0.100 M solution of a weak acid, HX, is known to be 15% ionized. The weak acid has a molar mass of 72 g/mol.

1. What is Ka for the weak acid?

2. What is the pH of the buffer prepared by adding 10.0 g of the sodium salt of the acid (NaX) to 100.0 mL of 0.250 M HX

To find the answers to these questions, we will use the concepts of acid ionization constant (Ka) and Henderson-Hasselbalch equation.

1. To find Ka for the weak acid HX, we need to calculate the ionization constant using the percent ionization and the initial concentration of HX.

The percent ionization is given as 15%, which means that the weak acid HX is 15% ionized. This implies that for every 100 molecules of HX, 15 molecules ionize to form H+ ions.

Let's assume the initial concentration of the weak acid HX is C (in M). Therefore, the concentration of H+ ions formed from ionization is 0.15C (15% of C).

The dissociation of HX can be represented as:
HX -> H+ + X-

The initial concentration of HX, C, will decrease by 0.15C due to the ionization. So, the concentration of the remaining undissociated HX after ionization is (C - 0.15C) = 0.85C.

The equilibrium expression for this dissociation reaction is:
Ka = [H+][X-] / [HX]

Since the concentration of the salt X- is the same as the concentration of H+, we can replace [X-] with [H+].

Ka = (0.15C)(0.15C) / (0.85C)

Simplifying the expression:
Ka = 0.022 / 0.85

Ka ≈ 0.0259

Hence, the Ka for the weak acid HX is approximately 0.0259.

2. To find the pH of the buffer prepared by adding 10.0 g of the sodium salt of the acid (NaX) to 100.0 mL of 0.250 M HX, we will first calculate the concentration of the X- ions in the solution.

The molar mass of HX is given as 72 g/mol. So, the moles of HX present in 10.0 g can be calculated as:
moles of HX = mass of HX / molar mass of HX
moles of HX = 10.0 g / 72 g/mol

The volume of HX solution is given as 100.0 mL. Since the concentration of HX is given as 0.250 M, the moles of HX can be calculated as:
moles of HX = concentration of HX x volume of HX solution
moles of HX = 0.250 M × 0.100 L

Now, the total moles of X- ions in the solution will be the sum of moles of X- from NaX and moles of X- from ionized HX.

To find the moles of X- from NaX, we need to use the balanced equation of the reaction between NaX and HX. Assuming a 1:1 stoichiometric ratio, the moles of X- from NaX will be equal to the moles of HX.

The total moles of X- ions = moles of X- from NaX + moles of X- from ionized HX

The total volume of the solution is given as 100.0 mL. So, the molarity of the X- ions can be calculated by dividing the total moles of X- ions by the total volume in liters.

Finally, to find the pH of the buffer solution, we can use the Henderson-Hasselbalch equation, which is given by:

pH = pKa + log([salt]/[acid])

Here, [salt] represents the concentration of the salt X- in the solution, and [acid] represents the concentration of the weak acid HX, which is given as 0.250 M. The pKa value can be determined from the Ka calculated in part 1.

Substitute the values into the equation and solve for pH.