how would you prepare 250 mL solution containing the following: 0.30 M mannitol, 0.025 M phosphate buffer pH 7.5? You are given solid mannitol, kh2po4, and k2hpo4. (pKa=6.86)
I assume this means you want a phosphate buffer of pH = 7.5 containing 0.3M mannitol. So the mannitol part is to weigh out 0.3 mol mannitol/L or you will want 0.3/4 mols for the 250 mL. Then grams mannitol = mols mannitol x molar mass mannitol. Place that in a 250 mL volumetric flask.
For the phosphate buffer you solve two equation simultaneously.
Here is equation 1. The Henderson-Hasselbalch equation is
7.5 = pKa2 + log base/acid
Solve for base/acid ratio, then
base = approx 2.3 so
base = 2.3*acid. I like to work in millimols so that would be mmols base = mmols acid*2.3
Equation 2 =
acid + base = 0.025 x 250
Solve for acid and base millimols, then from
grams = mols x molar mass, calculate g KH2PO4 and g K2HPO4, weigh, place in the 250 mL volumetric flask and make to the mark. Mix thoroughly and stopper.
To prepare a 250 mL solution containing 0.30 M mannitol and 0.025 M phosphate buffer (pH 7.5), you will need to follow these steps:
1. Calculate the amount of mannitol needed:
- Mannitol has a molecular weight of 182.17 g/mol.
- To prepare a 0.30 M solution, you need 0.30 moles of mannitol per liter.
- So, for 250 mL (0.250 L) of solution, you will need 0.30 * 0.250 = 0.075 moles of mannitol.
- Multiply the moles by the molecular weight to get the grams needed: 0.075 * 182.17 = 13.66 grams of mannitol.
2. Prepare the mannitol solution:
- Weigh out 13.66 grams of solid mannitol using a balance.
- Dissolve the solid mannitol in a small volume of distilled water to ensure complete dissolution.
- Once dissolved, transfer the solution to a 250 mL volumetric flask.
- Add distilled water to the flask until the solution reaches the mark on the flask, leading to a final volume of 250 mL.
3. Calculate the amounts of KH2PO4 and K2HPO4 needed for the phosphate buffer:
- The pH of the buffer needs to be 7.5, and the pKa is given as 6.86.
- Using the Henderson-Hasselbalch equation: pH = pKa + log ([A-]/[HA])
- Rearrange the equation to solve for the ratio [A-]/[HA]: [A-]/[HA] = 10^(pH - pKa)
- Plugging in the values: [A-]/[HA] = 10^(7.5 - 6.86) = 3.74
- Since we want a total concentration of 0.025 M, we can assign a value of 3.74x to the concentration of KH2PO4 (in moles) and 1x to the concentration of K2HPO4 (in moles).
- Let's assume the total volume of the buffer solution will be 250 mL. Using the ratios, we can find the moles required for the two buffer components:
Moles of KH2PO4 = 3.74x
Moles of K2HPO4 = 1x
Total buffer volume in liters (V) = 0.250 L
4. Calculate the amounts of KH2PO4 and K2HPO4 needed:
- The molar mass of KH2PO4 is 136.09 g/mol, and the molar mass of K2HPO4 is 174.18 g/mol.
- Multiply the moles of each compound by its respective molar mass to get grams needed.
- For KH2PO4: 3.74x * 0.13609 g/mol = Y grams (Y is the grams required)
- For K2HPO4: 1x * 0.17418 g/mol = Z grams (Z is the grams required)
5. Prepare the phosphate buffer solution:
- Weigh out Y grams of KH2PO4 and Z grams of K2HPO4 using a balance.
- Dissolve each salt individually in a small volume of distilled water to ensure complete dissolution.
- Once dissolved, transfer both solutions to the 250 mL volumetric flask containing the mannitol solution.
- Add distilled water to the flask until the solution reaches the mark on the flask, leading to a final volume of 250 mL.
By following these steps, you will have prepared a 250 mL solution containing 0.30 M mannitol and 0.025 M phosphate buffer (pH 7.5) using solid mannitol, KH2PO4, and K2HPO4.