c) Now make up 500 mL of a 0.025M phosphate buffer using the 0.1M phosphate buffer. Show all your workings. The 0.1M is made of 120.1ml conjugate base and 379.9ml acid.
To make 500 mL of a 0.025M phosphate buffer using the 0.1M phosphate buffer, we need to calculate the volume of the 0.1M conjugate base and acid required to achieve the desired concentration.
Step 1: Convert the concentrations to moles.
Given:
0.1M phosphate buffer = 120.1 mL conjugate base + 379.9 mL acid
We can calculate the number of moles of the conjugate base and acid using their respective molarities (M) and volumes (V) in liters (L):
Moles of conjugate base = Molarity × Volume (in L)
Moles of conjugate base = 0.1 mol/L × 0.1201 L (convert mL to L)
Moles of conjugate base = 0.01201 mol
Moles of acid = Molarity × Volume (in L)
Moles of acid = 0.1 mol/L × 0.3799 L (convert mL to L)
Moles of acid = 0.03799 mol
Step 2: Determine the desired moles for the 0.025M phosphate buffer.
To make a 0.025M phosphate buffer, the moles of conjugate base and acid should be adjusted. The ratio of moles of conjugate base to acid should be 1 to 1, as it creates a buffer with equal concentrations of the conjugate acid and conjugate base.
Therefore, we need to calculate the adjustment factor:
Adjustment factor = Desired moles / Starting moles
Desired moles = Final molarity × Final volume (in L)
Desired moles = 0.025 mol/L × 0.5 L (convert mL to L)
Desired moles = 0.0125 mol
Conjugate base adjustment factor = Desired moles / Starting moles
Conjugate base adjustment factor = 0.0125 mol / 0.01201 mol
Conjugate base adjustment factor ≈ 1.04
Acid adjustment factor = Desired moles / Starting moles
Acid adjustment factor = 0.0125 mol / 0.03799 mol
Acid adjustment factor ≈ 0.33
Step 3: Calculate the volumes required.
To determine the volumes required for the 0.025M phosphate buffer, we multiply the adjustment factors with the starting volumes.
Volume of conjugate base required = Conjugate base adjustment factor × Starting volume of conjugate base
Volume of conjugate base required = 1.04 × 120.1 mL
Volume of conjugate base required ≈ 124.85 mL
Volume of acid required = Acid adjustment factor × Starting volume of acid
Volume of acid required = 0.33 × 379.9 mL
Volume of acid required ≈ 125.37 mL
Therefore, to make 500 mL of a 0.025M phosphate buffer, you need to add approximately 124.85 mL of the 0.1M conjugate base and 125.37 mL of the 0.1M acid to a total volume of 500 mL.
To make up 500 mL of a 0.025M phosphate buffer using the 0.1M phosphate buffer, you will need to calculate the volumes of the conjugate base and the acid required.
Given information:
- 0.1M phosphate buffer is made of 120.1 mL conjugate base and 379.9 mL acid.
- Target concentration: 0.025M
- Total volume required: 500 mL
Step 1: Calculate the moles of each component in the 0.1M phosphate buffer:
- Moles of conjugate base = volume (in liters) x concentration = 120.1 mL x (1 L / 1000 mL) x 0.1M
- Moles of acid = volume (in liters) x concentration = 379.9 mL x (1 L / 1000 mL) x 0.1M
Step 2: Calculate the required moles of each component for the target concentration:
- Moles of conjugate base required = target concentration x total volume (in liters) = 0.025M x (500 mL / 1000 mL)
Step 3: Determine the volumes of the conjugate base and the acid required based on their moles:
- Volume of conjugate base required = Moles of conjugate base required / concentration of conjugate base = (0.025M x 500 mL / 1000 mL) / 0.1M
- Volume of acid required = Moles of acid required / concentration of acid = (0.025M x 500 mL / 1000 mL) / 0.1M
Step 4: Convert the volumes from liters to milliliters for the required volumes:
- Volume of conjugate base required (in mL) = Volume of conjugate base required (in L) x 1000 mL / 1 mL
- Volume of acid required (in mL) = Volume of acid required (in L) x 1000 mL / 1 mL
After performing the calculations, you will have the volumes of the conjugate base and the acid required to make up the desired 0.025M phosphate buffer in 500 mL.