Calculate the pH of a 100mL solution of 0.10M acetic acid ka=1.8x10(-5)

i calculated the pH to be 2.87

from the square root of
(1.8x10(-5) * 0.1, the negative log gives me the pH.

The next question wants you to calculate the pH with 50mL HCl added. I found the pH to be 2.78 by just adding .05 to the bottom [HA] value are these correct so far?

2.87 is correct for the first one.

For #2, you don't provide the (HCl). Although (HCl) is not listed; I suspect your answer of 2.78 is not right. Assume (HCl) is 0.1M and you add 50 mL so that is 5 millimoles/150 mL = 0.0333M HCl.
Since HCl is 100% ionized (and acetic acid is only about 1% ionized) most of the H^+ will be contributed by HCl and pH = 1.48.
If (HCl) is 0.01M, we add 0.5 millimole HCl and that in 150 mL = 0.00333 which is 2.48 for pH.

To calculate the pH of a solution of acetic acid, you need to consider its dissociation constant, Ka, which is given as 1.8x10^(-5).

To start, you correctly calculated the pH of the initial acetic acid solution. To do this, you used the expression [H+] = √(Ka * [HA]), where [HA] represents the initial concentration of acetic acid. Given that the concentration of acetic acid is 0.10M, you can substitute these values into the equation:

[H+] = √(1.8x10^(-5) * 0.1)
[H+] = 1.34x10^(-3) mol/L

Next, you take the negative logarithm of the hydrogen ion concentration to find the pH:

pH = -log[H+]
pH = -log(1.34x10^(-3))
pH = 2.87

Therefore, your calculation of the initial pH as 2.87 is correct.

Now, let's move on to the second part where you have added 50mL of HCl to the solution. The concentration of HCl added can be determined by calculating the moles of HCl in the 50mL solution. Assuming HCl is a strong acid and fully dissociates, its concentration will be the same as the moles of HCl divided by the total volume of the solution (original volume + volume of HCl):

[HCl] = (moles of HCl) / (total volume)

To find the moles of HCl, you need to know the concentration of HCl solution. Once you have that information, you can calculate the moles using the formula:

moles = concentration (in M) × volume (in L)

Once you determine the moles, you can calculate the concentration of HCl in the solution by dividing the moles by the total volume.

After finding the concentration of HCl in the solution, you can apply the Henderson-Hasselbalch equation, which relates the pH to the concentration of the acid and its conjugate base:

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

In this case, acetic acid (HA) is acting as the acid, and its conjugate base (acetate, A-) is formed by the dissociation of acetic acid. The pKa value of acetic acid can be calculated using the given Ka value:

pKa = -log(Ka)
pKa = -log(1.8x10^(-5))
pKa ≈ 4.74

To calculate the concentration of acetate ([A-]), subtract the concentration of HCl from the initial concentration of acetic acid:

[A-] = [HA] - [HCl]

Now, you can substitute the values you calculated into the Henderson-Hasselbalch equation:

pH = 4.74 + log(([A-]/[HA]))

To find the concentration of acetate ([A-]), divide the moles of acetate by the total volume:

[A-] = (moles of acetate) / (total volume)

Using the same approach described earlier for calculating moles, you can determine the moles of acetate based on the concentrated solution added. Then, divide by the total volume of the solution to find the concentration of acetate.

Now, plug in the values into the Henderson-Hasselbalch equation, solve for pH, and compare the result with your calculated pH of 2.78. If the values match, then your calculation is correct. Keep in mind that rounding errors may be present, so slight variations are expected.