Please help with this problem Divers get the bends when bubbles of N2 gas form i
ID: 940309 • Letter: P
Question
Please help with this problem
Divers get the bends when bubbles of N2 gas form in their blood stream if they rise too rapidly from a deep dive. Calculate the solubility (mol/L) of N2 in water (this roughly equals to its value in blood) at a depth of 300 ft below the ocean surface and at sea level. Divers have about 3.2 L of blood. How much volume of N2 gas, measured at 37C and 1 atm., is trapped in a diver's blood at 300ft? (Hint: Use the density of water to calculate the pressure at this depth) The Henry's law contant for N2 gas is 9.04•10^4 bar at 298 K.
Explanation / Answer
Henry's law constant k = 9.04 x10^-4 mol/ l-atm
Henry's law: C = K x P
Mole fraction of N2 in air is 78.09 %.
So the partial pressure of nitrogen at 300 ft . depth will be
PN2 = 0.7809*(1 + 300*1000*9.8*0.3048/1.01325*10^5) atm
= 7.687 atm
Concentration c = 9.04 x 10^-4 x 7.687
= 6.95 x 10^-3M
Moles of nitrogen = concentration x volume
= 6.95 x 10^-3 x 3.2
= 0.0222 moles
to calculate volume
R = 0.0821 L-atm/mol.K
Volume V = n R T/P
=0.0222 x 0.0821x (273+37) / 7.687
= 0.074 L
volume of N2 gas = 0.074 L