The freezing point of a sample of abnormal blood was found to be -0.402 degree celsius. Estimate its osmotic pressure at 37 degree celsius. Kf(water)=1.86
To estimate the osmotic pressure of a sample of abnormal blood at 37 degrees Celsius, you can use the equation:
π = i * M * R * T
Where:
- π represents the osmotic pressure
- i represents the vant Hoff factor, which is the number of particles the solute dissociates into (assume it to be 1 for simplicity in this case)
- M represents the molarity of the solute
- R represents the ideal gas constant (0.0821 L·atm/(mol·K))
- T represents the temperature in Kelvin
To convert Celsius to Kelvin, use the formula: K = °C + 273.15
First, convert the given freezing point (-0.402 °C) to Kelvin:
T = -0.402 + 273.15 = 272.748 K
Next, we can calculate the osmotic pressure at 37 °C (310 K).
Given:
Kf (freezing point depression constant for water) = 1.86 (°C·kg/mol)
We can use the relationship between freezing point depression and osmotic pressure:
ΔT = Kf * m
Where:
- ΔT is the change in temperature from the normal freezing point of pure water (0 °C)
- m is the molality of the solute (moles of solute per kilogram of solvent)
Rearranging the equation, we get:
m = ΔT / Kf
Substituting the values:
m = (-0.402) / 1.86 = -0.216 mol/kg
Now, we can calculate the osmotic pressure using the equation mentioned at the beginning:
π = i * M * R * T
Assuming i = 1 (as mentioned earlier) and let's assume the molarity of blood to be equal to its molality (-0.216 M).
Substituting the values:
π = (1) * (-0.216) * (0.0821) * (310)
π = -5.864 atm
The osmotic pressure of the abnormal blood sample at 37 °C is approximately -5.864 atm. Note that osmotic pressure is typically reported in positive values, so it would be 5.864 atm.