Starting out with 50 mL of 0.20 M NaHCO3, calculate how many mL of 0.50 M NaOH solution to add to make 100 mL of approximately 0.10 M (total) buffer solution with a pH of 10.35. By adding NaOH, some of the NaHCO3 gets converted to the conjugate Na2CO3. This conjugate acid/base pair has an effective pKa of 10.00. Calculate mL of 0.50 M NaOH needed from the following calculations:

Question

Starting out with 50 mL of 0.20 M NaHCO3, calculate how many mL of 0.50 M NaOH solution to add to make 100 mL of approximately 0.10 M (total) buffer solution with a pH of 10.35. By adding NaOH, some of the NaHCO3 gets converted to the conjugate Na2CO3. This conjugate acid/base pair has an effective pKa of 10.00. Calculate mL of 0.50 M NaOH needed from the following calculations:

10.35-pK =log[(mol CO3^2-)/(mol HCO3^-)]

There is initially Na2CO3 present in the 50 mL of 0.20 M NaHCO3 solution. By adding some NaOH, you will create some Na2CO2 in the solution and also decrease the mol of NaHCO2. In fact, mol NaOH added = mol Na CO in buffer solution. Therefore,
10^(10.35−𝑝𝐾𝑎)= [(mol NaOH added)/(0.20 M×0.050 L−mol NaOH added)]

Solve for mol NaOH added in the above equation. Then, use the concentration of the NaOH (0.50 mol/L) to calculate the calculate the mL of NaOH necessary to prepare the buffersolution.

Answer 1

To calculate the mL of 0.50 M NaOH solution needed to prepare the buffer solution, we need to follow the steps provided.

Step 1: Calculate the moles of CO3^2- and HCO3^- in the buffer solution.
To do this, we use the equation:

10.35 - pK = log[(mol CO3^2-) / (mol HCO3^-)]

We are given the pH, which is 10.35, and the pKa, which is 10.00.
Substituting these values into the equation, we have:

10.35 - 10.00 = log[(mol CO3^2-) / (mol HCO3^-)]

0.35 = log[(mol CO3^2-) / (mol HCO3^-)]

Now, let's solve for (mol CO3^2-) / (mol HCO3^-).

Take the antilog of both sides to eliminate the logarithm:

10^0.35 = (mol CO3^2-) / (mol HCO3^-)

Now, we have the ratio of (mol CO3^2-) to (mol HCO3^-).

Step 2: Determine the moles of NaOH added.
In the buffer solution, we have NaHCO3, which gets converted to Na2CO3 when NaOH is added. The moles of NaOH added must be equal to the moles of Na2CO3 in the buffer solution.

So, we can set up the equation:

mol NaOH added = mol Na2CO3

Step 3: Calculate the moles of NaOH added using the equation:

mol NaOH added = (10^0.35) / (0.20 M * 0.050 L - mol NaOH added)

Here, we are given the concentration of NaHCO3 (0.20 M) and the initial volume (50 mL). We subtract "mol NaOH added" from the total volume to account for the decrease in moles of NaHCO3 when NaOH is added.

Solve this equation for "mol NaOH added" using algebraic methods.

Step 4: Calculate the mL of 0.50 M NaOH needed to prepare the buffer solution.
Now that we have the moles of NaOH added, we can calculate the mL of 0.50 M NaOH needed.

mL NaOH needed = (mol NaOH added) / (0.50 mol/L)

Substitute the value of "mol NaOH added" into this equation and calculate the mL of NaOH needed.

Follow these steps to obtain the final answer for the mL of 0.50 M NaOH needed to prepare the buffer solution.