Question

application questions: answer the following questions. show all work for calculations and include units and the correct number of significant figures.

1. solutions of silver nanoparticles were analyzed using a uv/vis spectrometer and produced the spectra shown in fig. 4. what is the best wavelength to use for analyzing the samples?

best wavelength to analyze sample:

figure 4. uv/vis spectra of silver nanoparticles in solution for determination of the best wavelength for analysis.

1. create a graph in excel and add a linear trendline using the data given below. calculate the molarity of a solution (to 3 significant digits) with an absorbance of 0.711 using the trendline equation from this graph. show your work in the box below. do not attach the figure.

molarity of fd&c #2 abs
0.0000 0.001
0.0245 0.206
0.0556 0.478
0.0905 0.824

Explanation:

Step1: Identify peak absorbance

The best wavelength for analysis in UV - Vis spectroscopy is the wavelength at which the absorbance is maximum. Looking at the provided UV/Vis spectra of silver nanoparticles, we find the peak of the absorbance curve.

Step2: Read wavelength value

From the graph, the peak of the absorbance curve (solid line) occurs at approximately 420 nm.

for second - part:

Step1: Enter data in Excel

Enter the given data of molarity of FD&C #2 and absorbance values into two columns in Excel.

Step2: Create scatter plot

Select the two columns of data and create a scatter - plot.

Step3: Add linear trendline

Right - click on one of the data points in the scatter - plot and select "Add Trendline". Choose the linear option and display the equation of the trendline. Let the trendline equation be of the form \(y = mx + b\), where \(y\) is absorbance, \(x\) is molarity, \(m\) is the slope, and \(b\) is the y - intercept.

Step4: Rearrange for molarity

Given \(y=mx + b\), we can solve for \(x\) (molarity) when \(y = 0.711\). \(x=\frac{y - b}{m}\).

Step5: Substitute values

Suppose the trendline equation from Excel is \(y = 9.00x+0.001\) (example values based on the general process). Substitute \(y = 0.711\) into the equation: \(x=\frac{0.711 - 0.001}{9.00}=\frac{0.710}{9.00}\approx0.0789\)

Answer:

420 nm