Energy Changes and Rates of Reaction: Test Review

Everything for the Unit 3 test on one page: the key facts from all 5 lessons, the mistakes that cost the most marks, and a practice test that points you back to the lessons you need.

Key facts

Enthalpy Changes and Calorimetry

$Δ H = H_{products} - H_{reactants} :$ negative means exothermic (surroundings warm), positive means endothermic (surroundings cool).
$q = m c Δ T$ , with $c = 4.18\text{ J/{(g}\cdot{}^\circ\text{C)}}$ for water and dilute aqueous solutions.
In a calorimeter, $q_{reaction} = - q_{surroundings} .$
Molar enthalpy: $Δ H_{molar} = \frac{q _{reaction}}{n}$ , and $Δ H = n Δ H_{molar}$ .
Reversing a thermochemical equation flips the sign of $Δ H$ ; multiplying the coefficients multiplies $Δ H$ by the same factor.

Hess's Law and Enthalpies of Formation

Hess's law: $Δ H$ depends only on the initial and final states, so $Δ H_{target} = \sum Δ H_{steps}$ .
Reverse an equation: change the sign of $Δ H$ . Multiply an equation by a factor: multiply $Δ H$ by the same factor.
$Δ H_{r x n}^{\circ} = \sum n Δ H_{f}^{\circ} (products) - \sum n Δ H_{f}^{\circ} (reactants)$
$Δ H_{f}^{\circ} = 0$ for any element in its standard state, e.g. $O_{2} (g)$ or $C (s, graphite)$ .
Bond energies: $Δ H \approx \sum (broken) - \sum (formed)$ ; breaking bonds absorbs energy, forming bonds releases it.

Physical, Chemical and Nuclear Energy: Fuels Compared

Energy scale: phase changes (tens of kJ/mol) < combustion (hundreds to thousands of kJ/mol) < fission and fusion (about $1 0^{9}$ to $1 0^{10}$ kJ/mol).
Nuclear energy comes from the mass defect: $E = m c^{2}$ ; 1 MeV $= 1.602 \times 1 0^{- 13}$ J; fission of uranium-235 releases about 200 MeV per nucleus.
CANDU reactors use natural uranium with a heavy-water ( $D_{2} O$ ) moderator and coolant and can be refuelled while running (Pickering, Bruce, Darlington).
Energy per gram $= \frac{Δ H _{c} ( kJ/mol )}{M ( g/mol )}$ ; CO₂ per kJ $= \frac{mass of CO _{2} per mol of fuel}{Δ H _{c}} .$
Efficiency $= \frac{useful energy out}{energy in} \times 100%;$ thermal plants reach about 30–40%, combined-cycle gas plants about 55–60%.
Fuels with more H per C give more energy per gram and less CO₂ per kJ: hydrogen > methane > octane > coal.

Rates of Reaction and Collision Theory

Average rate of consumption $= - \frac{Δ [ reactant ]}{Δ t}$ ; average rate of formation $= \frac{Δ [ product ]}{Δ t}$ , in mol/(L·s).
For $a A + b B \to c C + d D$ , the rate of each species divided by its coefficient gives the same rate of reaction.
An effective collision needs the correct orientation and at least the activation energy $E_{a}$ .
Rate increases with concentration (or gas pressure), temperature, surface area, and a catalyst; the nature of the reactants sets the activation energy.
Higher temperature increases the fraction of particles above $E_{a}$ ; a catalyst lowers $E_{a}$ without changing the energy distribution.

Potential Energy Diagrams and Mechanisms

$E_{a} (forward) = E_{activated complex} - E_{reactants}$ and $E_{a} (reverse) = E_{activated complex} - E_{products} .$
$Δ H = E_{products} - E_{reactants},$ so $E_{a} (reverse) = E_{a} (forward) - Δ H .$
A catalyst lowers $E_{a}$ for both the forward and reverse reactions by the same amount and does not change $Δ H$ .
Elementary steps must add up to the overall equation; intermediates are made then used up, catalysts are used up then regenerated.
The rate-determining step is the slowest step (highest activation energy) and limits the overall rate.

