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In a vastly simplified view of human metabolism

In a vastly simplified view of human metabolism, we can assume that the body is deriving energy primarily from the following two reactions that are happening at the same time: 

1- C15H31COOH + 23O2 -> 16CO2 + 16 H2O 

2- C6H12O6 + 6O2-> 6 CO2 + 6H2O 

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The first reaction more or less corresponds to "burning fat" while the second one corresponds to "burning sugar." 


In a metabolic experiment, an individual running on a treadmill is fitted with a mask delivering air and analyzing exhaled gas. Fresh air is delivered to the individual at a rate of 10 L/min, and is assumed to contain 77.4% N2, 20.6% O, and 2.0% H20 only. The exhaled gas steady-state composition is measured to be 15.1% 02, 3.7% CO2, 6.2% H20, and 75.0% N2. 


a) Calculate the rate of production of CO2 and the rate of consumption of O2 in L/min. Using the ideal gas law, calculate the corresponding rates in moles/min assuming that the temperature of all gases is 25°C and the total pressure is 1 atm at time of measurement. Note: ideal gas constant = 0.08205 L atm mol-1K-1 

b) Using the information from part (a), calculate the rate of palmitic acid oxidation (due to reaction 1) and the rate of glucose oxidation (due to reaction 2). 

c) What is the fractional conversion of oxygen due palmitic acid oxidation and due to glucose oxidation, respectively? 

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Answer #1

a) The rate of production of CO2 is

The rate of consumption of O2 is

The rate of production of CO2 in mol/min is

The rate of consumption of O2 is

b) Let x mol/min be the rate of palmitic acid oxidation and y mol/min be the rate of glucose oxidation.

The rate of formation of CO2 due to oxidation of palmitic acid and glucose are 16x and 6y respectively.

The rate of consumption of O2 during oxidation of palmitic acid and glucose are 23x and 6y respectively.

......(1)

......(2)

Substract first equation from second equation.

Hence, the rate of palmitic acid oxidation is 0.00106 mol/min.

Substitute the value of x in equation (1)

The rate of oxidation of glucose is 0.000302 mol/min.

c) The fractional conversion of oxygen due to palmitic acid oxidation is

The fractional conversion of oxygen due to glucose oxidation is

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