Calculating concentrations

Different ways to express concentration:

• Number of grams of solute per liter of solution (g/L)

• Number of grams of solute per 100 ml of solution (%mass /volume = %m/V)

• Number of millilitres of solute per 100 ml of solution (% volume/volume = %V/V)

• Number of grams of solute per 100 grams of solution (% mass/ mass = %m/m)

c =amount solute

amount solution

grams of solute per liter of solution (g/L)

c =amount solute

amount solutionc =

mass of solutevolume of solution

c =mv

in gin L

conversions1.000 L =

0.100 L =

10 mL =

1 mL =

1000 mg =

100 mg =

0.010 g =

0.001 g =

1000 mL

100 mL

0.010 L

0.001 L

1.000 g

0.100 g

10 mg

1 mg

mg

19 g sugar

m = 19 gv = 200 ml

c = 19 g 0.2 L

c =mv

c = 95 g /L

m = 53.5 mg

v = 1 L

c =mv

c = 0.0535 g 1 L

c = 0.0535 g /L

known:

formula:

known:

formula:

= 0.2 L

= 0.0535 g

example• How much sugar do you need if you want to

make 20 ml of a sugar solution with a concentration of 50 g/L?

c =mv

c = 50 g/L

v = 20 mL = 0.02 L

m = ?

50 g/L = x g 0.02 L

x = 1 g

known: formula:

m = 1 g

Different ways to express concentration:

• Number of grams of solute per liter of solution (g/L)

• Number of grams of solute per 100 ml of solution (%mass /volume = %m/v)

• Number of millilitres of solute per 100 ml of solution (% volume/volume = %v/v)

• Number of grams of solute per 100 grams of solution (% mass/ mass = %m/m)

c =amount solute

amount solution

grams of solute per 100 ml of solution: % m/v

• 3.25 % MF

• 1 % MF

3.25 g milk fat100 ml milk

100 ml milk 1 g milk fat

c =amount solute

amount solution

grams of solute per 100 ml of solution: % m/v

0.243 g Sodium fluoride

100 ml of tooth paste

example• Determine the concentration of a solution of

20 g solute in 250 mL final solution in % m/v.

m = 20 gv = 250 mL

c =mv

x 20 g 250 mL

x g = 20 g × 250 mL

100 mL

x = 8 gc = 8 %m/v

known: formula:

c = xg /100 mL = x %m/v

100 mL=

g

Different ways to express concentration:

• Number of grams of solute per liter of solution (g/L)

• Number of grams of solute per 100 ml of solution (%mass /volume = %m/v)

• Number of millilitres of solute per 100 ml of solution (% volume/volume = %v/v)

• Number of grams of solute per 100 grams of solution (% mass/ mass = %m/m)

c =amount solute

amount solution

100 ml of vinegar

5 ml acetic acid

milliliters of solute per 100 ml of solution, % v/v

100 ml of beer

7.9 ml ethanol

example• How much ethanol (in mL) is there in a 750 mL

bottle of wine with an alcohol concentration of 12 %v/v?

c =amount solute

amount solution

12 mL x mL

known:

c = 12 mL / 100 mL

v = 750 mL

amount of solute = x mL

c = 100 mL

= 750 mL

x = 90 mL

amount of solute in 750 mL = 90 mL

Different ways to express concentration:

• Number of grams of solute per liter of solution (g/L)

• Number of grams of solute per 100 ml of solution (%mass /volume = %m/v)

• Number of millilitres of solute per 100 ml of solution (% volume/volume = %v/v)

• Number of grams of solute per 100 grams of solution (% mass/ mass = %m/m)

c =amount solute

amount solution

grams of solute / 100 g of solution: % m/m

18 Ka = 750 / 1000

75 g gold 100 g alloy

= 75 % m/m

example• What is the % m/m carbon concentration of

steel made by adding 3g of Carbon to 147 g of iron?

c =amount solute

amount solutionknown:

c = x g / 100 g

amount of solution = 147 + 3 g

amount of solute = 3 g c = x g

100 g = 3 g

150 g

x = 2 g

c = 2 g / 100 g = 2 % m/m

Homework

• Work book page 8 / 9; # 1, 2, 3, 6, 7• Conversion work sheet

c =amount solute

amount solution

100ml