A beaker with 150 mL of an acetic acid buffer with a pH of 5.00 is sitting on a benchtop. The total molarity of acid and conjugate base in this buffer is 0.100 M. A student adds 5.60 mL of a 0.280 M HCl solution to the beaker. How much will the pH change? The pKa of acetic acid is 4.760.
[CH3COOH] + [CH3COO-]= 0.100 M
pH = pKa + log [CH3COO-] / [CH3COOH]
5.00 = 4.760 + log [CH3COO-] / [CH3COOH]
10^0.24 =1.74 = [CH3COO-]/ [CH3COOH]
I have an idea how to solve it but i dunt know how to get the M of CH3COO AND CH3COOH
So far so good. To save time in typing, I'll call CH3COO- (acetate) = B (for base) and CH3COOH(acetic acid) = A (for acid).
So what you have is B/A = 1.74 and we can rearrange that to
B = 1.74 x A (I would carry that out to one more place; i.e., instead of 1.74 I would go with 1.738.
Now you know that
B + A = 0.1 so substitute for B from above to obtain
1.738A + A = 0.1
and solve for A, then B.
That's how you obtain A and B (concn in moles/L = M). Then in short, the rest of the problem is
How much acid is in the buffer of 5.00? That is 150 mL x (A) = ??
How much base is in the buffer of 5.00?
That is 150 mL x (B) = ??
Now, when you add the 0.280 M HCl what is happening?
Base + HCl ==> acid + Cl^-
So how much acid are you adding? That is 0.280 M x 5.60 mL = ??= I'll say x.
So you add x to acid and subtract x from the base, then reset pH = pKa + log (B/A) and solve for the new pH.
I did a quickie calculation and obtained 4.81 or so. You need to redo the whole thing. Check my work. Does that answer make sense? Yes, because it was pH = 5.00 and we added HCl, a strong acid to it, so it should become more acid and 4.81 is more acid than 5.00.
To determine how much the pH will change after adding the HCl solution, we need to calculate the change in the concentration of the acid and conjugate base in the buffer. The change in concentration will then allow us to calculate the new pH using the Henderson-Hasselbalch equation.
Here are the steps to calculate the change in concentration of the acid and conjugate base:
1. Calculate the initial moles of acid in the buffer solution:
Moles of acid = initial volume of buffer (in L) * initial molarity of acid
In this case, the initial volume of the buffer is 150 mL = 0.150 L, and the initial molarity of acid is 0.100 M:
Moles of acid = 0.150 L * 0.100 M
2. Calculate the initial moles of conjugate base in the buffer solution:
Moles of conjugate base = initial volume of buffer (in L) * initial molarity of conjugate base
Since the acid and conjugate base are in a 1:1 ratio in the buffer, the initial moles of conjugate base will be the same as the moles of acid.
3. Calculate the moles of acid added from the HCl solution:
Moles of acid added = volume of HCl solution added (in L) * molarity of HCl solution
In this case, the volume of HCl solution added is 5.60 mL = 0.00560 L, and the molarity of HCl solution is 0.280 M:
Moles of acid added = 0.00560 L * 0.280 M
4. Calculate the final moles of acid in the solution:
Final moles of acid = initial moles of acid + moles of acid added
5. Calculate the final moles of conjugate base in the solution:
Final moles of conjugate base = initial moles of conjugate base
6. Calculate the final volume of the solution:
Final volume of solution = initial volume of buffer + volume of HCl solution added
7. Calculate the final concentration of acid:
Final molarity of acid = final moles of acid / final volume of solution
8. Calculate the final concentration of conjugate base:
Final molarity of conjugate base = final moles of conjugate base / final volume of solution
Now, we can use the Henderson-Hasselbalch equation to calculate the new pH:
pH = pKa + log10(concentration of conjugate base / concentration of acid)
1. Calculate the initial pH using the given initial molarity of acid and pH:
pH = pKa + log10(initial molarity of conjugate base / initial molarity of acid)
2. Calculate the new pH using the final concentrations of acid and conjugate base:
new pH = pKa + log10(final molarity of conjugate base / final molarity of acid)
3. Calculate the change in pH:
pH change = new pH - initial pH
By following these steps, you should be able to calculate the change in pH after adding the HCl solution to the acetic acid buffer.