Molarity, Dilution, and pH

1
Molarity, Dilution, and pH

• Main Idea Solution concentrations are measured
  in molarity. Dilution is a useful technique for
  creating a new solution from a stock solution. pH
  is a measure of the concentration of hydronium
  ions in a solution.

2
Molarity Review

• One of the most common units of solution
  concentration is molarity.
• Molarity (M) is the number of moles of solute per
  liter of solution.
• Molarity is also known as molar concentration,
  and the unit M is read as molar.
• A liter of solution containing 1 mol of solute is
  a 1M solution, which is read as a one-molar
  solution.
• A liter of solution containing 0.1 mol of solute
  is a 0.1 M solution.

3
Molarity Equation

• To calculate a solutions molarity, you must know
  the volume of the solution in liters and the
  amount of dissolved solute in moles.
• Molarity (M) moles of solute
• liters of solution

4
Molarity Example

• A 100.5-mL intravenous (IV) solution contains
  5.10 g of glucose (C6H12O6). What is the molarity
  of the solution? The molar mass of glucose is
  180.16 g/mol.
• SOLUTION
• Calculate the number of moles of C6H12O6 by
  dividing mass over molar mass 0.0283 mol
  C6H12O6
• Convert the volume of H2O to liters by dividing
  volume by 1000 0.1005 L
• Solve for molarity by dividing moles by liters
  0.282 M

5
Preparing Molar Solutions

• Now that you know how to calculate the molarity
  of a solution, how would you prepare one in the
  laboratory?
• STEP 1 Calculate the mass of the solute needed
  using the molarity definition and accounting for
  the desired concentration and volume.
• STEP 2 The mass of the solute is measured on a
  balance.
• STEP 3 The solute is placed in a volumetric
  flask of the correct volume.
• STEP 4 Distilled water is added to the flask to
  bring the solution level up to the calibration
  mark.

6
http//www.ltcconline.net/stevenson/2008CHM101Fall
/CHM101LectureNotes20081022.htm
7
Diluting Molar Solutions

• In the laboratory, you might use concentrated
  solutions of standard molarities, called stock
  solutions.
• For example, concentrated hydrochloric acid (HCl)
  is 12 M.
• You can prepare a less-concentrated solution by
  diluting the stock solution with additional
  solvent.
• Dilution is used when a specific concentration is
  needed and the starting material is already in
  the form of a solution (i.e., acids).

8
PROBLEM You have 50.0 mL of 3.0 M NaOH and you
want 0.50 M NaOH. What do you do?

• Add water to the 3.0 M solution to lower its
  concentration to 0.50 M
• Dilute the solution!

9
PROBLEM You have 50.0 mL of 3.0 M NaOH and you
want 0.50 M NaOH. What do you do?
But how much water do we add?
10
PROBLEM You have 50.0 mL of 3.0 M NaOH and you
want 0.50 M NaOH. What do you do?

• How much water is added?
• The important point is that ---gt

11
PROBLEM You have 50.0 mL of 3.0 M NaOH and you
want 0.50 M NaOH. What do you do?

• Amount of NaOH in original solution
• M V
• (3.0 mol/L)(0.050 L) 0.15 mol NaOH
• Amount of NaOH in final solution must also 0.15
  mol NaOH
• Volume of final solution
• (0.15 mol NaOH) / (0.50 M) 0.30 L
• or 300 mL

12
PROBLEM You have 50.0 mL of 3.0 M NaOH and you
want 0.50 M NaOH. What do you do?

• Conclusion
• add 250 mL of water to 50.0 mL of 3.0 M NaOH to
  make 300 mL of 0.50 M NaOH.
  

13
Preparing Solutions by Dilution

• A shortcut
• M1 V1 M2 V2
• Where M represents molarity and V represents
  volume. The 1s are for the stock solution and the
  2s are for the solution you are trying to create.

14
The pH scale is a way of expressing the strength
of acids and bases. Instead of using very small
numbers, we just use the NEGATIVE power of 10 on
the Molarity of the H (or OH-) ion.Under 7
acid 7 neutralOver 7 base
15
pH of Common Substances
16
Calculating the pH

• pH - log H
• (The means Molarity)
• Example If H 1 X 10-10pH - log 1 X
  10-10
• pH - (- 10)
• pH 10
• Example If H 1.8 X 10-5pH - log 1.8 X
  10-5
• pH - (- 4.74)
• pH 4.74

17
pH calculations Solving for H

• If the pH of Coke is 3.12, H ???
• Because pH - log H then
• - pH log H
• Take antilog (10x) of both sides and get
• 10-pH H
• H 10-3.12 7.6 x 10-4 M
• to find antilog on your calculator, look
  for Shift or 2nd function and then the log
  button

18
pH calculations Solving for H

• A solution has a pH of 8.5. What is the Molarity
  of hydrogen ions in the solution?

pH - log H 8.5 - log H -8.5 log
H Antilog -8.5 antilog (log H) 10-8.5
H 3.16 X 10-9 H
19
More About Water

• H2O can function as both an ACID and a BASE.
• In pure water there can be AUTOIONIZATION

Equilibrium constant for water Kw Kw H3O
OH- 1.00 x 10-14 at 25 oC
20
More About Water
Autoionization

• Kw H3O OH- 1.00 x 10-14 at 25 oC
• In a neutral solution H3O OH-
• so Kw H3O2 OH-2
• and so H3O OH- 1.00 x 10-7 M

21
pOH

• Since acids and bases are opposites, pH and pOH
  are opposites!
• pOH does not really exist, but it is useful for
  changing bases to pH.
• pOH looks at the perspective of a base
• pOH - log OH-
• Since pH and pOH are on opposite ends,
• pH pOH 14

22
pH
H
OH-
pOH
23
H3O, OH- and pH

• What is the pH of the 0.0010 M NaOH
  solution?
• OH- 0.0010 (or 1.0 X 10-3 M)
• pOH - log 0.0010
• pOH 3
• pH 14 3 11
• OR Kw H3O OH-
• H3O 1.0 x 10-11 M
• pH - log (1.0 x 10-11) 11.00

24
OH-
1.0 x 10-14 OH-
10-pOH
1.0 x 10-14 H
-LogOH-
H
pOH
10-pH
14 - pOH
-LogH
14 - pH
pH
25
HOMEWORK

1. How much calcium hydroxide Ca(OH)2, in grams,
   is needed to produce 1.5 L of a 0.25 M solution?
2. What volume of a 3.00M KI stock solution would
   you use to make 0.300 L of a 1.25 M KI solution?
3. How many mL of a 5.0 M H2SO4 stock solution would
   you need to prepare 100.0 mL of 0.25 M H2SO4?
4. If 0.50 L of 5.00 M stock solution is diluted to
   make 2.0 L of solution, how much HCl, in grams,
   is in the solution?

26
HOMEWORK

• 5) Calculate the pH of solutions having the
  following ion concentrations at 298 K.
• a) H 1.0 x 10-2 M b) H 3.0 x 10-6 M
• 6) Calculate the pH of a solution having OH-
  8.2 x 10-6 M.
• 7) Calculate pH and pOH for an aqueous solution
  containing 1.0 x 10-3 mol of HCl dissolved in 5.0
  L of solution.
• 8) Calculate the H and OH- in a sample of
  seawater with a pOH 5.60.