Organic Chemistry I How do I get the value of k? I have this equation: ln(1 – [V

Question

Organic Chemistry I

How do I get the value of k? I have this equation: ln(1 – [V/Vinf]) = -kt

First, I am asked to find the values of k using the equation above. I already have a data table and a graph of ln(1-[V/Vinf]) versus time in seconds. So, should I only divide the values found for ln(1-[V/Vinf]) by each time to get the value of k?

Second, I am asked to find the value of k from the slope of the line. The slope of the line that was found is -0.001619628. What should I do in this case to find the value of k?

Third, I am asked to find an average value of k--which I am fine with that. But, then I am asked to find the absolute value of the deviation of each value from the average value. So, my question here is how do I find the absolute value of the deviation of each value from the average value?

Please note that what we are doing here is a standard statistical way of measuring reproducibility. Theoretically, the value of k should be the same for all trials. In practice, however, you almost certainly will observe some variation in the calculated values of k. The average deviation is a way of expressing in a single number how much variability you have in your data. Low average deviations mean your numbers are all close together; high average deviation means you have a lot of “noise” or “scatter” in your data.

Please note that I just want to understand how to find these value. I am not asking to do it all for me. Thank You In Advance!!

My graph is shown below:

Elapsed Time ln(1-[V/Vinf]) 80 -0.041 133 -0.126 167 -0.145 207 -0.189 245 -0.214 266 -0.276 295 -0.313 322 -0.352 359 -0.413 397 -0.456 447 -0.535 501 -0.609 535 -0.675 580 -0.716 615 -0.79 655 -0.853 735 -0.974 794 -1.07 870 -1.2 923 -1.3 1004 -1.4 1009 -1.62 1212 -1.77 1342 -2.05 1518 -2.37 -0.001619628 Slope

Explanation / Answer

Answer:

Just follow the simple stpes:

1) take Antilog of the equation..(make both side to the power of e), so it becomes

e^ln(1-[V/Vinf] = e^-kt

the antilog and log on left hand side get cancel and on left hand side you will get (1-[V/Vinf])

hence equation becomes (1-[V/Vinf] = e^-kt hence your third column will be of (1-[V/Vinf])

2) you know the time escape which in in t. please enusure the units in calculations.

so you will find out e^t values of time .

3) Now the eqution becomes like

(1-[V/Vinf] ) = e^-k * e^t

here (1-[V/Vinf] = y and e^t is your value of x and the slope will be e^-k and hence slope will be same.

Important note: you will get slope e^-k which is slope and not the value of k . for getting value of k you will inverse it and take log of it. and you will get answer. any further information if required...let me know... Thanks

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