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3.2 – To dilute a solution of known concentration to a given concentration
DILUTIONS
To make a solution less concentrated
A dilute solution contains less solute than a more
concentrated solution
Example: 5 g/L to 2 g/L
Use the following formula to dilute a solution
Concentration of original solution
Concentration of original solution
Volume of original solution
Volume of original solution
Concentration of “new” solution
Concentration of “new” solution
Volume of “new” solution
Volume of “new” solution
11 2 2VC V C
Given 550 mL of a calcium chloride water solution concentrated to 15g/L, what will be its concentration if we add 50 mL of water to the solution?
0.5 L0.5 L
C1 x V1 = C2 x V2
Write down all information
Original Sol. New (diluted) Sol.
Write down all information
Original Sol. New (diluted) Sol.
1
1
15 /
.55
C g L
V L
2
2
?
.600
C
V L
0.55 + 0.050 = 0.60 L
0.55 + 0.050 = 0.60 L
0.5 L0.5 L
1
1
15 /
.55
C g L
V L
2
2
?
.600
C
V L
Set up formula and solveSet up formula and solve
C1 x V1 = C2 x V2
15 x .55 = C2 x 0.60
8.25 = 0.60C28.25 = 0.60C2
C2 = 13.75 g /L
What is the volume of a 70 g/L solution if, after diluting it to a volume of 4 L, its new concentration becomes 15 g/L
0.5 L0.5 L
C1 x V1 = C2 x V2
Write down all information
Original Sol. New (diluted) Sol.
Write down all information
Original Sol. New (diluted) Sol.
1
1
70 /
?
C g L
V
2
2
15 /
4
C g L
V L
0.5 L0.5 L
Set up formula and solveSet up formula and solve
C1 x V1 = C2 x V2
70 x V1 = 15 x 4
70V1 = 6070V1 = 60
V1 = 0.86 g /L
1
1
70 /
?
C g L
V
2
2
15 /
4
C g L
V L
A 250mL solution of orange juice is too strong. 100mL of water is added, to give the orange juice a concentration of 10g/L. What was the original concentration of the orange juice before it was diluted?
Write down all information
Original Sol. New (diluted) Sol.
Write down all information
Original Sol. New (diluted) Sol.
C1 = ?
V1 = 0.25L
C1 = ?
V1 = 0.25L
C2 = 10 g/L
V2 = 0.35L
C2 = 10 g/L
V2 = 0.35L
C1 x V1 = C2 x V2
(C1)(0.25) = (10)(0.35)
(C1)(0.25) = (3.5)
C1 = 14 g/L
1.5L of a 12.75g/L salt solution is diluted to a concentration of 10g/L. What is the final volume of the diluted solution?
C1 = 12.75g/L
V1 = 1.5 L
C1 = 12.75g/L
V1 = 1.5 L
C2 = 10 g/L
V2 = ?
C2 = 10 g/L
V2 = ?
C1 x V1 = C2 x V2
(12.75)(1.5) = (10)(V2)
(19.125) = (10)(V2)
V2 = 1.9125 L
A 500mL solution with a concentration of 2.5g/L is diluted to a concentration of 0.25 g/L. How much water was added in order to dilute the original solution?
C1 = 2.5 g/L
V1 = 0.5 L
C1 = 2.5 g/L
V1 = 0.5 L
C2 = 0.5 g/L
V2 = ?
C2 = 0.5 g/L
V2 = ?
C1 x V1 = C2 x V2
(2.5)(0.5) = (0.25)(V2)
V2 = 5 L
5L – 0.5L = 4.5L5L – 0.5L = 4.5L
This is the FINAL volume, not how much was added!!!
This is the FINAL volume, not how much was added!!!
4.5 L of water was
added
You have 400mL of salt solution and add TWO 200mL containers of water to obtain a new concentration of 200 g/L. What was the original concentration in g/L?
C1 = ?
V1 = 0.4 L
C1 = ?
V1 = 0.4 L
C2 = 200 g/L
V2 = 0.8 L
C2 = 200 g/L
V2 = 0.8 L
C1 x V1 = C2 x V2
(C1)(0.4) = (200)(0.8)
C2 = 400 g/L
Recall, you added
400mL to the 400mL
Recall, you added
400mL to the 400mL
You have 500mL of a 10g/L solution and want to dilute it to a concentration of 2g/L. What procedure would you perform in order to carry out this dilution?
