Dilutions!

On this day, we learned all about dilutions. Mr. Doktor took a "six month old pop bottle" and poured 50mL of Coke into a beaker. He then added 100mL of water to the beaker, and asked the class, "How much pop is there in the beaker now?" Some of us were quite surprised to learn that there was actually still 50mL of Coca-Cola in the beaker.

Dilution is the action of making a liquid more dilute; when we add a solvent (usually water), the concentration decreases. In fact, the amount of solute does not change, as Mr. Doktor demonstrated with the pop. So, we can conclude that when two solutions are mixed, the concentration changes.

Also, recall that concentration (M) is actually mol/L. So, we can write C = n/V and n = CV. Therefore, C₁V₁ = C₂V₂. Let's say that we wanted to cut a concentration of a solution in half (eg. 1.00 M glucose solution). If we mix 1.0 L of this solution with 1.0 L of distilled water, the volume is doubled to 2.0 L. The concentration is now cut in half to 0.50 M.

 

In the above diagram, the solutions become less and less concentrated (moving from the left to the right). Next class, we will need to determine which one of these has a specific concentration, without touching any of the test tubes.

EXAMPLES:

1. What is the final concentration if 0.045L of a 6.00M HCL solution are diluted to a final volume of 0.250L?

(C1)(V1) = (C2)(V2)

(6.00)(0.045) = (C2)(0.250)

C2 = [(6.00)(0.045)] / (0.250)

C2 = 1.08M

2. What volume of water should be added to 400mL of a 0.1M NaOH solution in order to change the concentration to 0.075M NaOH?

(C1)(V1) = (C2)(V2)

(0.1)(0.4) = (0.075)(V2)

V2 = [(0.1)(0.4)] / (0.075)

V2 = 0.5333 or 0.533L or 533mL

Vchange = Vf - Vi

Vchange = 533 - 400

Vchange = 133mL

3. How much water must be evaporated from 3.25L of 0.254M KCl solution for the final concentration to be 2.82M?

(C1)(V1) = (C2)(V2)

(0.254)(3.25) = (2.82)(V2)

V2 = [(0.254)(3.25)] / 2.82

V2 = 0.2927 or 0.293L

Vchange = Vf - Vi

Vchange = (0.293) - (3.25)

Vchange = -2.957 or -2.96L

4. If 200mL of 0.230M HCl is mixed with 300mL of 0.250M HCl, what concentration does this give?

0.230mol/L x 0.200L = 0.046mol

0.250mol/L x 0.300L = 0.075mol

0.046 + 0.075 = 0.121mol

0.200 + 0.300 = 0.500L

0.121mol / 0.500L = 0.242mol/L

5. What mass of HCl is needed to make 84.0mL of a 0.143M solution?

0.143mol/L x 0.084L x 36.5g/mol = 0.4384 or 0.44g

As usual, here's a video for more information on today's lesson:

 
Next time: Diluting & Creating Solutions!