How many grams of Na2CO3 should be mixed with 50.00g of NaHCO3 to produce 2000mL of buffer with pH=10?
Use the Henderson-Hasselbalch equation.
Na2CO3 is the base
NaHCO3 is the acid.
You want to use pK2.
How do i calculate the pKa??
pKa2 = -log(Ka2)
To determine the amount of Na2CO3 to mix with NaHCO3, we need to consider the equation for the reaction between these two compounds:
2NaHCO3 + Na2CO3 → 3H2O + 3CO2 + 2NaOH
Since we want to create a buffer solution with a pH of 10, we need to ensure that the concentration of the weak base (NaHCO3) is in excess compared to the strong base (Na2CO3). This will allow the buffer to resist changes in pH when acids are added.
To start, let's calculate the number of moles for each compound:
Given:
Mass of NaHCO3 = 50.00 g
Volume of buffer = 2000 mL = 2 L
First, convert the mass of NaHCO3 to moles:
Molar mass of NaHCO3:
Na = 22.99 g/mol
H = 1.01 g/mol
C = 12.01 g/mol
O = 16.00 g/mol (x3)
Total molar mass = 22.99 + 1.01 + 12.01 + (16.00 x 3) = 84.01 g/mol
Moles of NaHCO3 = mass / molar mass
Moles of NaHCO3 = 50.00 g / 84.01 g/mol
Next, convert the volume of buffer solution to moles of HCO3- ion (provided by NaHCO3):
The volume of 2000 mL corresponds to 2 L.
Moles of NaHCO3 = concentration of NaHCO3 x volume of NaHCO3 solution
Since NaHCO3 is a weak acid and partially dissociates, it acts as a source of HCO3-, so the concentration of HCO3- is the same as the concentration of NaHCO3.
Moles of HCO3- = moles of NaHCO3
Next, calculate the concentration (in moles per liter) of NaHCO3:
Concentration = moles / volume
Concentration of NaHCO3 = moles of NaHCO3 / 2 L
Now, let's determine the concentration of NaOH required to obtain a pH of 10:
From the pH value, we know that the concentration of hydroxide ions (OH-) is 10^-4 M (since pH = 10 corresponds to [H+] = 10^-10 M, and in water, [H+] x [OH-] = 10^-14 M^2).
For every mole of Na2CO3, we get two moles of OH- ions:
Concentration of NaOH = 2 x (10^-4 M)
Finally, determine the number of moles of Na2CO3 required to provide the desired concentration of NaOH:
Moles of NaOH = concentration of NaOH x volume (in liters) of buffer solution
Since the pH is specified for the buffer solution, we assume that the [H2O] is constant, so we can ignore it in the equation.
Moles of Na2CO3 = Moles of NaOH / 2
The number of grams of Na2CO3 required can then be calculated by multiplying the moles of Na2CO3 by its molar mass (106.0 g/mol).
I hope this clarifies the process of calculating the required amount of Na2CO3.