Question

Lithium (ppb)	Signal (mV)
0	0
2	0.384
10	0.928
20	1.69
30	2.419
40	7.973
50	4.267
60	5.003
75	6.039
100	7.886
125	8.357
150	8.811

A researcher is testing the concentration of Lithium in lake water after four times the average signal is 4.463 mV. Determine the concentration of lithium in the water and find the uncertainty of the calculated concentration.

So for the concentration I just graphed it to find the Y=mx+b and plug the signal into the y value to find my concentration is that correct?

I really need help with uncertainty not sure how to go about determing that from the information given

Answer 1

S No	Lithium (ppb)	Signal (mV)
1	0	0
2	2	0.384
3	10	0.928
4	20	1.69
5	30	2.419
6	40	3.973
7	50	4.267
8	60	5.003
9	75	6.039
10	100	7.886
11	125	8.357
12	150	8.811

Consider Lithium (ppm) as X axis and signal (mV) as Y axis

Find slope from above table: since X=0, Y=0 shows that this straight line does not have origin with the general formula Y=mX, where m is slope (∆Y/∆X)

Average of the slope we will get from the above data is 0.07

(Y3-Y2)/(X3-X2) = (0.928-0.384)/(10-2) = 0.068

(Y4-Y3)/(X4-X3) = (1.69-0.928)/(20-10) = 0.076

Do the same for other data you will get slope average of 0.07 now construct the equation using this slope,

Signal (mV), Y= 0.07*X, lithium(ppb)

Thereore, 4.463 = 0.07*X

So, X = 4.463/0.07 = 63.76 ppb