Question

You can analyze for a copper compound in water using an instrument called a spectrophotometer. [A spectrophotometer is a scientific instrument that measures the amount of light (of a given wavelength) that is absorbed by the solution.] The amount of light absorbed at a given wavelength of light (A) depends directly on the mass of compound per liter of solution. To calibrate the spectrophotometer, you collect the following data

Absorbance (A)	Mass Per Liter of copper compound (g/L)
0	0
0.257	1.029 X 10^-3
0.518	2.058 X 10^-3
0.771	3.087 X 10^-3
1.021	4.116 X 10^-3

Plot the absorbance (A) against the mass of copper compound per liter (g/L), and find the slope (m) and the intercept (b) (assuming that A is y and the amount in solution is x in the equation for a straight line, y= mx+b). What is the mass of copper compound in the solution in g/L and mg/ mL when the absorbance is 0.635?

Answer 1

From the equation let us take any two points to find the equation

(1.029 X 10^-3, 0.257), ( 2.058 X 10^-3, 0.518)

the equation of a line given a point and a slope using the formula

(Y-Y1) = m (X-X1)

Where m = slope = Y2-Y1 /X2-X1 =[0.518 - 0.257)] / [(2.058-1.029) x 10^-3]

                                                       = [0.261] / [1.029 x 10^-3] = 253.644

slope (m)= 253.644

(Y-Y1) = m (X-X1)

(Y- 0.257) = 253.644 (X-1.029 X 10^-3)

Y = 253.644 X + (- 0.2609)

intercept (b) = - 0.2609

mass of copper compound for the absorbance 0.635

Y = 0.635 if substituted in above equation

0.635 = 253.644 X + (- 0.2609)

X = 3.53 x 10^-3