Question

Two large glass bulbs of identical volume are connected by means of a stopcock. One bulb initially contains$\mathbf{1}\mathbf{.00}\mathbf{}\mathbf{\text{mol}}$${\mathbf{\text{H}}}_{\mathbf{2}}$; the other contains$\mathbf{1}\mathbf{.00}\mathbf{}\mathbf{\text{mol}}$helium ($\mathit{H}\mathit{e}$). The stopcock is opened and the gases are allowed to mix and reach equilibrium. What is the probability that all the${\mathbf{\text{H}}}_{\mathbf{2}}$in the first bulb will diffuse into the second bulb and all thegas in the second bulb will diffuse into the first bulb?

Short answer

The total probability for the interchange of gases from one bulb to other when connected is${10}^{-3.6*{10}^{23}}$

Step-by-step solution

Given information

The number of moles of ${\text{H}}_2$is $1.00\text{mol}$and the number of moles of helium is$1.00\text{mol}$ .

Concept of probability

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

In addition to being expressed as percentages ranging from to, probabilities can alsobe expressed as proportions.

Calculate the probability

The volume increases from V to 2V when the bulbs are connected. The probability to find a single${\mathrm{H}}_2$in the other bulb is$=1/2$(selecting one out of the two bulbs present).

The probability to find the whole mole$\left(6^{*}{10}^{23}\right)$in the other bulb.$=1/2^{6*{10}^{23}}$

The probability to find a singlemolecule in the other bulb is$=1/2$

(Selected one out of the two bulbs are sent).

The probability to find the whole mole$\left(6^{*}{10}^{23}\right)$in the other bulb.$=1/2^{6*{10}^{23}}$

Now, the total probability for the interchange of gases from one bulb to other when connected.

Probability$=1/2^{6*{10}^{23}}+1/2^{6*{10}^{23}}$

Probability$={10}^{-3.6*{10}^{23}}$