Chemistry 121
Prof. Mines, Spring 2009
Answer Key, Problem Set 8a
1.
(a) True or false (correct if false):
(i) F: When a chemical bond is broken, energy is used (or absorbed).
(ii) F: When a chemical reaction takes place, energy is sometimes released and
sometimes absorbed (overall).
(b) If a process involving the breaking and making of bonds is endothermic (overall), what does that “mean” and what
must be true about the relative energies of making and breaking of the bonds involved?
ANSWER: It means that, overall, energy must flow INTO the atoms and molecules that are
getting rearranged in order for that rearrangement to take place. That is, the process
(overall) requires energy.
Energy is always required to break bonds (P.E. of atoms is raised) and energy is always
released when bonds are made (P.E. of atoms goes down). Thus, if a process involving
some bonds breaking and new bonds being formed is endothermic, the total amount of
energy required to break all the bonds that are broken must be greater than the total
amount of energy released upon formation of all the new bonds that are formed.
For example, if it requires 856 kJ to break two moles of certain bonds, and then 765 kJ of
energy is released when the (separated) atoms recombine to form new bonds, the overall
process requires a net amount of energy equal to 856 – 765 = 90 kJ. Overall, 90 kJ would
be required to flow into the system in order for that amount of “rearranging” to occur. Note
that this is a “net” amount; during the course of the process, 856 kJ would effectively flow in
and 765 kJ would flow out, so overall, 90 kJ ended up flowing in.
2.
+
-
When one mole of Ag (aq) and one mole of Cl (aq) come together in solution to form the precipitate AgCl(s) (insoluble),
65.5 kJ is released.
+
(a) What is the ΔH corresponding to the reaction of one mole of Ag (aq) and one mole of Cl (aq)?
+
(b) What is the ΔH corresponding to the reaction of 3.2 moles of Ag (aq) and 3.2 moles of Cl (aq)?
+
(c) What is the ΔH corresponding to the reaction in which 4.3 moles of AgCl(s) is converted into Ag (aq) and Cl (aq)?
+
(d) How many moles of AgCl(s) must be formed (from Ag and Cl ) in order for 88.5 kJ to be released?
(e) Write the (simplest) thermochemical equation corresponding to the precipitation reaction described above. Use the ΔH
convention rather than the other one. Remember that the amount of energy change shown must correspond to the amount of
chemical reaction indicated by the coefficients (interpreted as moles rather than nanoscopic amounts)
Answers:
NOTE: You can use the energy change per amount of chemical change as a conversion
factor. The more moles of reaction that occur, the more energy change occurs. The energy
is part of the “stoichiometry” of a balanced chemical equation.
(a) ΔH = -65.5 kJ (The negative sign is needed if the question asks for the change [i.e., the
ΔH]; if the word “released” is used, one can say (+)65.5 kJ is released [one cannot “absorb” nor
“release” a negative amount of energy!)
(b) ΔH = 3.2 mol Ag + reacted x
-65.5 kJ
= −209.6 = −210 kJ
1 mol Ag + reacted
+65.5 kJ
= +281.65 kJ = +280 kJ
1 mol AgCl reacted
[NOTE: The sign of the energy change was changed from – to + because the reverse reaction was
occurring here.
(c) ΔH = 4.3 mol AgCl reacted x
(d) If 65.5 kJ is released when (i.e. "for every") one mole of AgCl(s) is formed, it must take a bit
more than one mole to form to release 88.8 kJ of energy! Specifically, one can use the
PS8a-1
Problem Set 8a
“energy per mol” value as a conversion factor here as above, but use the energy value as
the initial “amount”. In this case, the reciprocal of the conversion factor is used:
88.8 kJl released x
1 mol AgCl formed
= 1.3557 = 1.36 moles
+ 65.5 kJ released
AgCl (must form)
(e) Ag (aq) + Cl (aq) → AgCl(s) ; ΔH = -65.5 kJ
+
3.
-
(a) If it costs an employer $22,000 to pay one employee for one year, how much will it cost to pay
i) 15 employees for 3 years?
ii) 8 employees for 5 years and 8 months (i.e., 5.67 years)?
Answers: I suspect that many of you just “knew” to multiply 22,000 by 15 and then by 3 to get
990000 dollars for (i), and 22000 x 8 x 5.67 = 997920 dollars for (ii).
(b) If you did not show any calculation above and/or did not include units, that’s fine, but now REDO the calculations
using the “salary” expressed as the following ratio:
22,000 dollars
1 employee ⋅ 1 year
, which should be read out loud as “22,000
dollars per employee per year”. This should mean something (unlike “dollars divided by employees times years”)
Answers:
22,000 dollars
x 15 employees x 3 years = 990,000 dollars
(i)
employee ⋅ year
(ii)
22,000 dollars
x 8 employees x 5.67 years = 997,920 dollars
employee ⋅ year
Note that the units of employee
and year cancel out in both
calculations here.
