Calculate the Distribution of Butane Conformations at a Particular Temperature
Assume that we have now an equilibrium combination of the gauche and anti conformations at 25°C (298 Okay).
gauche⇋anti
Okay= [anti ] [ gauche]
To calculate the worth of Okay, we’ll use the following equation.
Okay=e −G RT
∆G can be calculated utilizing ∆G=∆H-T∆S
∆H is the distinction in potential power between the anti and gauche conformations. At 25˚C, this worth is -Three.eight kJ/mol.
Whereas it’d seem that there is no such thing as a entropy change on this course of, ∆S is just not equal to zero. There are two potential gauche conformations with the identical potential power, whereas there is just one potential anti conformation. Thus there exists extra potential microstates for the gauche conformation than for the anti. To calculate the worth of ∆S, we’ll use the following equation.
∆S=RlnWanti-RlnWgauche
R is the fuel fixed (eight.31 J/mol Okay) W is the quantity of potential microstates for every conformation
Thus for butane: ∆S=Rln1 – Rln2
=Zero-(eight.31 J/mol Okay x ln2) =5.76 J/mol Okay
Now again to ∆G
∆G = -Three.8×103 J/mol Okay – (298Okay x -5.76 J/mol Okay) =-2100 J/mol
Returning to the calculation of Okay
Okay=e 2100 J /mol
eight.31J /mol Okay×298Okay
Okay=2.Three To calculate the p.c anti conformation current at 298Okay, we recall that the worth of Okay is that this course of is basically the ratio of anti:gauche
Thus, since the ratio is 2.Three:1.Zero, the proportion could be calculated as follows.
2.Three 2.Three1.Zero
×100
= 70% (anti)
