Question

What is the change of entropy for the following reactions?
a. 100 pennies are changed from all heads to all tails.
b. 100 pennies are changed from all heads to 50 heads plus
50 tails.
c. 1 mol of heads is mixed with 1 mol of tails to give 2 mol
of half heads and half tails.

Answer 1

a) The number of ways that you can arrange 100 pennies, all heads up is 1. Likewise, the number of ways to arrange 100 pennies all tails up is 1.

So S_100up = kBln(1) = 0 and S_100dn = kBln(1) = 0.

Thus ΔS = S100dn - S100up = 0 – 0 = 0.

b) The number of ways of arranging 100 pennies with 50 heads up and 50 tails up

t = N!/Nh₁ x Nt! whete N! = factorial of N

N = 100

Nh = 50 and Nt = 50

t = 100!/50! x 50!

= 1.01 x 10²⁹

we already know that

S_100up = kBln(1) = 0

S50/50 = kBln(1.01×10²⁹) = 66.78kB

S50/50 = (66.78)(1.38×10^-23 J/K)

S 50/50 = 9.22 × 10^-22 J/K.

The change is entropy is ΔS = S50/50 - S100up = 9.22 × 10^-22 J/K – 0 = 9.22 × 10^-22 J/K.

c) To do this calculation for 1 moles we will need to compute

t = 2NA!/N! x N! wher2 2NA! = 2 x 6.023 x 10²³! which cannot be computed so we wil stop here.