Determine the concentration of a dioxin solution whose percent absorbance is 0.40%

This is the resulting:
Absorbance Dioxin
0.64 5.5
0.76 6.3
1.0 8.0

But why can't I figure out the concentration whose percentage is .40%?

I am unfamiliar with an absorbance of 0.40%. 0.40, yes, but not the percent. If it really is 0.4%, then I would use 0.004 for A.

A = kc where A = absorbance, c is concn and k is a constant. You must calculate the k.
Use any one of the data points, for example, the first one, to calculate k.
A = kc
0.64 = k*5.5 (I wonder if that is 5.5 molar, 5.5%, 5.5 mole fraction or just what?). Calculate c.
Frankly, I would calculate c for each run you have listed, then take an average to obtain an average for c and use that.
Then A =kc.
Plug in 0.4 (if that is the absorbance), the value of k you found, and calculate c.

To determine the concentration of a dioxin solution with a percent absorbance of 0.40%, you can use a calibration curve. The data you provided, with absorbance values and corresponding dioxin concentrations, can be used to create this calibration curve.

A calibration curve is a graph that relates the concentration of a substance to its corresponding absorbance. By plotting the absorbance values on the y-axis and the dioxin concentrations on the x-axis, you can create a curve that represents the relationship between absorbance and concentration.

To create the calibration curve, plot the absorbance (y-axis) against the dioxin concentrations (x-axis) using the given data points:

Absorbance Dioxin
0.64 5.5
0.76 6.3
1.0 8.0

Once you have plotted the data points, draw a best-fit line or curve that represents the relationship between absorbance and concentration.

To determine the concentration corresponding to a percent absorbance of 0.40%, you can use the calibration curve. Draw a horizontal line at the 0.40% absorbance level and see where it intersects with the calibration curve. The corresponding concentration value at this intersection point is the concentration of the dioxin solution.

It seems that you may have encountered difficulty in determining the concentration because the given data did not include a data point near the 0.40% absorbance level. In this case, you can estimate the concentration by drawing a tangent line connecting the two closest data points on the calibration curve and extrapolating it to the 0.40% absorbance level. The concentration value at the point where the tangent line intersects the absorbance line of 0.40% will provide an approximate estimate of the concentration.

It is important to note that the accuracy of your concentration determination will depend on how well the calibration curve represents the relationship between absorbance and concentration.