Question

Evan obtained the following absorbance data: Concentration (mM) 13,16.2,19.4,22.6,25.8

Absorbance: 0.095,0.143,0.205,0.241,0.312

A graph of this data revealed the line equation is y = 0.0166x – 0.1223 with an R2 =0.99234.

A). Evan measures an unknown solution with an absorbance of 0.448. What is the concentration of the solution?

B).Evan takes 1.0 mL of a solution and dilutes it to 50.0 mL. The absorbance is 0.192. What is the concentration of the original solution?

Answer 1

A) Use the regression equation: y = 0.0166x – 0.1223 with R² = 0.99234.

The unknown solution has an absorbance of 0.448; put y = 0.448 and use the above equation to obtain the value of x.

0.448 = 0.0166x – 0.1223

===> 0.0166x = 0.448 – 0.1223 = 0.3257

===> x = 0.3257/0.0166 = 19.620 ≈ 19.62

The concentration of unknown solution is 19.62 mM (ans).

B) The absorbance of the dilute solution is 0.192; use the regression equation to obtain the concentration of the dilute solution. Plug in y = 0.192 and obtain

0.192 = 0.0166x – 0.1223

===> 0.0166x = 0.192 – 0.1223 = 0.0697

===> x = 0.0697/0.0166 = 4.199 ≈ 4.20

The concentration of the dilute solution is 4.20 mM. We took 1.0 mL of the unknown solution and diluted the volume to 50.0 mL so that the dilution factor is (50.0 mL)/(1.0 mL) = 50.0; therefore the concentration of the unknown in the original solution is (4.20 mM)*(50.0) = 210.0 mM = (210.0 mM)*(1 M/1000 mM) = 0.21 M (ans).