Question

What is the probability that 100 ideal gas particles will spontaneously contract their volume by 0.1%? What about 1000 ideal gas particles? How many molecules do you need to consider before the probability of contraction becomes less than 1%. Do you ever expect a mole of ideal gas particles to undergo a spontaneous contraction in volume?

Answer 1

Pprobability is proportional to the volume raised to the number of molecules, that is, W V^N.

Volume contraction is a decrease in the volume of body fluid, including the dissolved substances that maintain osmotic balance (osmolytes).

1) W = V^N = (0.1)¹⁰⁰ = 1*10^-100

2) Similarly, if N = 1000 than W = (0.1)¹⁰⁰⁰= 0

3) 1 = (0.1)^N ====> N = 1/0.1 = 10

4) 1 mol = 6.023*10²³

W = V^N = (0.1)^{6.023*10^23} = 0 (No, a mole of ideal gas particles donot undergo a spontaneous contraction in volume)