Analytical Problem with Coulomb's Law

[antonisz]

Homework Statement

Consider a parallel universe where the laws of nature as we know them are different, and aqueous solutions can have an excess charge. Two beakers are separated 1.20 meters and each contains 0.300 L of an aqueous solution of 6.40 × 10^-6 M excess charge. One beaker has a net positive charge, and one beaker has a net negative charge. Calculate the force between the beakers using the formula below,

where F is force, ε₀ is the permittivity constant and is equal to 8.85 × 10^-12 C²/(N·m²)·, q₁ is the charge contained in the first beaker, q₂ is the charge contained in the second beaker, and r is the distance between the beakers. Note that 1 mole of charge is 96,485 C, and because one of the beakers contains a net negative charge, one q will be negative, and F will be negative. A negative F corresponds to an attractive force.

Homework Equations

The Attempt at a Solution

I found the charge on the solutions to be to be .1853 and -.1853. I did this by multiplying the molarity by the volume .300L and then 96468 C.

After getting those numbers, I plugged into the formula and got an insanely large number for the force, -2.31 x 10⁹. I'm not sure if I'm not understanding the problem or if it is an arithmetic error.Thank you!

 

[gneill]

I found the charge on the solutions to be to be .1853 and -.1853. I did this by multiplying the molarity by the volume .300L and then 96468 C.

After getting those numbers, I plugged into the formula and got an insanely large number for the force, -2.31 x 10⁹. I'm not sure if I'm not understanding the problem or if it is an arithmetic error.

You can expect the force to be crazy large, but not quite as large as that; your result looks to be about an order of magnitude too large to me, so recheck your calculation. Your numerical value for the charges looks okay. Be sure to always include units on any result values that you present! Otherwise the result will be determined to be meaningless by a marker...

 

[Avatrin]

Well, if that's the formula you are supposed to use, then yes, an insanely large number is what you will get. I do not know why you got -2.31 x 10⁹. It's a little too large.

Also, please always remember units. They can remind you if you have forgotten anything, or done anything wrong.

 

[antonisz]

Well, if that's the formula you are supposed to use, then yes, an insanely large number is what you will get. I do not know why you got -2.31 x 10⁹. It's a little too large.

Also, please always remember units. They can remind you if you have forgotten anything, or done anything wrong.

Sorry, I did have the units on my scratch work.

I tried it on my TI-83+ and I got 2.14 x 10⁸, so it must have been me using the google calculator!

Thank you everyone!

 

[BvU]

Funny, I get -2.14 x 10⁸. Still big. Goes to show that excess charge is not to be made fun of.

This 96468 C/mol is Avogadro's number 6.02214E+23 / mol times electron charge 1.60217E-19 C and it's a huge number. One coulomb is an awful lot of charge.