Suppose you have to prepare 1.00 L of the solution ( KH2 PO4 and Na2 HPO4 pH=7.31) and that this solution must be isotonic with blood (have the same osmotic pressure as blood). What mass of KH2 PO4 would you use?
b) What mass of Na2 HPO4 . 12 H2O would you use
To find the mass of KH2PO4 and Na2HPO4 · 12H2O needed to prepare the solution, we need to consider the osmotic pressure of blood and the molar masses of the compounds involved.
1. Determine the osmotic pressure of blood:
The osmotic pressure of blood is typically around 7.31 pH. However, pH alone does not give the osmotic pressure. Instead, we need to convert the pH value to osmolarity. Osmolarity refers to the total concentration of solutes in a solution.
Osmolarity can be estimated using the relationship between pH and pOH for a solution at 25°C:
pH + pOH = 14
Since the pH is given as 7.31, we can calculate the pOH:
pOH = 14 - 7.31 = 6.69
From the pOH value, we can determine the hydroxide ion concentration ([OH-]) in the solution using the equation:
[OH-] = 10^(-pOH)
[OH-] = 10^(-6.69)
Next, we need to convert the hydroxide ion concentration to osmolarity. Blood primarily contains sodium, potassium, calcium, chloride, bicarbonate, and other ions. To account for these ions, we can use an empirical conversion factor. For simplicity, we'll assume the conversion factor is 1, meaning that 1 mmol of hydroxide ions is equivalent to 1 mOsm (milliosmole).
Therefore, the osmolarity of the solution required is equal to the concentration of [OH-] in mOsm.
2. Calculate the mass of KH2PO4:
The molar mass of KH2PO4 is:
K (39.10 g/mol) + H2 (2.02 g/mol) + P (30.97 g/mol) + O4 (4×16.00 g/mol)
Add up the molar masses to find the total molar mass of KH2PO4.
Next, we need to calculate the number of moles of KH2PO4 required to achieve the desired osmolarity. This can be done using the equation:
Number of moles = Osmolarity (mOsm) / Molar mass (g/mol)
Multiply the number of moles by the molar mass of KH2PO4 to find the mass of KH2PO4 to use.
3. Calculate the mass of Na2HPO4 · 12H2O:
The molar mass of Na2HPO4 · 12H2O is:
Na (2×22.99 g/mol) + H (3×1.01 g/mol) + P (30.97 g/mol) + O (4×16.00 g/mol) + 12H2O (12×18.02 g/mol)
Add up the molar masses to find the total molar mass of Na2HPO4 · 12H2O.
Next, calculate the number of moles of Na2HPO4 · 12H2O required to achieve the desired osmolarity using the same equation as before.
Multiply the number of moles by the molar mass of Na2HPO4 · 12H2O to find the mass of Na2HPO4 · 12H2O to use.
By following these steps, you can determine the mass of KH2PO4 and Na2HPO4 · 12H2O required to prepare the isotonic solution.