(ignoring sig figs here)
(c) If it takes 4.184 J of energy to raise the temperature of one gram of water by one Celcius degree, how many J will be
required to raise the temperature of:
i) 15 g of water by 3 Celcius degrees?
188 J (ignoring sig figs)
ii) 156.6 g of water by 76.3 Celcius degrees?
iii) 2.64 moles of water from 23 °C to 87 °C?
5.00 x 104 J
1.3 x 104 J (2.64 moles = 47.5 g)
Reasoning/Work:
4.184 J
x 15 g x 3 °C = 188 J (ignoring sig. figs.)
(i)
g ⋅ °C
(ii)
4.184 J
x 156.6 g x 76.3 °C = 49993 = 5.00 x 104 J
g ⋅ °C
(iii) First convert the moles of water into grams: 2.64 mol H2O x 18.0 g / mol = 47.52 g H2O.
4.184 J
4.184 J
x 47.5 g x (87 - 23) °C =
x 47.5 g x 64 °C = 12719 = 1.3 x 104 J
g ⋅ °C
g ⋅ °C
(d) I did my calculations as asked already in my answer to (c)
4.
How many moles of AgCl(s) must be formed in order for enough energy to be released to raise the temperature of 95
grams of water from 23 °C to 42 °C?
Answer:
7,552 J needed
= 0.12 mol AgCl(s) formed
65,500 J/mol AgCl(s) formed
Explanation: You are essentially asked how many moles of a reaction must occur to generate a certain
amount of energy. What amount of energy needs to be generated? The amount of energy needed to
PS8a-2
Problem Set 8a
raise the temperature of some water. So first calculate how much energy is actually needed, and THEN
figure out how much reaction needs to occur to generate that amount of energy.
1) raising the T of some water: Use the specific heat capacity, just as you did in Problem 3.
4.184 J
x 95 g x (42 - 23) °C = 7552 J (needed)
g ⋅ °C
**NOTE: I only use 4.184 J/g C here because it is liquid WATER that is being heated up. The specific heat of
other substances is different!
2) Figuring out how much reaction must occur (how much AgCl(s) must be formed) to generate 7,552 J.
Think about it: if 65,500 J is released for every mole of AgCl(s) that is formed, then the number of
moles of AgCl needed to be formed to generate about 7,600 J must be less than one mole, right?
7,552 J needed
=0.1153... mol AgCl(s) = 0.12 mol AgCl(s) must be formed
65,500 J/mol AgCl(s) formed
or one could multiply by the reciprocal of the conversion factor as was done in Problem 2:
7,552 J x
5.
1mol AgCl(s) formed
= 0.1153... mol AgCl(s) = 0.12 mol AgCl(s) must be formed
65,500 J
I hope the following statements now make sense to you: 1) It requires energy to separate things that are attracted to one another.
2) Energy is released if things that attract one another are allowed to come closer together. Based on these notions (as well as your
knowledge of what chemical entities and samples “look like” at the nanoscopic level), state whether each of the five processes
below [(a)-(e)]
(i) requires energy or releases energy; (ii) is endothermic or exothermic; and
(iii) has a positive or negative ΔH.
(a) H atoms separate from the O atoms in a sample of water to make free (separated) atoms.
(b) A sample of an ionic solid melts (Note: the cations separate from the anions when this occurs; see the nanoscopic pictures in
the handout from Week 4!)
(c) Steam (gaseous water) condenses into liquid water (Note: water molecules have an attraction for one another. Hint: remember
our nanoscopic pictures of liquids and gases!).
+
(d) Electrons are added to Na ions to make atoms of Na.
(e) Pairs of free Cl atoms join to make Cl2 molecules. (Note: if Cl2 molecules exist, then the two atoms must have an attraction for
each other otherwise they would not stay together!!)
ANSWERS:
(a) requires; endo; ΔH > 0 (final H is HIGHER than the initial H because energy flowed IN)
Bond breaking always requires energy (is always endothermic) because atoms are attracted
to one another if they’re in a bond.
(b) requires; endo; ΔH > 0
Melting is always endothermic; nanoscopic particles of some kind are being “freed” up the
lattice (i.e., separated to some degree from one another).
(c) releases; exo; ΔH < 0 (final H is LOWER than the initial H because energy flowed OUT)
Condensation is exothermic—water molecules (which attract one another) come closer
together). Note: Vaporization (and evaporation) are endothermic
(d) releases; exo; ΔH < 0
Electrons are negative and cations are, by definition, positive. Positive and negative things
attract one another, so when they come together, energy is released. Note: to pull an electron
away from a neutral atom will always require energy because electrons are attracted to the nucleus in
any neutral atom.
(e) releases; exo; ΔH < 0
Bond making always releases energy (is always exothermic) because atoms that form bonds
must attract one another (or they would not “bond” together).
PS8a-3