what is the ph of a buffer made by mixing 2.00g of sodium acetate with 20.00ml of 1.20 mol/l acetic acid and adding enough water so the final volume of the mixture is 100.0 ml?
(base) = (sodium acetate) = grams/molar mass/0.100 = ?M.
(acid) = (acetic acid) = 1.20M x (20/100) = ?M
pH = pKa + log (base)/(acid)
Substitute and solve for pH. The answer should be about 4.8 or so.
Well, if a chemist and a comedian teamed up to create a pH buffer, it might go like this:
Chemist: Let's take 2.00 grams of sodium acetate and dissolve it in 20.00 ml of 1.20 mol/l acetic acid.
Comedian: Ah, a recipe for disaster! Are you making a volatile concoction or cooking up a pH buffer soup?
Chemist: Well, a pH buffer is like a bouncer at a comedy club. It regulates the pH levels, just like a bouncer keeps the rowdy crowd under control.
Comedian: So, it's like keeping pH levels from getting too dramatic or unpredictable?
Chemist: Exactly! Now, to find the pH, we add enough water to make the final volume 100.0 ml. The sodium acetate will react with acetic acid, creating a buffer solution.
Comedian: A buffer solution, huh? Sounds like the "chill pill" of the chemical world!
Chemist: Indeed! Now, to calculate the pH, we need to know the pKa of the acetic acid, which is approximately 4.75.
Comedian: 4.75? Sounds like the ideal pH for a chemist with a sense of humor. Not too basic, not too acidic.
Chemist: Well said! Now, using the Henderson-Hasselbalch equation, we can find the pH:
pH = pKa + log ([A-]/[HA])
Comedian: Hold on, let me get my pH-calculator comedy routine ready!
Chemist: Alright, let's plug in the values! We have [A-] (concentration of acetate ion) from the sodium acetate and [HA] (concentration of acetic acid).
Comedian: Is that it? [A-] acetate, [HA] ha-ha?
Chemist: You've got it! In this case, [A-] = mols of sodium acetate / total volume, and [HA] = mols of acetic acid / total volume.
Comedian: Got it! Now, we divide [A-] by [HA], take the logarithm, and add it to the pKa.
Chemist: Exactly! That gives us the pH of our comedy club buffer solution.
Comedian: Drumroll, please! *ba dum tss*
Chemist: And the pH of this buffer solution is approximately 4.77!
Comedian: Ah, a well-balanced comedy club indeed! The pH of laughter is set just right.
Chemist: That's chemistry and comedy working together in perfect harmony!
To determine the pH of the buffer solution, we need to consider the equation for the dissociation of acetic acid:
CH3COOH ⇌ CH3COO- + H+
Given information:
Mass of sodium acetate (CH3COONa): 2.00 g
Volume of acetic acid (CH3COOH): 20.00 mL
Concentration of acetic acid: 1.20 mol/L
Final volume of the mixture (including added water): 100.0 mL
First, let's convert the mass of sodium acetate to moles:
Molar mass of sodium acetate (CH3COONa): 82.03 g/mol
Number of moles of sodium acetate (CH3COONa) = mass (g) / molar mass (g/mol)
Number of moles of sodium acetate (CH3COONa) = 2.00 g / 82.03 g/mol = 0.0244 mol
Next, let's calculate the number of moles of acetic acid in the solution:
Number of moles of acetic acid (CH3COOH) = concentration (mol/L) x volume (L)
Volume of acetic acid (CH3COOH) = 20.00 mL = 0.0200 L
Number of moles of acetic acid (CH3COOH) = 1.20 mol/L x 0.0200 L = 0.0240 mol
Now, let's calculate the total number of moles of acetic acid and acetate in the solution:
Total moles of acid = moles of acetic acid = 0.0240 mol
Total moles of conjugate base = moles of sodium acetate = 0.0244 mol
Since the concentration ratio of acid to conjugate base in a buffer solution determines the pH, and the ratio of moles is approximately 1:1, we can consider the equivalence of moles when calculating pH.
Next, we need to calculate the total volume of the mixture (including added water):
Volume of the mixture = volume of acetic acid + volume of added water
Volume of the mixture = 20.00 mL + (100.0 mL - 20.00 mL) = 100.0 mL
Now, let's calculate the concentration of the acid and base in the solution:
Concentration (mol/L) = moles / volume (L)
Concentration of acetic acid = 0.0240 mol / 0.1000 L = 0.240 mol/L
Concentration of acetate = 0.0244 mol / 0.1000 L = 0.244 mol/L
To determine the pH of the buffer solution, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Here, [A-] represents the concentration of the conjugate base (acetate) and [HA] represents the concentration of the acid (acetic acid).
The pKa value for acetic acid is 4.76.
Let's calculate the pH using the Henderson-Hasselbalch equation:
pH = 4.76 + log(0.244/0.240)
pH = 4.76 + log(1.017)
Using logarithmic properties, we can simplify the calculation:
pH = 4.76 + 0.0086
pH ≈ 4.7686
Therefore, the pH of the buffer solution is approximately 4.77.
To determine the pH of the buffer, you first need to calculate the moles of the sodium acetate and acetic acid in the solution. Then, you can use the Henderson-Hasselbalch equation to find the pH of the buffer.
Let's break down the calculations step by step:
Step 1: Calculate the moles of sodium acetate.
The molar mass of sodium acetate (CH3COONa) is:
C = 12.01 g/mol
H = 1.01 g/mol
O = 16.00 g/mol
Na = 22.99 g/mol
The molar mass of sodium acetate is 82.03 g/mol, so:
Number of moles of sodium acetate = mass / molar mass
= 2.00 g / 82.03 g/mol
= 0.0244 mol
Step 2: Calculate the moles of acetic acid.
Since we have the concentration and volume of the acetic acid, we can calculate the moles using the formula:
Molarity = moles / volume (in liters)
Number of moles of acetic acid = molarity x volume
= 1.20 mol/L x 0.020 L
= 0.024 mol
Step 3: Calculate the total moles of the buffer components.
For a buffer, the moles of the acid and its conjugate base should be roughly equal, so we can add the moles of the sodium acetate and acetic acid:
Total moles of buffer components = moles of sodium acetate + moles of acetic acid
= 0.0244 mol + 0.024 mol
= 0.0484 mol
Step 4: Calculate the concentrations of the acid and its conjugate base.
Using the total moles and the final volume of the mixture, we can calculate the concentrations of the acid and its conjugate base (sodium acetate):
Concentration = moles / volume (in liters)
Concentration of acetic acid = moles / final volume
= 0.024 mol / 0.100 L
= 0.240 mol/L
Concentration of sodium acetate = moles / final volume
= 0.0244 mol / 0.100 L
= 0.244 mol/L
Step 5: Use the Henderson-Hasselbalch equation to calculate the pH of the buffer.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log ([A-] / [HA])
Since acetic acid is a weak acid, we can use the pKa value of acetic acid, which is 4.76.
pH = 4.76 + log (0.244 mol/L / 0.240 mol/L)
Calculating the logarithm and the division:
pH = 4.76 + log (1.017)
Finally:
pH = 4.76 + 0.008
= 4.768
Therefore, the pH of the buffer made by mixing 2.00g of sodium acetate with 20.00ml of 1.20 mol/l acetic acid and adding enough water to make a 100.0 ml solution is approximately 4.768.