Chapter 7: Kinetic Theory, Thermochemistry, Calorimetry, & Hess's Law

1 Calorie (Cal) or kilocalorie (kcal) =

1000 cal = 4184 J

1 Kilowatt-hour (Kwh) =

3.60 * 10^6 J

ΔE =

Efinal - Einitial

Effusion

The movement of gas molecules through a tiny hole into a vacuum

q

heat (thermal) energy

Heat exchange

heat is exchanged of thermal energy between a system and surroundings

q =

m*cs*∆T

Define heat

the flow of energy caused by a temperature difference

System

the material or process within which we are studying the energy changes within

∆Hrxn =

Σn∆Hf (products) - Σn∆Hf (reactants)

C(s) + O2(g) > CO2(g) ∆H = -393.5 kJ 2 C(s) + 2 O2(g) > 2 CO2 (g) CO2(g) > C(s) + O2(g)

∆H = 2(-393.5 kJ) = -787.0 kJ ∆H = +393.5 kJ

Using the following equation for the combustion of octant, calculate the heat associated with the combustion of 150.0 g of octant assuming complete combustion. The molar mass of octant is 114.33 g/mole/ the molar mass of oxygen is 31.9988 g/mole 2 C8H18 + 25 O2 > 16 CO2 + 18 H2O ∆Hrxn = -11018 kJ

∆Hrxn = -7228 kJ

Use the standard reaction enthalpies given below to determine ΔH°rxn for the following reaction: 4 NO(g) + 2 O2(g) > 4 NO2(g) ΔH°rxn = ? Given: N2(g) + )2(g) > 2 NO(g) ΔH°rxn= +183 kJ 1/2 Ns(g) + O2(g) > NO2(g) ΔH°rxn= +33 kJ

-234 kJ

Two solutions, initially at 24.69 °, are mixed in a coffee cup calorimeter. When a 200.0 mL volume of 0.100 M AgNO3 solution is mixed with a 100.0 mL samples of 0.100 M NaCl solution, the temperature in the calorimeter rises to 25.16°. Determine the ΔH°rxn, in units of kJ/mol AgCl/ Assume that the density and heat capacity of the solution is the same as that of water. Hint: Write a balanced reaction for the process. The specific heat capacity of water = 4.18 J/g°C.

-59 kJ/mol AgCl

Which of the following (with specific heat capacity provided) would show the largest temperature change upon gaining 200 J of heat? 50.0 g Al, CAl = 0.903 J/g°C 50.0 g Zn, CZn = 0.39 J/g°C 25.0 g Ag, CAg = 0.235 J/g°C 25.0 g Hg, CHg = 0.14 J/g°C 25.0 g granite, Cgranite = 0.79 J/g°C

25.0 g Hg, CHg = 0.14 J/g°C

Use the standard reaction enthalpies given below to determine ΔH°rxn for the following reaction: 8 SO3(g) > 8 S(s) + 12 O2(g) ΔH°rxn= ? Given: SO2(g) > S(s) + O2(g) ΔH°rx= +296.8 kJ 2 SO2(g) + O2(g) > 2 SO3(g) ΔH°rxn= -197.8 kJ

3166 kJ

1 calorie (cal) =

4.184 joules (J)

What volume of benzene (C6H6, d= 0.88 g/mL, molar mass = 78.11 g/mol) is required to produce 1.5 × 103 kJ of heat according to the following reaction? 2 C6H6(l) + 15 O2(g) → 12 CO2(g) + 6 H2O(g) ΔH°rxn = -6278 kJ

42 mL

Bomb Calorimeter

Has a constant volume & is used to measure ∆E for combustion reactions

Thomas Graham

discovered that the effusion rate of a gas is inversely proportional to the square root of its density (d)

Exchange of work

w = -pressure * ∆Volume

Thermal equilibrium

when two objects are at the same temperature and no heat flows

w

work energy

Conservation of energy requires that the total energy change in the system & the surrounding must be zero

ΔEnergyUniverse = 0 = ΔEnergySystem + ΔEnerguSurroundings

Insulated cup with 75.0 g of H2O @ 24.00 °C 26.00 g sample of metal @ 82.25°C Final temperature of water & metal = 28.34°C What is the specific heat of the metal?

*No loss of heat, heat is directly transferred from water to metal of vice versa. (insulated cup) 82.25-28.34=53.91°C 28.34-24.00=4.34°C qH2O = 75g*4.184J/g°C*4.34°C qH2O = 1360.59 J 1360.59 J = 26.00 g * Cs * 53.91 °C Csmetal = 1360.59/26.00g*53.91°C Csmetal = 0.9706 J/g°C

When energy flows into the surroundings, ΔEsurroundings is

+

When energy flows out of a system, ΔEsystem is

-

First law or thermodynamics

- Energy can neither be created not destroyed, but can be transferred from one type of energy to another - The total energy of the universe is constant - Example: chemical energy > thermal energy

When a system absorbs energy...

- The system is said to be "endothermic" - The system becomes warmer, & the surroundings become colder

When a system releases energy...

