the freezing point of blood serum is about -0.56 deg C. What is the osmotic pressure at 37 deg C?
i don't knw
delta T = Kf*m
Solve for m
In dilute solutions m and M are almost th same, Substitute m for M in
pi = MRT and solve for pi.
To determine the osmotic pressure at 37 degrees Celsius, we need to consider the freezing point depression equation. The freezing point depression (∆Tf) is related to the molality of the solute (m), the molal freezing point depression constant (Kf), and the number of particles dissociated in the solution (i).
The equation can be written as: ∆Tf = Kf * m * i
Since blood serum is a complex mixture, we can assume it behaves ideally as an electrolyte solution. For electrolytes, i represents the number of particles produced by the solute when it dissolves. For example, table salt (NaCl) dissociates into two ions (Na+ and Cl-) when dissolved in water, so i is 2.
Given that the freezing point of blood serum is -0.56 degrees Celsius (∆Tf), and assuming the molal freezing point depression constant (Kf) is 1.86 °C⋅kg/mol, we can calculate the molality (m).
∆Tf = Kf * m * i
-0.56 = 1.86 * m * i
Since blood serum doesn't dissociate into ions like a typical electrolyte, we assume i = 1.
-0.56 = 1.86 * m
Now, let's solve for m, which represents the molality of the blood serum solution:
m = -0.56 / (1.86)
m ≈ -0.301 mol/kg
Now that we have the molality, we can calculate the osmotic pressure (π) using the following formula:
π = m * R * T
Where:
- R is the ideal gas constant (0.0821 L⋅atm/(mol⋅K))
- T is the temperature in Kelvin (37 + 273.15)
π = (-0.301) * (0.0821) * (37 + 273.15)
π ≈ -6.7 atm