass is too small to be simply weighed on a scale. Therefore, a stock solution should be prepared then a certain volume of the stock solution containing the required number of moles is used in the preparation.

Step 3. Make calculations for stock solution and required dilution(s).

To prepare 0.115 M stock solution we need to dissolve 6.9 g acetic acid in water to make 1 liter solution. Calculate the volume of this stock solution which contains 

1.15 × 10^-5 mole using the following equation:

Volume = number of moles/ concentration

Volume = 1.15 × 10^-5 mole/ 0.115 M

Volume = 0.0001 liter

Volume = 0.0001 liter * 1000 ml/ liter = 0.1 ml.

The calculated volume of 0.1 ml is too small to be accurately taken. Therefore, further dilution is required as the following:

Take 10 ml (0.01 liter) from the stock solution to prepare 1 liter solution. The concentration of this solution is calculated as the following:

concentration = number of moles/ volume

concentration = (0.01 liter × 0.115 mole/ liter) / 1 liter

concentration = 0.00115 M

The diluted solution with concentration of 0.00115 M can be used to prepare the needed solution as the following:

volume = number of moles/ concentration

volume = 1.15 × 10^-5 mole/ 0.00115 M

volume = 0.01 liter

volume = 0.01 liter * 1000 ml/ liter = 10 ml.

Thus, add 10 ml of the diluted solution (0.00115 M) to a 1 liter volumetric flask then complete volume to 1 liter mark wit water and mix.