BEER'S LAW, STANDARD CURVES, AND DETERMINATION OF AN UNKNOWN

The first thing we should do is calculate the actual concentration of the four standards.

Standard 1 is a 1:250 dilution of 0.027 M solution. Therefore, we determine its concentration like this:

0.027 M/250 = 0.000108 M = 0.108 mM

Standard 2 is a 2:250 dilution. Therefore,

0.027 M/125 = 0.000216 M = 0.216 mM

Standard 3 is a 4:250 dilution. Therefore, 0.027 M/62.5 = 0.000432 M = 0.432 mM

Standard 4 is a 6:250 dilution. Therefore, 0.027 M/41.66667 = 0.000648 M = 0.648 mM

Therefore, now we can rechart the data as follows:

Std Conc Abs
1 0.108 mM 0.15
2 0.216 mM 0.30
3 0.432 mM 0.60
4 0.648 mM 0.90

Now, we plot the data using Excel. To do this transfer the data to an Excel file. Highlight the two columns of data, click on Chart Wizard, select XY (Scatter) plot type, and then click Finish.

After you do that you will see the graph with the data points on it, but without a trendline.

To add the trendline, right click on any one of the data points and select Add Trendline from the drop down menu.

Select linear Trend/Regression type. Go to the Options tab and select Set Intercept = 0 and also select Display equation on chart. Click OK.

Now, you see the graph with the trendline and with the equation.

The slope of the line is defined by the following equation:

y = 1.3889x

Therefore, the slope is 1.3889, right? The units must be mM^-1.

Now, to determine the concentration of the unknown, we are told that the unknown solution has an absorbance of .42 when 1 ml of the solution is diluted with 4 ml of water.

First, we shall determine the concentration of the diluted sample. Its absorbance was 0.42. So, what's the concentration? Plug the number into the equation for the line and determine concentration.

y = 1.3889x
0.42 = 1.3889x
Solve for x.
x = 0.302 mM

However, the actual unknown was diluted 1:4, right? Therefore, the original sample must be 4 times as concentrated.

0.302 mM x 4 = 1.21 mM

please see the attached file.