Question

Below is data that a researcher collected on the observed decay of a chemical in water as a function of time. The Researcher used an analytically technique to quantify the chemical that reports relative “peak area” or “response” values. As a result, the researcher analyzed a series of known “standards” of chemical “A” to construct a standard curve, from which the concentrations of “A” in the experimental samples could be calculated. It is known that the chemical decays by a first-order process. (always use the “xy scatter” option under graph type).

Standard Curve:
[A], Concentration of A (Molarity)	Peak Area
0.002	1220
0.004	2520
0.006	3680
0.008	4940
0.01	6120

Experimental Data:
Time (hours)	Peak Area
0	6120
10	4320
20	3060
30	2250
40	1660
50	1170
60	830

Data Table 2)

From the standard curve and the peak areas of the samples, calculate the concentrations of “A” in each sample. Find the natural logarithm (ln) of these values. Find the slope, intercept, and correlation coefficient for the least-squares analysis of time (x-axis) versus ln([A]) (y-axis) (use the built-in functions). Using the slope and intercept, calculate points on the regression “line”. Plot the experimental values of ln[A] versus time and the regression line on a graph (Figure 2). From the regression (slope and intercept), calculate [A]_t=0 and k. (note that k is always positive).  

Useful headings:

time(hrs) Peak Area A(Molarity) ln(A) ln(A)_calculated

Data Table 3)

Use Solver to calculate [A]_t=0 and k without “transforming the data."

Useful table headings:

time(hrs) A_expected (Molarity) A_calc (Molarity) (A_expected - A_calculated)²

For these data, does the Solver solution agree well with the transformed (i.e., logarithmic) model results? Why or why not.

Table 5) Calculate the “model" fit at 5 hours or smaller increments, using the values of [A]_t=0 and k calculated both ways, and convert to miliMolar concentrations. Plot the original data (Table 4) and the 2 model lines (solid and dashed) (Table 5) on the same plot (Figure 3).

Useful table headings:

Transformed Solver   

time (hrs) A (Molarity) A(miliMolar) A(Molarity) A(miliMolar)

Format all Tables and Figures on 2 pages in Excel.

Please only give answers for Table 3 and Table 5.

Answer 1