Physical Chemistry , 1st ed.

17.2 for an example of how to use this formula.) For a well-behaved probabil- ity function, the summation of all probabilities, ...

This is the probability function for the velocities of gas molecules in three dimensions. If we want to focus on the scalarpart ...

Now that the probability distribution function has been found, different “average” speeds can be defined. For example, each plot ...

Again, this integral can be evaluated using the integral table in Appendix 1. We find that v  8 k m T  1/2   8 R M T  1/2 ...

this plot should point out is that there is no single useful definition of an “average speed” of gas particles, and care should ...

Suppose we consider a sample of a pure gas. (We will consider gas mixtures later, briefly.) How often does any one gas particle ...

whereas the average volume V/Nis more of a three-dimensional average vol- ume. However, equation 19.38 gives us an idea of how f ...

have to be pumped down to in order that a nitrogen molecule has a reason- able chance of not colliding with another nitrogen mol ...

This expression can be made more accurate by recognizing that a collision of two masses minvolves the motion of two particles wi ...

c.However, our volume is only 0.02271 m^3. The total number of collisions occurring in 1.000 mol of Xe is therefore 5.23  1034 ...

particles (and usually no gas of any sort) existed previously. It is usually a slow process, so that the concentration of gas pa ...

This integral has a known form and can be simplified.* We get average velocity   2 k T m  1/2 (19.49) Thus we have rate of ef ...

The units inside the square root term are s^2 /(kg^2 m^2 ), so the square root of this unit is s/(kgm). Outside of the square ...

and concentrating on the flow of P 1 into the right side of the system. (The equation we will derive will apply to either gas, u ...

The answers to these questions are the topic of one of Einstein’s seminal manuscripts that were published in 1905. (Other topics ...

Contrary to expectations, gas diffusion is rather slow. For example, in one minute the average displacement of NH 3 molecules un ...

19.2 Postulates and Pressure 19.1.Define “postulate” in the scientific sense. You may have to consult a good dictionary that can ...

19.24.The vapor pressure of Hg at room temperature (taken as 22.0° C) is 0.001426 mmHg. What is the average collision frequency ...

20 O NE MOLECULE OF A REACTANT SPECIES collides with another mol- ecule, chemical bonds are rearranged all at once, and voilà—mo ...

will proceed. Rate laws that have similar mathematical forms imply that their reactions behave a certain way as the reaction pro ...