Question

If 5.0 mL of a Sports Drink with an absorbance reading of 0.34 was diluted with water to 10.0 mL and was read by the colorimeter, what is the expected absorbance of the solution

Answer 1

the expected absorbance of the solution = 0.17

Step-by-step explanation:

From the information given:

Using Beer's Lambert Law, we have

A = ∈CL

where;

A = Absorbance

∈ = extinction coefficient

C = concentration

L = cell length

Since Absorbance is associated with concentration.

Assuming the measurement were carried out in the same solution; Then ∈ and L will be constant and A ∝ C ----- (1)

Let consider the concentration to be C (mol/L)

5.0 mL of a Sports Drink = 5.0 mL × C (mol)/1000 mL

= 5C/1000 mL

was diluted with water to 10.0 mL

So, when diluted with water to 10.0 mL; we have:

The new concentration to be :
`((5 C * 1000) \ mol )/((1000 * 10 * 1000)\ mL)`

Since :1000mL = 1 L

The new concentration =
`(C \ mol )/(2 \ L)`

As stated that the initial absorbance reading
`A_1` = 0.34

The expected absorbance reading will be
`A_2` = ???

From (1)

A ∝ C

∴

`(A_2)/(A_1)=(C_2)/(C)`

`A_2 = (A_1)/(C)`

`A_2 = (0.34)/(2)`

`A_2 = 0.17`

Thus ; the expected absorbance of the solution = 0.17