CHEM1001 Worksheet 6: Concentration
Model 1: Concentration
Most chemical reactions occur in solution, including almost all of those occurring in our bodies. When
dealing with solutions, we measure out volumes instead of weighing out quantities. Volume is related to the
number of moles present using the concentration or molarity. Concentration (symbol c) is defined as the
number of moles of a substance dissolved in one litre of solution:
𝑛
(mol)
𝑐 = 𝑉
(L)
Critical thinking questions
1.
The units of concentration are often written as M. Use the equation above to work out the units of
concentration in terms of mol and L.
2.
What is the concentration of the solution obtained when 0.50 mol of NaCl is dissolved into 0.20 L of
water?
3.
The concentration of carbon dioxide in the oceans around Australia is about 0.05 × 10-3 M. How
many moles of CO2 are present in 3.2 L of seawater?
4.
What mass of CO2 does this correspond to?
5.
A 500. mL solution of HCl with a concentration of 0.10 M is diluted to 1500. mL. What is the new
concentration? (Hint: work out the number of moles present.)
6.
A 500. mL solution of HCl with a concentration of 0.10 M is diluted to 750. mL. What is the new
concentration?
When dealing with dilutions such as those in questions 5 and 6, a handy trick can be used. If the
concentration and volume of the initial solution are c1 and V1 respectively and the concentration and volume
of the final solution are c2 and V2 respectively then the number of moles present in each is:
moles present initially = n = c1V1
moles present in diluted solution = n = c2V2
The number of moles is unchanged when a solution is diluted, so n is the same for these two equations.
Hence:
c1V1 = c2V2
7.
300. mL of a 0.25 M solution of NaCl is diluted to 500. mL. What is the new concentration?
8.
What volume of water must be added to 2.0 L of 5.0 M HCl solution to reduce its concentration to
0.70 M?
Model 2: Concentrations and Dissolution Reactions
When ionic salts are dissolved in water, the solid splits up into cations and anions. For example:
NaCl(s) → Na+(aq) + Cl–(aq)
(1)
+
–
A solution of NaCl contains equal amounts of Na (aq) and Cl (aq). A 0.10 M solution of NaCl is 0.10 M in
Na+(aq) and 0.10 M in Cl–(aq).
When MgCl2(s) dissolves in water, the ionic equation is:
MgCl2(s) → Mg2+(aq) + 2Cl–(aq)
(2)
A solution of MgCl2 contains twice as much Cl–(aq) as Mg2+(aq). A 0.10 M solution of MgCl2 is 0.10 M in
Mg2+(aq) but 0.20 M in Cl–(aq).
When writing concentrations of the species in solution, square brackets are used around the species. For
example, in the solutions above:
(1)
(2)
[Na+(aq)] = 0.10 M and [Cl–(aq)] = 0.10 M
[Mg2+(aq)] = 0.10 M and [Cl–(aq)] = 0.20 M
Critical thinking questions
1.
Write the ionic equation for the dissolution of the following salts:
(a)
NaOH(s)
(b)
Ca(OH)2(s)
2.
3.
(c)
MgSO4(s)
(d)
Na2SO4(s)
A 0.10 M solution of each of these salts is prepared. Write down the concentrations of each of the
ions present using the square bracket notation.
(a)
0.1 M NaOH(s):
(b)
0.1 M Ca(OH)2(s):
(c)
0.1 M MgSO4(s):
(d)
0.1 M Na2SO4(s):
How many moles of OH–(aq) are present in the solutions below?
(a)
500. mL of a 0.50 M solution of NaOH
(b)
25 mL of a 0.10 M solution of Ca(OH)2
Model 3: Concentrations and Titration Reactions
Volumetric analysis is a technique that employs the measurement of volumes to determine quantitatively the
amount of a substance in solution. In any reaction, the reaction equation shows the ratio of reacting species.
If the concentration of one of the solutions is known, the concentrations of the others can be determined
from the volumes used.
Critical thinking questions
To work out the concentration of different table vinegars, a food chemist reacts a solution of brand A with
25 mL of a 0.100 M NaOH solution. Vinegar is CH3COOH and it reacts with OH- as below:
CH3COOH(aq) + OH–(aq) → CH3CO2–(aq) + H2O(l)
1.
What is the concentration of OH–(aq)? (Hint: remember to use the square bracket notation.)
2.
How many moles of OH–(aq) are present in 25 mL?
3.
In the experiment, the food chemist needs 28 mL of vinegar to completely react with the hydroxide
solution. From the chemical equation, how many moles of CH3COOH must this volume contain?
4.
What is the concentration of brand A?
5.
Brand B claims to have a concentration of 0.10 M. What volume of this vinegar would be needed to
completely react with the hydroxide solution if this claim is true?
6.
To check the results obtained from this analysis, a second laboratory tests the same vinegars using 25
mL of a 0.025 M solution of Ca(OH)2. Using the concentrations you calculated above, work out the
volumes of each brand needed to completely react with the calcium hydroxide solution.
(a)
Brand A
(b)
Brand B
Question from June 2007 exam: If 50. mL of a 0.10 M solution of AgNO3 is mixed with 50. mL of a
0.40 M solution of Na2CO3, what mass of Ag2CO3 will precipitate from the reaction?