Physical Chemistry math not working out

In summary, the conversation discusses a student who procrastinated on an assignment and is now struggling to derive an equation from another equation. They provide the equations and attempt to solve it, but are having trouble getting the correct answer. They ask for help from anyone still awake and reading.
  • #1
Roo2
47
0
I put off an assignment until the last minute and on the very last question it came back to bite me in the butt. I'm supposed to derive an equation from another equation, and the math is not working out for me. If there's anyone still up and reading this and that can point me in the right direction within the next 9 hours, I'd appreciate it :D

Homework Statement


Derive equation b from equation a using equation c

Homework Equations



equation a: P(v) = [m/(2*pi*Kb*T)]^(3/2) * e^-[(mv^2)/(2*Kb*T)] * 4*pi*v^2

equation b: <v> = sqrt[(8*Kb*T)/(pi*m)]

equation c: <v> = integral (from 0 to infiniti) v*P(v) dv

The Attempt at a Solution



P(v) = (c1*v^2) * e^-(c2*v^2)

c1 = {[m/(2*pi*Kb*T)]^(3/2)}/(4*pi)

c2 = m/(2*Kb*T)

Therefore, int(v*P(v)dv) = c1 * int[(v^3)*e^(-c2*v^2)]

According to wiki, http://en.wikipedia.org/wiki/Lists_of_integrals (which our prof said to use):

integral (x^3) e^-ax^2 = 1/a^2
The integral is the 5th one down in the section "Definite integrals lacking closed-form antiderivatives"

Therefore, my integral evaluates to c1/(c2^2)

However, when recompile my constants, they are not in a form that is very easily rearrangeable to the desired form. Furthermore, I tried plugging in values to both formulas and obtained different results. Could someone please tell me where I made a mistake?
 
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  • #2
Welcome to PF!

Roo2 said:
c1 = {[m/(2*pi*Kb*T)]^(3/2)}/(4*pi)

Shouldn't the first factor be multiplied by 4pi and not divided by it?


Roo2 said:
integral (x^3) e^-ax^2 = 1/a^2
The integral is the 5th one down in the section "Definite integrals lacking closed-form antiderivatives"

I'm looking at it right now, and it says that it's equal to 1/(2a2).
 
  • #3
I took the liberty of reformatting your post. Here at Physics Forums, we use the LaTeX typesetting system to create mathematical equations, which is very powerful. It might be useful for you to learn. There's a thread that goes over some of the basics, but for now, you can click on the equation graphics that are generated to see the LaTeX code that was used to generate them.

Roo2 said:
I put off an assignment until the last minute and on the very last question it came back to bite me in the butt. I'm supposed to derive an equation from another equation, and the math is not working out for me. If there's anyone still up and reading this and that can point me in the right direction within the next 9 hours, I'd appreciate it :D

Homework Statement


Derive equation b from equation a using equation c

Homework Equations



[tex]\textrm{(a)}~~~P(v) = \left[\frac{m}{2\pi k_B T}\right]^{3/2} \exp\left(-\frac{mv^2}{2k_B T}\right) 4 \pi v^2 [/tex][tex]\textrm{(b)}~~~\langle v \rangle = \sqrt{\frac{8 k_B T}{\pi m}}[/tex]

[tex]\textrm{(c)}~~~\langle v \rangle \equiv \int_0^\infty v P(v)\, dv [/tex]

The Attempt at a Solution



[tex] P(v) = (C_1 v^2) e^{-C_2 v^2} [/tex]

[tex] C_1 \equiv 4\pi \left[\frac{m}{2\pi k_B T}\right]^{3/2} [/tex]

[tex] C_2 \equiv \frac{m}{2k_B T} [/tex]

Therefore,

[tex] \int_0^\infty vP(v)\,dv = C_1 \int_0^\infty v^3 e^{-C_2 v^2}\,dv [/tex]
 
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  • #4
Thank you for the notice! I tried to do two steps in one and spliced it. I still can't get the 8 to come through, nor can I isolate a square root. Also, you are right about the integral; it was a typo on my part and I used the correct integral in my work. In the interest of saving time, here's is my simplified work so far (sorry, no latex but it simplified down a lot):

Z = m/kBT

<v> = c1/2*c2 = sqrt(Z/2pi) / Z

The 8 stubbornly refuses to show up. Am I forgetting some basic algebra?

P.S. I'll learn LaTeX for future posts; I'm still trying to crank out this problem though.
 
  • #5
Roo2 said:
Thank you for the notice! I tried to do two steps in one and spliced it. I still can't get the 8 to come through, nor can I isolate a square root. Also, you are right about the integral; it was a typo on my part and I used the correct integral in my work. In the interest of saving time, here's is my simplified work so far (sorry, no latex but it simplified down a lot):

Z = m/kBT

<v> = c1/2*c2 = sqrt(Z/2pi) / Z

The 8 stubbornly refuses to show up. Am I forgetting some basic algebra?

P.S. I'll learn LaTeX for future posts; I'm still trying to crank out this problem though.

Shouldn't that be: c1 / 2c22
(meaning that your c2 is supposed to be squared)?

EDIT: also, from your definition of Z, shouldn't it be that:

c1 = 4pi * (Z/2pi)3/2

EDIT: and,

c2 = Z/2

EDIT: Yes, I got the algebra to work out for me using these expressions.
 
Last edited:

1. Why is my physical chemistry math not working out?

There could be several reasons why your physical chemistry math is not working out. It could be due to incorrect calculations, using the wrong equations or units, or a lack of understanding of the underlying concepts. It is important to double-check all calculations and consult with a teacher or textbook for clarification if needed.

2. What should I do if my physical chemistry math is not working out?

If your physical chemistry math is not working out, the first step is to identify where the mistake is being made. Double-check all calculations and make sure you are using the correct equations and units. If you are still having trouble, seek help from a teacher or tutor who can provide additional guidance and practice problems.

3. How can I improve my physical chemistry math skills?

To improve your physical chemistry math skills, it is important to have a strong foundation in mathematical concepts such as algebra, calculus, and geometry. Practice using equations and units regularly and seek help from a teacher or tutor if needed. Additionally, understanding the underlying principles of physical chemistry can help with problem-solving and applying mathematical concepts.

4. What resources can I use to help with my physical chemistry math?

There are many resources available to help with physical chemistry math, such as textbooks, online tutorials, and practice problems. Additionally, seeking help from a teacher or tutor can provide personalized support and guidance. It is also helpful to study and review regularly to solidify your understanding of the concepts.

5. Is physical chemistry math difficult?

Physical chemistry math may be challenging for some individuals, but with practice and a solid understanding of the underlying concepts, it can be mastered. It is important to approach each problem with a step-by-step approach, double-check all calculations, and seek help if needed. With dedication and perseverance, physical chemistry math can become easier over time.

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