Approach the component reactions as you would in a Hess' law calculation by manipulating them to sum into the equilibrium reaction.
the reaction...
Hb + O2 -> HbO2
...needs to be reversed so that HbO2 is on the reactants side (as it is in the equilibrium equation), which looks something like...
HbO2 -> Hb + O2
Recall that the value for deltaG also needs to be reversed, so our new value for deltaG = (+)70kJ/mol
The other component reaction (Hgb + CO -> HgbCO) already conforms to the equilibrium reaction, so no further reaction manipulation needs to be done.
We can now sum the component reactions (and their respective deltaG values) to the equilibrium reaction and its deltaGrxn value.
Hb02 -> Hb + O2 (deltaG = 70kJ/mol)
Hb + CO -> HbCO (deltaG = -80kJ/mol}
By adding the reactants and products of the reactions together, we get...
HbO2 + Hb + CO -> Hb + O2 + HbCO
...with a deltaG value of (70kJ/mol + (-80kJ/mol) = -10kJ/mol
Canceling out Hb gives us...
HbO2 + CO -> HbCO + O2 (deltaGrxn = -10kj/mol)
...our target reaction.
The equilibrium constant K can then be calculated by using the following formula
deltaGrxn = -RT ln K
where R is the universal gas constant and T is the temperature in units of Kelvin.
Now for a bit of step-by-step algebraic manipulation to isolate K
Dividing each side of the equation by (-RT) gives us...
deltaGrxn / -RT = ln K
To get rid of the natural logarithm, we take the inverse natural logarithm (e^x) of both sides, which gives us...
e^(deltaGrxn / -RT) = K
Now to plug in and solve, all the while being mindful of our units
K = e^(-10kJ/mol / (-8.314J/mol*K * 298K * 1kJ/1000J))
It's kind of nasty looking in text, so to be clear, we're dividing our deltaG value (-10kJ/mol) by the product of the gas constant, the temperature (298K), and the conversion factor from J to kJ (1kJ/1000J) so that the units agree. If executed properly, all of our units cancel out for a unitless exponent value, as it should be.
Hopefully, for x, you get something like 4.0362
Using our calculator, we plug our newly attained value of x into e^x and get something like 56.6114
Taking into account significant figures, your answer will be K = 60.
Hope that helps! :D
Carbon monoxide is toxic because it bonds much more strongly to the iron in hemoglobin (Hgb) than does O2. Consider the following reactions and approximate free energy changes:
Hgb + O2 ---> HgbO2 ∆G⁰ = -70 kJ
Hgb + CO ---> HgbCO ∆G⁰ = -80 kJ
Using these data, estimate the equilibrium constant value at 25⁰C for the following reaction:
HgbO2 + CO ---> HgbCO + O2
1 answer
2 answers