You are preparing 500 mL of a 0.300 M acetate buffer at pH 4.60 using only sodium acetate, 3.00 M HCl, 3.00 M NaOH, and water. Calculate the quantities needed for each of the following steps in the buffer preparation.
1. Add sodium acetate to ~400 mL of water in a large beaker. How many grams of sodium acetate do you need? Report your answer to the nearest mg.
2. Add 3.00 M while stirring and monitor the pH with a pH electrode until the pH = 4.60. What volume of HCl or NaOH do you calculate that you will need? Ignore activity coefficients and report your answer to the nearest mL.
3. Quantitatively transfer the beaker contents to a 500 mL volumetric flask, fill to the mark with water, and mix thoroughly.
pH = pKa + log(base)/(acid)
4.60 = 4.74+ log b/a
b/a = about 0.7 but that's approximate and you need to do it better than that.
You want the buffer to be 0.3M in acetate which means
a + b = 0.3
Solve the two equations simultaneously to obtain a and b. I obtained about 0.2M for (a) and about 0.1M for (b).
Since you want only 500 mL of the buffer, divide those numbers by 2 to obtain mol.
For #1, mols b x molar mass NaC2H3O2 = grams sodium acetate.
for #2, M = moles HCl/L HCl. You know moles and M, solve for L and convert to mL.
To calculate the quantities needed for each step in the buffer preparation, we can follow these steps:
1. Calculating the quantity of sodium acetate needed:
- We are preparing a 500 mL buffer solution, so we need to find the moles of sodium acetate required to achieve a concentration of 0.300 M.
- The formula weight of sodium acetate is 82.03 g/mol.
- Using the formula: moles = concentration × volume, we can rearrange it to calculate the mass of sodium acetate: mass = moles × formula weight.
- The moles of sodium acetate required will be: moles = concentration × volume = 0.300 M × 0.500 L = 0.150 moles.
- The mass of sodium acetate needed will be: mass = 0.150 moles × 82.03 g/mol = 12.30 g (rounded to the nearest mg).
- Therefore, you will need approximately 12.30 grams of sodium acetate.
2. Calculating the volume of 3.00 M HCl or NaOH needed:
- Since we want to adjust the pH to 4.60, we can either add HCl or NaOH depending on the starting pH.
- If the starting pH is higher than 4.60, we need to use HCl to lower the pH, and if it is lower, we will use NaOH to increase the pH.
- To calculate the volume required, we need to determine the change in pH and the amount of HCl or NaOH required to achieve that change.
- The Henderson-Hasselbalch equation can be used: pH = pKa + log(base/acid), where base represents the concentration of sodium acetate and acid is the concentration of acetic acid.
- The pKa of acetic acid is 4.75. Let's assume the starting pH is 3.00 (lower than 4.60).
- We need to increase the pH by 4.60 - 3.00 = 1.60 units.
- From the Henderson-Hasselbalch equation, we can rearrange it to calculate the ratio of base to acid: base/acid = 10^(pH - pKa).
- The required ratio of base to acid will be: base/acid = 10^(4.60 - 4.75) = 0.316.
- Since the concentration of acetic acid is the same as sodium acetate (0.300 M), to achieve a ratio of 0.316, we need the concentration of sodium acetate to be 0.316 M.
- The change in sodium acetate concentration will be: 0.316 M - 0.300 M = 0.016 M.
- Using the formula: moles = concentration × volume, and rearranging to calculate the volume: volume = moles / concentration, we can calculate the volume needed.
- The moles of sodium acetate required will be: moles = concentration × volume = 0.016 M × 0.500 L = 0.008 moles.
- Since the concentration of the HCl or NaOH solution is 3.00 M, we can calculate the volume required: volume = moles / concentration = 0.008 moles / 3.00 M = 0.0026 L.
- Converting the volume from liters to milliliters: volume = 0.0026 L × 1000 mL/L = 2.6 mL (rounded to the nearest mL).
- Therefore, you will need approximately 2.6 mL of 3.00 M HCl or NaOH to adjust the pH to 4.60.
3. Quantitatively transferring the beaker contents to a 500 mL volumetric flask:
- After adding sodium acetate to ~400 mL of water, you need to transfer the contents to a 500 mL volumetric flask and fill it to the mark with water.
- The initial volume before transferring the contents to the volumetric flask is approximately 400 mL.
- When transferring, make sure to rinse the beaker with water to ensure you transfer all the contents.
- After transferring, fill the volumetric flask to the mark with water, ensuring the bottom of the meniscus is precisely on the mark.
- Finally, mix the solution thoroughly by gently swirling or inverting the flask several times.
By following these steps, you can prepare a 500 mL acetate buffer at a pH of 4.60 using the given chemicals and quantities.
To calculate the quantities needed for each step in the buffer preparation, we will use the following information:
Molar mass of sodium acetate (CH3COONa) = 82.03 g/mol
Desired final volume = 500 mL
Step 1: Add sodium acetate to ~400 mL of water in a large beaker.
To calculate the quantity of sodium acetate needed, we can use the following equation:
moles = (Molarity × Volume) / 1000
Given:
Molarity = 0.300 M
Volume = 400 mL = 0.400 L
Substituting the values into the equation:
moles = (0.300 M × 0.400 L) / 1000
moles = 0.120
To obtain the mass in grams, we multiply the number of moles by the molar mass:
mass = moles × molar mass
mass = 0.120 mol × 82.03 g/mol
mass = 9.84 g
Therefore, you would need approximately 9.84 grams of sodium acetate.
Step 2: Add 3.00 M HCl or NaOH while stirring until the pH = 4.60.
To determine the volume of either HCl or NaOH needed, we need to calculate the number of moles required to adjust the pH.
Using the equation:
moles = Molarity × Volume
Given:
Molarity = 3.00 M
Desired pH = 4.60
We don't know the volume, so we'll label it as "V" mL.
moles = (3.00 M × V ml) / 1000
moles = 0.003 V
Since NaOH and HCl react in a 1:1 ratio with acetate ions, the number of moles of NaOH or HCl needed will be equal to the number of moles of acetate ions present in the solution.
For example, since the initial acetate concentration is 0.300 M and the final volume is 500 mL:
moles (acetate ions) = 0.300 M × (500 mL / 1000)
moles (acetate ions) = 0.150
Now we can set up an equation using the balanced chemical equation and the known concentrations:
moles (acetate ions) = moles (NaOH or HCl)
0.150 = 0.003 V
V = 0.150 / 0.003
V ≈ 50 mL
Therefore, you would need approximately 50 mL of either 3.00 M HCl or 3.00 M NaOH to adjust the pH to 4.60.
Step 3: Quantitatively transfer the beaker contents to a 500 mL volumetric flask, fill to the mark with water, and mix thoroughly.
After adding the sodium acetate and adjusting the pH, you need to transfer the solution to a 500 mL volumetric flask.
Since the solution is already in a beaker with a volume close to 400 mL, you can directly transfer the solution to the flask. Then, fill the flask to the mark with water. Ensure thorough mixing to distribute the components evenly throughout the solution.
No specific quantities are given for this step, as it depends on the volumes used in the previous steps.