A healthy adult has 135 mM sodium chloride in 6.0 L of blood. Severe symptoms of

Question

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

Explanation / Answer

a)

Osmotic P = i*M*R*T

OP = 2*(100*10^-3)(0.082)(37+273) = 5.084 atm

so the Osmotic pressure must be 5.084 atm in blood

b)

Calculate...

DP = rho*g*H

where H is height of colume of water

so

5.084 atm = 1000 kg/m3 * 9.8 m/s^2 * H

change 5.084atm --> 5.084*101325 Pa = 515136.3 Pa

so

515136.3= 1000*9.8 * h

h = 515136.3/1000/9.8

H = 52.564 meters under water

c)

Tf = -2°C

OSM P for blod at 37°C

find... molality

dTF = -Kf*m

-2 = -1.86*m*2

m = (2/1.86/2) = 0.53763440 mol of ions / kg blood

assume 1 kg of blood --> 1 Liter of blood

so

Molarity = 0.53763440 M

P = i*M*RT

P = 2*0.53763440*0.082*(310) = 27.333 atm

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