Hello, I have a set of data comprised of pressure as a function of time. This set of data follows a first-order reaction rate.
[TABLE="width: 200"]
Pressure (atm)
time (hr)
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]0.00E+00
[/TABLE]
[/TD]
0
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]1.18E-05
[/TABLE]
[/TD]
1
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]1.96E-05
[/TABLE]
[/TD]
2
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]2.62E-05
[/TABLE]
[/TD]
3
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]3.14E-05
[/TABLE]
[/TD]
4
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]3.93E-05
[/TABLE]
[/TD]
5
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]3.93E-05
[/TABLE]
[/TD]
6
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]5.24E-05
[/TABLE]
[/TD]
7
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]5.50E-05
[/TABLE]
[/TD]
8
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]5.50E-05
[/TABLE]
[/TD]
9
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]5.76E-05
[/TABLE]
[/TD]
10
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]5.76E-05
[/TABLE]
[/TD]
11
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]6.28E-05
[/TABLE]
[/TD]
12
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]6.28E-05
[/TABLE]
[/TD]
13
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]6.28E-05
[/TABLE]
[/TD]
14
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]6.54E-05
[/TABLE]
[/TD]
15
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]6.54E-05
[/TABLE]
[/TD]
16
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]6.81E-05
[/TABLE]
[/TD]
17
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]6.54E-05
[/TABLE]
[/TD]
18
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]6.54E-05
[/TABLE]
[/TD]
19
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]6.81E-05
[/TABLE]
[/TD]
20
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]7.07E-05
[/TABLE]
[/TD]
21
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]7.07E-05
[/TABLE]
[/TD]
22
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]7.07E-05
[/TABLE]
[/TD]
23
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]7.07E-05
[/TABLE]
[/TD]
24
[TABLE="width: 85"]
[TD="class: xl65, width: 85, align: right"]7.07E-05
[/TABLE]
[/TD]
25
[/TABLE]
The equation I am using to solve for P(t) is:
P(t)=Pf * (1- exp(-k*t))
where Pf = final pressure, which in this set of data is 7.07E-05 atm.
I am trying to find the 'best fit' k for these data. Using goal seek would only get me the value of k for a single value of t, but I'm trying to find a k that would work the best for the entire data range. I understand there would be some error in this 'best-fit' k, as it couldn't get all of the calculated p values [P(t)] exactly as what is in the table. Any help is appreciated, thank you!