Calculate the pH of a buffer solution obtained by dissolving 16.0 g of KH2PO4(s) and 27.0 g of Na2HPO4(s) in water and then diluting to 1.00 L. (pKa=7.21)

Convert grams to mols. mols = grams/molar mass.

Then pH = pKa + log(base)/(acid) and solve for pH.

Calculate the molar mass of KH2PO4 and Na2HPO4. Then, determine the moles of the compounds by grams x 1mol/molar mass = moles.

After finding the moles, use the Henderson-Hasselbach equation to solve for pH.
Your Ka=6.2 x 10^-4 and pKa=7.21.
pH=7.21 + log(base/acid)
Base=Na2HPO4
Acid=KH2PO4

To calculate the pH of a buffer solution, we need to use the Henderson-Hasselbalch equation, which is:

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

In this case, KH2PO4 acts as the acid (HA) and Na2HPO4 acts as the conjugate base (A-). Let's start by calculating the concentrations of [HA] and [A-].

First, we need to find the number of moles of each compound:

Molar mass of KH2PO4 = 39.10 g/mol + 2 * 1.01 g/mol + 31.00 g/mol + 16.00 g/mol = 136.09 g/mol
Number of moles of KH2PO4 = 16.0 g / 136.09 g/mol = 0.1174 mol

Molar mass of Na2HPO4 = 22.99 g/mol + 2 * 1.01 g/mol + 31.00 g/mol + 4 * 16.00 g/mol = 141.96 g/mol
Number of moles of Na2HPO4 = 27.0 g / 141.96 g/mol = 0.1903 mol

Now, we can calculate the concentrations:

[HA] = moles of HA / volume of solution = 0.1174 mol / 1.00 L = 0.1174 M
[A-] = moles of A- / volume of solution = 0.1903 mol / 1.00 L = 0.1903 M

Now, let's substitute these values into the Henderson-Hasselbalch equation:

pH = 7.21 + log ( 0.1903 / 0.1174 )

pH = 7.21 + log ( 1.620 )

pH = 7.21 + 0.209

pH = 7.42

Therefore, the pH of the buffer solution is 7.42.

To calculate the pH of a buffer solution, we need to determine the concentrations of the acidic and basic components of the buffer.

First, let's find the moles of KH2PO4 and Na2HPO4 separately by using their molar masses.

Molar mass of KH2PO4 = (1 x atomic mass of K) + (2 x atomic mass of H) + (1 x atomic mass of P) + (4 x atomic mass of O)
= (1 x 39.10) + (2 x 1.01) + (1 x 31.00) + (4 x 16.00)
= 136.09 g/mol

Moles of KH2PO4 = mass of KH2PO4 / molar mass of KH2PO4
= 16.0 g / 136.09 g/mol
= 0.1175 mol

Similarly,

Molar mass of Na2HPO4 = (2 x atomic mass of Na) + (1 x atomic mass of H) + (1 x atomic mass of P) + (4 x atomic mass of O)
= (2 x 22.99) + (1 x 1.01) + (1 x 31.00) + (4 x 16.00)
= 141.96 g/mol

Moles of Na2HPO4 = mass of Na2HPO4 / molar mass of Na2HPO4
= 27.0 g / 141.96 g/mol
= 0.1902 mol

Next, we need to determine the concentrations of the acidic (KH2PO4) and basic (Na2HPO4) components in the buffer solution.

Concentration of KH2PO4 = moles of KH2PO4 / volume of the solution
= 0.1175 mol / 1.00 L
= 0.1175 M

Concentration of Na2HPO4 = moles of Na2HPO4 / volume of the solution
= 0.1902 mol / 1.00 L
= 0.1902 M

Now that we have the concentrations of the acidic and basic components, we can calculate the pH of the buffer solution using the Henderson-Hasselbalch equation:

pH = pKa + log([Na2HPO4] / [KH2PO4])

Substituting the values:

pH = 7.21 + log(0.1902 / 0.1175)

Using a scientific calculator, we can calculate:

pH ≈ 7.21 + log(1.6187)

pH ≈ 7.21 + 0.2097

pH ≈ 7.42

Therefore, the pH of the buffer solution is approximately 7.42.