You need to prepare 100.0 ml of a ph 4.00 buffer solution using 0.100 m benzoic acid (pka = 4.20) and 0.120 m sodium benzoate. how many milliliters of each solution should be mixed to prepare this buffer?

The volume of 0.100 M benzoic acid required is 65.6 mL and the volume of 0.120 M sodium benzoate is 34.4 mL.

Buffer solutions

Buffer solutions are solutions that resists changes in its pH when a little quantity of acid or base is added to it them.

The Henderson-Hasselblach equation

The Henderson-Hasselblach equation is used to determine the weak base/weak acid ratio in a buffer solution

Henderson-Hasselblach equation is given as: pH = Pka + ㏒[A]/[HA]

From the data provided:

pH of buffer = 4.00

pKa of acid = 4.20

A is benzoate and benzoic acid is HA

Using the Henderson-Hasselbach equation:

4.00 = 4.20 + ㏒[A]/[HA]

[A]/[HA] = 0.63

Also; Molarity = number of moles × volume

[A] = 0.12 × V1

[HA] = 0.10 × V2

Hence:

0.1 2 × V1 / 0.10 × V2 = 0.63

V1 = 0.10 × 0.63 × V2 / 0.12

V1 = 0.525 × V2 eqn 1

Also, since V1 + V2 = 100 mL

V2 = 100 - V1

Substitute V2 = 100 - V1 in eqn 1

V1 = 0.525 × {100 - V1}

V1 = 52.5 - 0.525V1

1.525V1 = 75.6

V1 = 52.5 ÷ 1.525

V1 = 34.4 mL

Then V2 = 100 - 34.4

V2 = 65.6

Therefore, the volume of 0.100 M benzoic acid required is 65.6 mL and the volume of 0.120 M sodium benzoate is 34.4 mL.

Learn more about buffers and Henderson-Hasselblach equation at: link

First, we have to use Henderson-Hasselblach equation to get the weak base/weak acid ratio:

PH = Pka + ㏒[A]/[HA]
when PH = 4

Pka = 4.2 

A  is the benzoate

HA is the benzoic acid

so,
4 = 4.2 + ㏒[A]/[HA]

∴[A]/[HA] = 0.631

when [A]/[HA] = 0.12 m * VA / 0.1 m * VHA

∴0.631 = 0.12m* VA / 0.1m * VHA

now, when we have the total volume of the solution is 100 mL

∴VA = 100 mL - VHA  ( we can substitute with 100 - VHA instead of VA)

∴0.631 = 0.12 * (100-VHA) / 0.1 * VHA

we can assume that VHA = X 

so,
0.631 = 0.12 * (100-X) / 0.1 * X  by  solving this equation for X

∴X = 65.5 

∴VHA = 65.5 mL

so, VA = 100mL - 65.5 ML 
           = 34.5 mL
 

Atomicity occurs to prevent updates of the database occurring only partially, which can cause greater problems than rejecting the whole series outright.some are monatomic, diatomic, triatomic etc because it shows the number of atoms. for example, monatomic means it contains only one atom.

You would do 1500/4 and the answer is 375