1. If a solution contains 10.5 g of sucrose (C12H22O11) per 100. mL, what is its osmotic pressure at 25 oC. What concentration (in g/100. mL solution) of salt (NaCl) would exhibit the same osmotic pressure. (Assume NaCl dissociates completely.)
2. A 50.0 mL sample of an aqueous solution containing 1.08 g of human serum albumin (HSA) has an osmotic pressure of 5.85 mmHg at 298 K. Calculate the molar mass of HSA.
2. A 50.0 mL sample of an aqueous solution containing 1.08 g of human serum albumin (HSA) has an osmotic pressure of 5.85 mmHg at 298 K. Calculate the molar mass of HSA.
Answers & Comments
Answer & Explanation:
1. To solve for the osmotic pressure of the sucrose solution, we first need to calculate the molar concentration of sucrose:
molar mass of C12H22O11 = 12(12.01) + 22(1.01) + 11(16.00) = 342.30 g/mol
moles of sucrose = 10.5 g / 342.30 g/mol = 0.0307 mol
volume of solution = 100. mL = 0.100 L
molarity of sucrose = 0.0307 mol / 0.100 L = 0.307 M
The osmotic pressure (π) of a solution can be calculated using the van't Hoff equation:
π = MRTi
where M is the molar concentration of solute, R is the gas constant (0.0821 L·atm/mol·K), T is the temperature in Kelvin, and i is the van't Hoff factor, which is the number of particles the solute dissociates into in solution. For sucrose, i = 1 because it does not dissociate.
π(sucrose) = (0.307 mol/L) x (0.0821 L·atm/mol·K) x (298 K) x (1) = 7.67 atm
To calculate the concentration of NaCl that would exhibit the same osmotic pressure, we can use the formula:
π = MRTi
π(NaCl) = π(sucrose)
M(NaCl) = π(sucrose) / (RT)i(NaCl)
The van't Hoff factor for NaCl is 2, since it dissociates into 2 ions in solution.
M(NaCl) = (7.67 atm) / [(0.0821 L·atm/mol·K) x (298 K) x (2)] = 0.123 M
So the concentration of NaCl that would exhibit the same osmotic pressure as the sucrose solution is 0.123 g/100 mL.
2. First, we need to convert the volume from milliliters to liters:
50.0 mL = 0.0500 L
Next, we can use the van't Hoff equation:
Π = MRT
where Π is the osmotic pressure, M is the molarity, R is the gas constant (0.08206 L·atm/(mol·K)), and T is the temperature in kelvin. We can solve for the molarity:
M = Π / RT
M = (5.85 mmHg / 760 mmHg/atm) / (0.08206 L·atm/(mol·K) * 298 K)
M = 0.00202 M
Finally, we can use the definition of molarity to calculate the moles of HSA:
moles = M * volume
moles = 0.00202 mol/L * 0.0500 L
moles = 0.000101 mol
And we can calculate the molar mass of HSA:
molar mass = mass / moles
molar mass = 1.08 g / 0.000101 mol
molar mass = 10,693.1 g/mol
Therefore, the molar mass of HSA is approximately 10,693.1 g/mol.
PA BRAINLIEST