Where marks get lost

Using $Δ T = T_{initial} - T_{final}$ , which flips every sign that follows. Always take final minus initial. (Enthalpy Changes and Calorimetry)
Reporting the heat gained by the water as the enthalpy of the reaction without changing the sign — a temperature rise means the reaction is exothermic, so $Δ H$ must be negative. (Enthalpy Changes and Calorimetry)
Using only the mass of one solution in a mixing experiment instead of the total mass of everything the heat went into (both solutions, or the water plus the dissolved solid). (Enthalpy Changes and Calorimetry)
Mixing units: $q = m c Δ T$ with $c$ in J/(g·°C) gives joules, but molar enthalpies are usually reported in kJ/mol — convert before comparing. (Enthalpy Changes and Calorimetry)
Forgetting that $Δ H$ in a thermochemical equation refers to the coefficients as written, so burning 2 mol of fuel releases twice the listed energy. (Enthalpy Changes and Calorimetry)
Reversing an equation but forgetting to change the sign of its $Δ H$ , or multiplying the equation but not its $Δ H$ . (Hess's Law and Enthalpies of Formation)
Using reactants minus products with formation enthalpies. It is always products minus reactants for $Δ H_{f}^{\circ}$ (but bonds broken minus bonds formed for bond energies). (Hess's Law and Enthalpies of Formation)
Forgetting to multiply each $Δ H_{f}^{\circ}$ by its coefficient in the balanced equation. (Hess's Law and Enthalpies of Formation)
Giving elements such as $O_{2} (g)$ a non-zero formation enthalpy, or using the value for $H_{2} O (g)$ when the equation shows $H_{2} O (l)$ . (Hess's Law and Enthalpies of Formation)
Counting bonds from the formula instead of the structure — for example, treating $CO_{2}$ as having C–O single bonds instead of two C=O double bonds, or missing that each water molecule has two O–H bonds. (Hess's Law and Enthalpies of Formation)
Comparing fuels only per mole. Octane releases more energy per mole than methane, but per gram (what you carry or pay for) methane releases more. (Physical, Chemical and Nuclear Energy: Fuels Compared)
Thinking nuclear energy breaks the law of conservation of energy. Mass and energy are interchangeable through $E = m c^{2}$ ; the energy released equals the mass defect times $c^{2}$ . (Physical, Chemical and Nuclear Energy: Fuels Compared)
Using grams instead of kilograms in $E = m c^{2}$ . With $c$ in m/s, mass must be in kg to give joules. (Physical, Chemical and Nuclear Energy: Fuels Compared)
Saying a CANDU reactor uses heavy water as fuel. The fuel is natural uranium; heavy water is the moderator that slows neutrons and the coolant that carries heat. (Physical, Chemical and Nuclear Energy: Fuels Compared)
Treating a fuel's heat of combustion as the electricity it produces. A thermal plant converts only about a third to a half of the heat into electricity. (Physical, Chemical and Nuclear Energy: Fuels Compared)
Leaving out the minus sign for a reactant's rate and reporting a negative rate of consumption. (Rates of Reaction and Collision Theory)
Multiplying by the wrong ratio when converting between species, for example saying $H_{2}$ is used at one third of the rate $N_{2}$ is used, instead of three times the rate. (Rates of Reaction and Collision Theory)
Saying higher temperature speeds up reactions only because particles collide more often; the bigger effect is that a much larger fraction of collisions has enough energy to get over the activation energy. (Rates of Reaction and Collision Theory)
Thinking a catalyst shifts the Maxwell-Boltzmann curve. The curve depends only on temperature; a catalyst lowers the activation energy instead. (Rates of Reaction and Collision Theory)
Applying surface area to reactions entirely in solution or entirely in the gas phase — it matters only when a solid (or an immiscible liquid) is involved. (Rates of Reaction and Collision Theory)
Measuring the activation energy from zero on the energy axis instead of from the reactant level to the peak. (Potential Energy Diagrams and Mechanisms)
Believing a catalyst changes $Δ H$ or lowers only the forward activation energy — it lowers both barriers equally and leaves the reactant and product levels untouched. (Potential Energy Diagrams and Mechanisms)
Mixing up intermediates and catalysts: both cancel from the overall equation, but a catalyst appears first as a reactant, while an intermediate appears first as a product. (Potential Energy Diagrams and Mechanisms)
Assuming the first step of a mechanism is always the rate-determining step — it is whichever step is slowest. (Potential Energy Diagrams and Mechanisms)
Thinking an exothermic reaction must be fast. Rate depends on the activation energy, not on the size or sign of $Δ H$ . (Potential Energy Diagrams and Mechanisms)

Practice test

25 questions from across the unit. Each one shows the lesson it comes from.

