Find the mass of sodium formate that must be dissolved in 200.00cm^3 of a 1.0M solution of formic acid to prepare a buffer solution with pH=3.40? I have no clue how to work this out. Please help me.

If you know how to use the Henderson-Hasselbalch equation that is the way to go. If not, let me know and it can be done another way.

Is it something like PH=pKa +log [base]/[acid]

3.40=??
How do I find the pKa?

To solve this problem, we need to understand the concept of a buffer solution and the Henderson-Hasselbalch equation.

A buffer solution is a solution that resists changes in pH when small amounts of acid or base are added to it. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid). In this case, the formic acid (HCOOH) is the weak acid and sodium formate (HCOONa) is the conjugate base.

The Henderson-Hasselbalch equation is used to calculate the pH of a buffer solution. It is given by:

pH = pKa + log([A-]/[HA])

Where pH is the desired pH of the buffer solution, pKa is the acid dissociation constant of the weak acid, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.

In our case, the desired pH is 3.40, and we need to find the mass of sodium formate required to prepare the buffer solution.

Step 1: Calculate the pKa value of formic acid.
The pKa value of formic acid is 3.75. This value should be provided in the problem or can be looked up in a reference table.

Step 2: Use the Henderson-Hasselbalch equation to find the ratio of [A-]/[HA].
pH = pKa + log([A-]/[HA])
3.40 = 3.75 + log([A-]/[HA])
log([A-]/[HA]) = 3.40 - 3.75
log([A-]/[HA]) = -0.35

Step 3: Convert the given volume of the solution to moles of formic acid.
1.0M solution means that there is 1.0 mole of formic acid per liter of solution.

Concentration (Moles/Liter) = Moles/Volume(Liter)
1.0M = Moles/0.200L
Moles = 1.0M x 0.200L
Moles = 0.2 moles

Step 4: Determine the moles of formate ions.
From the balanced chemical equation, we know that 1 mole of formic acid (HCOOH) reacts with 1 mole of sodium formate (HCOONa).

Therefore, the moles of formate ions (A-) will also be 0.2 moles.

Step 5: Calculate the mass of sodium formate required.
Since the molar mass of sodium formate (HCOONa) is approximately 68.01 g/mol, we can use the formula:

Mass (g) = Moles x Molar mass
Mass (g) = 0.2 moles x 68.01 g/mol
Mass (g) = 13.602 g (rounded to three decimal places)

Therefore, approximately 13.602 grams of sodium formate must be dissolved in 200.00 cm^3 of a 1.0M solution of formic acid to prepare a buffer solution with pH = 3.40.