Entropy of mixing? EK1001 Q46

[MCATMadness]

hexane is infinitely soluble in octane due the increase in entropy. Can someone explain the basics of the entropy of mixing? and why there is an increase in S to make this mixture more favorable than an octane-octane or hexane-hexane soln?

ek 1001 gchem question 448

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[loveoforganic]

Entropy is a thing that's hard to explain/define, but makes kind of logical sense. It can be looked at as a measure of the randomness of a system.

Say you have 3 red gas molecules (R) and 3 blue gas molecules (b) in two containers separated by an infinitely short pipe.

Those gas molecules can exist in any of several states

..... A...|..B..|..C...|..D...|..E...|..F...|...G..|..H..|

1 - RRR | RBB | BRB | BBR | RRB | RBR | BRR | BBB |

2 - BBB | RRB | RBR | BRR | RBB | BRB | BBR | RRR |

So there's one state with 3 reds in 1 and 3 blues in 2, one state with 3 reds in 2 and 2 blues in 1, 3 states with 2 reds 1 blue in 1 and 2 blues 1 red in 2, and 3 states with 2 reds 1 blue in 2 and 2 blues 1 red in 1.

1
3
3
1

More random states have more possible ways of having that state, and thus they're more likely.

The same principle applies with solutions.

A note though is that in some cases, the solvation of a salt can actually be unfavorable entropically (even though you're essentially going from one particle to two) because of the solvation shell that forms around the ions (think extensive hydrogen bonding networks forming a cage around an ion).

 

[MCATMadness]

Entropy is a thing that's hard to explain/define, but makes kind of logical sense. It can be looked at as a measure of the randomness of a system.

Say you have 3 red gas molecules (R) and 3 blue gas molecules (b) in two containers separated by an infinitely short pipe.

Those gas molecules can exist in any of several states

..... A...|..B..|..C...|..D...|..E...|..F...|...G..|..H..|

1 - RRR | RBB | BRB | BBR | RRB | RBR | BRR | BBB |

2 - BBB | RRB | RBR | BRR | RBB | BRB | BBR | RRR |

So there's one state with 3 reds in 1 and 3 blues in 2, one state with 3 reds in 2 and 2 blues in 1, 3 states with 2 reds 1 blue in 1 and 2 blues 1 red in 2, and 3 states with 2 reds 1 blue in 2 and 2 blues 1 red in 1.

1
3
3
1

More random states have more possible ways of having that state, and thus they're more likely.

The same principle applies with solutions.

A note though is that in some cases, the solvation of a salt can actually be unfavorable entropically (even though you're essentially going from one particle to two) because of the solvation shell that forms around the ions (think extensive hydrogen bonding networks forming a cage around an ion).

great explanation! thank you so much!