What is the pH when 0.40 g of NaOH is added to 50.0 mL of 0.10 M HCooh? No volume change. (The Ka for HCOOH = 1.8 x 10^4.)

To determine the pH when NaOH is added to HCOOH, we need to perform a series of calculations. Let's break down the steps:

Step 1: Calculate the number of moles of NaOH.
We can use the formula: moles = mass / molar mass.

Given: mass of NaOH = 0.40 g; molar mass of NaOH = 23.0 g/mol.
moles of NaOH = 0.40 g / 23.0 g/mol.

Step 2: Calculate the initial number of moles of HCOOH.
We can use the formula: moles = concentration x volume.

Given: concentration of HCOOH = 0.10 M; volume of HCOOH = 50.0 mL = 0.050 L.
moles of HCOOH = 0.10 M x 0.050 L.

Step 3: Determine the reaction between NaOH and HCOOH.
NaOH is a strong base, and HCOOH is a weak acid. When they react, they form water (H2O) and the conjugate base of HCOOH, which is HCOO-.

The balanced chemical equation for the reaction is:
HCOOH (aq) + NaOH (aq) → HCOO- (aq) + H2O (l)

Step 4: Determine the moles of HCOOH that react with NaOH and the moles of HCOOH remaining.
Since NaOH and HCOOH react in a 1:1 ratio (based on the balanced equation), the moles of HCOOH reacting with NaOH are equal to the moles of NaOH added.

moles of HCOOH remaining = initial moles of HCOOH - moles of HCOOH reacting with NaOH.

Step 5: Calculate the concentration of HCOOH remaining.
We can use the formula: concentration = moles / volume.

Given: volume of HCOOH = 50.0 mL = 0.050 L.
concentration of HCOOH remaining = moles of HCOOH remaining / volume of HCOOH.

Step 6: Calculate the concentration of the conjugate base, HCOO-.
Since the moles of HCOOH and HCOO- are equal at equilibrium, the concentration of HCOO- is equal to the concentration of HCOOH remaining.

Step 7: Calculate the pH using the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is: pH = pKa + log ([conjugate base]/[weak acid]).

Given: pKa of HCOOH = 1.8 x 10^4.
pH = pKa + log ([HCOO-]/[HCOOH remaining]).

Substitute the values and calculate the pH.

Note: Since the volume of the solution is not changing, the pH remains the same throughout the process.

By following these steps and performing the calculations, you can determine the pH when 0.40 g of NaOH is added to 50.0 mL of 0.10 M HCOOH.