I am dealing with the integrated rate laws. Can somebody please help me with my algebra?
First order ln(A)=-kt+ln(B)
solve for t,and k and B
Second order 1/(A) = kt+1/(B)
solve for k and t and B
Sure! I can help you with solving these integrated rate laws algebraically.
First Order Integrated Rate Law:
The first order integrated rate law equation you provided is ln(A) = -kt + ln(B). To solve for t, k, and B, we can rearrange the equation as follows:
1. Solving for t:
Start by isolating the term with t on one side of the equation:
ln(A) + kt = ln(B)
Next, subtract ln(A) from both sides:
kt = ln(B) - ln(A)
Finally, divide both sides by k:
t = (ln(B) - ln(A))/k
So, to find the value of t, substitute the given values of A, B, and k into this equation.
2. Solving for k:
To find the value of k, we already have an equation with k isolated:
kt = ln(B) - ln(A)
Divide both sides by t:
k = (ln(B) - ln(A))/t
Substitute the given values of A, B, and t into this equation to determine k.
3. Solving for B:
To solve for B, rearrange the equation to isolate ln(B):
ln(A) = -kt + ln(B)
Subtract ln(A) from both sides:
ln(B) = -kt + ln(A)
Finally, exponentiate both sides by taking the antilog of ln(B):
B = e^(-kt + ln(A))
Thus, to find the value of B, substitute the given values of A, k, and t into this equation.
Second Order Integrated Rate Law:
The second order integrated rate law equation you provided is 1/A = kt + 1/B. Similarly, we can solve for k, t, and B by rearranging the equation:
1. Solving for k:
First, subtract 1/B from both sides:
1/A - 1/B = kt
Next, divide both sides by t:
k = (1/A - 1/B)/t
Plug in the given values of A, B, and t to find the value of k.
2. Solving for t:
To find the value of t, rearrange the equation to isolate t:
1/A - 1/B = kt
Divide both sides by k:
1/k(A - B) = t
Thus, to determine the value of t, substitute the given values of A, B, and k into this equation.
3. Solving for B:
To solve for B, rearrange the equation to isolate 1/B:
1/A - 1/B = kt
Subtract 1/A from both sides:
1/B = kt - 1/A
Finally, take the reciprocal of both sides to isolate B:
B = 1/(kt - 1/A)
So, substitute the given values of A, k, and t into this equation to obtain the value of B.
Remember to use consistent units when substituting values. I hope this helps you with solving your algebraic problems in the integrated rate laws!