Posted by Yasemine on .
We have an important chemsitry test due and I want to make sure that I do not mess up on my algebra. I am dealing with the integrated rate law, but my question is purely algebraically in nature. I hope, somebody can help me.
1) ln(A) = kt+ln(B)
solve for t
solve for k
solve for B
2) 1/(B) = kt + 1/(B)
solve for k
solve for t
solve for B
Thank you so much for your help. It is greatly appreciated

Math 
Reiny,
1)
ln(A) = kt+ln(B)
kt = lnB  lnA
kt = ln(B/A)
t = ln(B/A) / k
k = ln(B/A) / t
lnB = lnA + kt
B = e^(lnA + kt)
2)
1/B = kt + 1/B
0 = kt
t = 0
or
k = 0
B is any value except B≠0
(are you sure you have no typo in 2) ? 
Math 
Yasemine,
2) should be 1/(B) = kt+1(A)
I am dealing with concentrations and A and B are just placeholders for the concentrations.
Thanks 
Math 
Reiny,
2) I thought there was something wrong with your first typing of the question
1/B = kt + 1/A
multiply each term by AB, the LCD
A = ABkt + B
A  B = ABkt
t = (AB)/(ABk)
k = (Ab)/(ABt)
from: A = ABkt + B
A = B(Akt + 1)
B = A/(Akt + 1)