Solving Number of Molecules for Entropy of 1.181x10^-12 J/K

[samueltak]

Homework Statement

Suppose a compound could point in any two directions in the solid and still have the same energy. How many molecules would there be if the total entropy of a solid sample of this compound was 1.181x10^-12 J/K?

Homework Equations

My plan that failed -

S = k*ln(W),
where S is entropy
k is Boltzmann constant = 1.38 x 10-23 (J/K) or equivalent to (Universal Gas Constant 8.314/Avogadro's number 6.02 x 1023 molecules/mol)
W is the number of microstates

The Attempt at a Solution

1.181x10^-12 J/K = (8.314/ x 6.02*1023)*(ln(2)), I put 2 in ln(2) because I thought the question stated the total microstates when it said "...point in any two directions".

I solved for x and got 3.242e13 which is wrong.

 

[Redbelly98]

Welcome to Physics Forums.

It would be 2 microstates if there were just 1 molecule. With many molecules, there are many many possible combinations of their orientations.

Treat W as an unknown, and solve for it. Once you have W, the final step will be to figure out how many molecules.