What would the units of the rate constant k be in a second order equation if rate was measured in mol/(L x s)and all concentrations in mol/L
a)L/(mol x s)
b)L2/(mol2 x s)
c)L3/(mol3 x s)
d)mol2/(L2 x s)
I think it's b) or a)
I tried to make this look pretty by using superscripts but it is painstaking to do it AND if I forgot to make one tiny tiny error it screws up; so if it looks funny, I'll try redoing it but using the conventional caret for superscripts.
Why are you guessing? Work it out.
rate = k(A)2
(mol/L*s) = k((mol/L)2
(mol/L*s) = k*(mol2/L2
To clear the fraction, multiply both sides by (L2/mol2 to obtain
(mol/L*s)*(L2/mol2 = k(mol2/L2)*(L2/mol2)
All of that on the right side cancels, except for k and on the left you have remaining, L/mol*s if I didn't make an algebra error. Here is a site that gives you the answer.
http://www.scribd.com/doc/11579759/Examvillecom-Units-of-Reaction-Rate-Constant
To find the units of the rate constant, let's start with the second order rate equation:
rate = k[A]^2
Where:
rate is measured in mol/(L x s)
[A] is measured in mol/L
k is the rate constant
To determine the units of k, we need to manipulate the equation to isolate k. Divide both sides of the equation by [A]^2:
rate/[A]^2 = k
Now, let's examine the units of each expression:
rate/[A]^2 has units of (mol/(L x s))/(mol^2/L^2)
To simplify, multiply the numerator and denominator by L^2:
rate/[A]^2 = (mol/L) / s
Now, the units of rate/[A]^2 are mol/(L x s), which matches the units given in the question.
Therefore, the correct answer is a) L/(mol x s).