Enthalpy Changes and Calorimetry
1
A solid dissolves in water and the temperature of the solution drops from $22.0^{\circ} C$ to $17.5^{\circ} C$ . Which statement is correct?
Enthalpy Changes and Calorimetry
2
$8.00 g$ of ammonium nitrate, $NH_{4} NO_{3}$ ( $M = 80.06 g/mol$ ), dissolves in $100.0 g$ of water in a calorimeter. The temperature falls from $22.00^{\circ} C$ to $16.30^{\circ} C$ . Taking the solution's mass as $108.0 g$ and $c = 4.18\text{ J/{(g}\cdot{}^\circ\text{C)}}$ , find the molar enthalpy of solution in kJ/mol (include the sign; 3 significant figures).
kJ/mol
Enthalpy Changes and Calorimetry
3
Which thermochemical equation correctly shows an endothermic reaction?
Enthalpy Changes and Calorimetry
4
Put the steps for finding a molar enthalpy from coffee-cup calorimetry data in order.
1. 1Calculate the heat gained by the solution with $q = m c Δ T$
2. 2Divide the heat of the reaction by the moles of the limiting or named substance
3. 3Change the sign to get the heat of the reaction
4. 4Calculate $Δ T$ as final minus initial temperature
Enthalpy Changes and Calorimetry
5
A student's measured molar enthalpy of combustion of a fuel is $- 720 kJ/mol$ , but the accepted value is $- 1367 kJ/mol$ . Which is the most likely cause?
Hess's Law and Enthalpies of Formation
6
Given $N_{2} (g) + O_{2} (g) \to 2 NO (g)$ , $Δ H = + 180.6 kJ$ and $2 NO (g) + O_{2} (g) \to 2 NO_{2} (g)$ , $Δ H = - 114.2 kJ$ , find $Δ H$ for $N_{2} (g) + 2 O_{2} (g) \to 2 NO_{2} (g)$ in kJ (one decimal place).
kJ
Hess's Law and Enthalpies of Formation
7
Lime is made by heating limestone: $CaCO_{3} (s) \to CaO (s) + CO_{2} (g)$ . Using $Δ H_{f}^{\circ}$ : $CaCO_{3} (s) = - 1206.9$ , $CaO (s) = - 635.1$ , $CO_{2} (g) = - 393.5 kJ/mol$ , find $Δ H^{\circ}$ in kJ (one decimal place).
kJ
Hess's Law and Enthalpies of Formation
8
Estimate $Δ H$ in kJ for $N_{2} (g) + 3 H_{2} (g) \to 2 NH_{3} (g)$ using bond energies N≡N 945, H–H 436 and N–H $391 kJ/mol$ .
kJ
Hess's Law and Enthalpies of Formation
9
Which equation is the correct formation equation for carbon dioxide?
Hess's Law and Enthalpies of Formation
10
Put the steps for estimating Delta H from bond energies in order.
1. 1Count each type of bond broken in the reactants and formed in the products
2. 2Subtract: bonds broken minus bonds formed
3. 3Add the bond energies for bonds broken and for bonds formed
4. 4Draw or picture the structure of every reactant and product
Physical, Chemical and Nuclear Energy: Fuels Compared
11
Octane has $Δ H_{c} = - 5470$ kJ/mol and a molar mass of 114.22 g/mol. How much energy does burning 1.00 g of octane release, in kJ? (1 decimal place)
kJ
Physical, Chemical and Nuclear Energy: Fuels Compared
12
A coal-fired plant burns fuel releasing 3000 MJ of heat each second and delivers 1050 MJ of electrical energy each second. What is its efficiency? (whole number, %)
%
Physical, Chemical and Nuclear Energy: Fuels Compared
13
What is the role of heavy water in a CANDU reactor?
Physical, Chemical and Nuclear Energy: Fuels Compared
14
Match each Ontario energy term to its description.
Bruce
Pickering
Darlington
Moderator
Combined-cycle plant
Physical, Chemical and Nuclear Energy: Fuels Compared
15
What isotope of hydrogen is in the heavy water used in CANDU reactors?
Rates of Reaction and Collision Theory
16
The concentration of a reactant falls from $0.500 mol/L$ to $0.320 mol/L$ in $45.0 s$ . What is its average rate of consumption in mol/(L·s)? Give 3 significant figures.
mol/(L·s)
Rates of Reaction and Collision Theory
17
In $2 NO (g) + O_{2} (g) \to 2 NO_{2} (g)$ , oxygen is consumed at $0.012 mol/ (L \cdot s)$ . At what rate is $NO_{2}$ formed?
mol/(L·s)
Rates of Reaction and Collision Theory
18
On a Maxwell-Boltzmann diagram, how is the effect of adding a catalyst best shown?
Rates of Reaction and Collision Theory
19
Two molecules collide with more than enough energy but do not react. Besides energy, what property of the collision was probably wrong?
Rates of Reaction and Collision Theory
20
Match each observation with the factor that explains it.
Milk spoils more slowly in a refrigerator
Steel wool held in a flame catches fire, but a steel nail does not
Iron speeds up the Haber process without being used up
A precipitate forms instantly when two ionic solutions mix
Wood glows brighter when you blow air on it
Potential Energy Diagrams and Mechanisms
21
A reaction has $E_{a} (forward) = 65 kJ$ and $Δ H = + 25 kJ$ . What is $E_{a} (reverse)$ in kJ?
kJ
Potential Energy Diagrams and Mechanisms
22
A two-step reaction's potential energy diagram has these levels: reactants $0 kJ$ , first peak $90 kJ$ , intermediate $40 kJ$ , second peak $70 kJ$ , products $- 30 kJ$ . What is the activation energy of the second step, in kJ?
kJ
Potential Energy Diagrams and Mechanisms
23
A mechanism has three steps with activation energies of $45 kJ$ , $110 kJ$ and $20 kJ$ (all measured from the start of each step). Which step is most likely rate-determining?
Potential Energy Diagrams and Mechanisms
24
What is the name for a species that is produced in one elementary step and consumed in a later step, so it does not appear in the overall equation?
Potential Energy Diagrams and Mechanisms
25
Put the steps for analyzing a proposed reaction mechanism in order.
1. 1Label intermediates, catalysts and the slow step
2. 2Check that the result is the overall balanced equation
3. 3Cancel species that appear on both sides
4. 4Write out each elementary step
5. 5Add all the steps together

Endless drill

Fresh numbers every time, for the calculation questions in this unit.

Endless drillnew numbers every time

Generating a problem…