Henry\'s Law (Thermo application) Our blood carries more oxygen per volume than

Question

Henry's Law (Thermo application)

Our blood carries more oxygen per volume than would be expected based on Henry's law. This extra capacity is due to hemoglobin, and typically is 9.4 mM oxygen (0.0094 mol O_2 per L blood). Let's examine how this compares with Henry's law. At 310 K the Henry's law constant for O_2 is 5.21 Times 10^9 Pa. A typical value of the partial pressure of oxygen in arteries is around 87 mm Hg = 11,600 Pa. For this pressure, what mole fraction of oxygen would Henry's law indicate should appear in human blood? How many moles per liter of water? Our blood carries times more oxygen than water would, due to hemoglobin. 0.45 213 3.41 8.6 76

Explanation / Answer

Given Henry's constant, KH = 5.21x109 Pa

Partial pressure of oxygen, P = 11600 Pa

Applying Henry's law

KH = P / X , where 'X' is mole fraction of oxygen.

=> 5.21x109 Pa = 11600 Pa / X

=> X = 11600 Pa / 5.21x109 Pa

=> X = 2.23x10-6

Hence mole fraction of oxygen is 2.23x10-6 (answer)

concentration of oxygen, C = X x (density of H2O / molar mass of H2O)

=> C = 2.23x10-6 x (1000 g.L-1 / 18 g.mol-1) = 1.24x10-4 moles O2 per Litre water (answer)

Hence calculated concentration of O2, C(calculated) =  1.24x10-4 M

Given the actual concentration of O2, C(actual) = 9.4 mM = 9.4x10-3 M

Hence fraction of more oxygen in blood = C(actual) / C(calculated) =  9.4x10-3 M / 1.24x10-4 M

= 76 (answer)

Hence option (e) is correct

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