Question

(f) the absorbance of the cuso₄ solution of unknown concentration is 0.219. determine the molarity of the solution.
(g) a second student performs the same experiment. there are a few drops of water in the cuvette before the second student adds the cuso₄(aq) solution of unknown concentration. will this result in a cuso₄(aq) concentration for the unknown that is greater than, less than, or equal to the concentration determined in part (f)? justify your answer.
(f) a = εbc
.219

Explanation:

Part (f)

Step1: Determine the slope (molar absorptivity relation)

From the graph, when concentration \( C = 0.0400 \, M \), absorbance \( A = 0.200 \). The Beer - Lambert law is \( A=\epsilon bc \), and the graph is linear (\( A \) vs \( C \)), so the slope \( m=\frac{\Delta A}{\Delta C}=\frac{0.200}{0.0400}=5.00 \, M^{-1} \) (since \( \epsilon b \) is constant for the same cuvette and wavelength).

Step2: Calculate the unknown concentration

We know \( A = 0.219 \) and from \( A = mC \) (since \( m = \epsilon b \)), we can solve for \( C \). Rearranging \( C=\frac{A}{m} \). Substituting \( A = 0.219 \) and \( m = 5.00 \, M^{-1} \), we get \( C=\frac{0.219}{5.00}=0.0438 \, M \) (we can also use the linear equation from the graph. The equation of the line: using two points \((0,0)\) and \((0.0400, 0.200)\), the equation is \( A = 5C \). So when \( A = 0.219 \), \( C=\frac{0.219}{5}=0.0438 \, M \)).

When there are drops of water in the cuvette before adding the \( \ce{CuSO4(aq)} \) solution, the water dilutes the \( \ce{CuSO4} \) solution. According to Beer - Lambert law \( A = \epsilon bc \), if the solution is diluted (concentration \( c \) decreases), the absorbance \( A \) will be lower than the absorbance of the undiluted solution. When we use the calibration curve (which is based on non - diluted standard solutions) to determine the concentration from the measured absorbance, a lower absorbance will be interpreted as a lower concentration. So the calculated concentration will be less than the actual concentration (or less than the concentration determined in part (f)). Another way: The water in the cuvette increases the volume of the solution, so the actual concentration of \( \ce{CuSO4} \) in the cuvette is lower than the concentration we think we added. When we measure the absorbance, the absorbance is lower than it should be for the intended (non - diluted) concentration. When we use the calibration curve (which relates absorbance to the concentration of the standard (non - diluted) solutions), a lower absorbance will give a lower calculated concentration.

Answer:

The molarity of the \( \ce{CuSO4} \) solution is \( \boldsymbol{0.0438 \, M} \) (or values around \( 0.044 \, M \) depending on more precise slope calculation from the graph).

Part (g)