Question

If a person drinks a large amount of water very quickly, it is possible to exceed the rate of water removal by the kidney (~1 L/hour), essentially diluting the blood. The resulting osmotic pressure causes cells to swell. Fat and muscle cells have a capacity to adjust to this change in volume, but neurons in the brain do not have room to accommodate this size increase. (The skull is so densely packed, there is no room for swelling!) Consequently, as water enters neuronal cells, pressure is exerted on the brain, causing headache, fatigue, mental disorientation, and in severe cases, loss of consciousness and death. A healthy adult has 135 mM sodium chloride in 6.0 L of blood. Severe symptoms of water intoxication manifest when sodium concentrations are 100. mM and lower.

a) Assuming that the blood of a normally hydrated person is isotonic with cells (i.e. same osmotic pressure inside and outside), what is the osmotic pressure that is generated under conditions of severe water intoxication? (Body temperature is 37^o C.)

b) To get an idea of how much pressure that is being imposed on the brain, calculate how far underwater you would have to descend to experience this amount of pressure. (The density of water is 1.0 kg/L.)

c) The freezing point of normal human blood is -2.0^o C. Based on this value, what is the osmotic pressure of blood at 37^o C? (Food for thought: how can we handle such a high osmotic pressure in the blood?)

Answer 1

a) the intial concentration = 135mM volume of blood is 6L

under severe water intoxication the concentration = 100mM

Pressure = concentration X R X T

T = 37⁰C = 310 Kelvin

Pressure = 0.1 Molar X 0.0821 X 310

Pressure = 2.55 atmosphere

b) Density of water = 1Kg / L

Pressure = h X density X gravity

Pressure due to atmosphere = 1atm

1.55 = height X 1 Kg /m^3 X 9.8 m/sec^2

Height = 15.8 m

c) the freezing point = -2 ⁰C

concentration in molality = depression in freezing point / Kf

concentration in molality = 2 / 3.86 = 0.518 moles / Kg = moles / Litre of solvent [almost 0.518 molar]

Osomotic pressure = concentration X R X T

osmotic pressure = 0.518 X 0.0821 X 310 = 13.18 atm