C1 x V1 = C2 x V2
(10)(0.5) = (2)(V2)
V2 = 2.5L
Carry out calculations.
Write out procedure.
1st – Take the 0.5L of 10g/L solution
2nd – Then ADD 2L of water to obtain 2.5L new diluted concentration of 2g/L.
FINAL volume. So, 2L of water was ADDED to the original 0.5L
You have 12g/L solution and you dilute it to a concentration of 4g/L. The volume of the diluted solution is 3L. Explain how to carry out such a dilution.
C1 x V1 = C2 x V2
(12)(V1) = (4)(3)
V1 = 1L
Carry out calculations.
Write out procedure.
1st – Take the 1L of 12g/L solution
2nd – Then ADD 2L of water to obtain 3L new diluted concentration of 4g/L.
INITIAL volume of concentrated solution
read question carefully and fill in all information before beginning
you will always be given 3 out of the 4 variables in the equation…solve for the unknown
do not forget that V2 is the FINAL volume of new solution
(original solution + water added to dilute it!)
Key Points:
A dilution means to make LESS concentrated
Formula: C1 x V1 = C2 x V2
Recall, V2 is the final volume
Know the procedure to carry out a dilution!
Worksheet # 5 Study guide, Module 3, page 16
AFTER YOU HAVE COMPLETED AND UNDERSTAND THESE TYPES OF PROBLEMS…….PROCEED TO THE NEXT SLIDES TO
TRY SOME TRICKIER PROBLEMS!!!
You have 2 different solutions of different concentrations. Which solution is more concentrated?
Solution Concentration
#1 10g/100mL
#2 10g/L
Can’t compare concentration if have different units!!!
So, put everything into g/L:So, put everything into g/L:
10g/100mL 10g/100mL 10g/0.1L10g/0.1L 100g/L100g/L
100g/L
Recall 1000mL = 1LRecall 1000mL = 1L
You have 3 different solutions of different concentrations. Rank from most to least concentrated.
Solution Concentration
#1 10g/L
#2 10% m/V
#3 10g/10mL
Can’t compare concentration if have different units!!!
10% m/V10% m/V 10g/100mL10g/100mL 10g/0.1L10g/0.1L
100g/L
100g/L100g/L
10g/10mL10g/10mL 10g/0.01L10g/0.01L 1000g/L1000g/L
1000g/L
Most to least concentrated: #3, #2 then #1
A 4L sugar solution has a concentration of 25% (m/v). The solution is diluted to a concentration of 10% (m/v). What is the volume of the diluted solution?
C1 = 250 g/L
V1 = 4 L
C1 = 250 g/L
V1 = 4 L
C2 = 100 g/L
V2 = ?
C2 = 100 g/L
V2 = ?
C1 x V1 = C2 x V2
(250)(4) = (100)(V2)
V2 = 10 L
Recall 25% =
25g/100mL =
25g/0.1L =
250 g/L
A salt solution has a concentration of 40% (m/V). The solution is diluted to a concentration of 25% (m/V) and has a volume of 1.2L. What is the volume of the concentrated solution?
C1 = 400 g/L
V1 = ?
C1 = 400 g/L
V1 = ?
C2 = 250 g/L
V2 = 1.2L
C2 = 250 g/L
V2 = 1.2L
C1 x V1 = C2 x V2
(400)(V1) = (250)(1.2)
V1 = 0.75 L or 750 mL
Recall 40% =
40g/100mL =
40g/0.1L =
400 g/L
Recall 25% =
25g/100mL =
25g/0.1L =
250 g/L
Key Points:
In order to compare concentrations or to do dilutions, ALL concentrations must be in the SAME UNITS: g/L
1g/100mL = 1g/0.1L = 10g/L
1% m/V = 1g/100mL = 1g/0.1L = 10g/L
These are SNEAKY!!!These are SNEAKY!!!
Worksheet # 6 (tricky problems!)
(review of both concentration and dilution problems)