- The system is said to be "exothermic" - The system becomes colder & the surroundings become warmer

q & w

- are not state functions - ΔE = q + w

Kinetic energy

- energy of motion - energy being transferred

Heat capacity, cs

- quantity of heat energy absorbed - J/degrees celsius

In practice, we can't observe temp. change of the individual chemicals involved in a reaction, so instead we measure the temp. change in the surroundings

- use insulated, controlled surroundings - +qsys = -qsurr.

Use the following equation for the combustion of octane, calculate the heat associated with the combustion of excess octant with 100.0 g oxygen assuming complete combustion. The molar mass of octane is 114.33 g/mole. The molar mass of oxygen is 31.9988 g/mole. 2 C8H18 + 25 O2 > 16 CO2 + 18 H2O ∆Hrxn = -11018 kJ

-1377 kJ

Use the standard reaction enthalpies given below to determine ΔH°rxn for the following reaction: 4 S(s) + 6 O2(g) > 4 SO3(g) ΔH°rxn= ? Given: SO2(g) > S(s) + O2(g) ΔH°rx= +296.8 kJ 2 SO2(g) + O2(g) > 2 SO3(g) ΔH°rxn= -197.8 kJ

-1583 kJ

335 g H2O 24.5 degrees celsius - 26.4 degree celsius Cs for H2O = 4.184 J/g °C

1.) Calculate heat, q q = m*cs*∆T q = 335g *4.18 J/g°C*1.9°C q = 2660.57 J 2.) Is the heat absorbed or released ABSORBED

Forms of potential energy

1.) Chemical 2.) Elastic 3.) Nuclear 4.) Gravitational

Kinetic theory of gases

1.) Gas particles are tiny & in constant, random motion 2.) Gas particles occupy a VERY small volume in comparison to their container 3.) Particles collide in perfectly elastic collisions, move in straight lines between collisions, and do not attract/repel each other

To solve constant pressure calorimetry problems, you need to:

1.) Pick the correct formula 2.) Plug in the correct values & solve for the unknown 3.) CHECK THE UNITS. Often the answer is requested in kJ/mol. You will have to divide your energy answer by the moles of substance related.

Form of kinetic energy

1.) Thermal 2.) Mechanical 3.) Electrical 4.) Magnetic

Ideal gas laws assume

1.) no attractions between gas molecules 2.) gas molecules do not take up space

100.0 mL sample of 0.300 M NaOH is mixed with a 100.0 mL of 0.300 M HNO3 in a coffee cup calorimeter. If both solutions were initially at 35.00 °C & the temp. of the resulting solution was recorded as 37.00°C, determine ∆T rxn (kJ/mol NaOH) for the neutralization rxn b/w aqueous NaOH & HNO3.

1.) no heat lost 2.) density & heat capacity are the same as H2O qsolution = m*Cs*∆T = m = 200.0 mL = 200.0g (100.0 mL + 100.0 mL) Cs = 4.148 J/g°C ∆T = 37.00 °C - 35.00 °C = 2.00°C qsol = 200 g * 4.184 J/g°C * 2.00°C qsol = 1673 J > - 1.673 kJ/mol (exothermic) 0.300 mol/ 1L * 0.100 L = 0.0300 mol ∆H = -1.673 kJ / 0.0300 mol = -55.76 kJ/mol

For a process at constant pressure, 5275 joules are release. This quantity is equivalent to...

1.261 * 10^3 cal

Determine the final temperature of a gold nugget (mass = 376 g) that starts at 288 K and loses 4.85 kJ of heat to a snowbank when it is lost. The specific heat capacity of gold is 0.128 J/g°C.

187 K

2 CO2(g) + H2O(g) > C2H2(g) + 5/2O2(g) C2H2(g) + 2H2(g) > C2H6(g) ∆H = -94.5 H2O(g) > H2(g) + 1/2 O2(g) ∆H = - 71.2 kJ C2H6(g) + 7/2 O2(g) > 2CO2(g) + 3H2O(g) ∆H = -283 kJ

2 CO2(g) + H2O(g) > C2H2(g) + 5/2O2(g) ∆H = 235 kJ

According to the following thermochemical equation, what mass of Hf (in g) must react in order to produce 690 kJ of energy? Assume excess SiO2. SiO2(2) + 4 HF(g) > SiF4(g) + 2 H2O(l) ∆Hrnx = -184 kJ

300.0 g

If 1.50 kg of H2O at 100°C loses 470.0 kj of heat, what is the final temperature?

460.0 kJ * 100 J/1 kJ = 460000J 470000 = 1500g*4.184J/g°C*∆T ∆T = 460000 J/1500g*4.184J/g°C ∆T = 74.96 °C 100 - 74.96 = 25.04°C

A 12.8 g sample of ethanol (C2H5OH) is burned in a bomb calorimeter with a heat capacity of 5.65 kJ/°C. Using the information below, determine the final temperature of the calorimeter if the initial temperature is 25.0°C. The molar mass of ethanol is 46.07 g/mol. C2H5OH(l) + 3 O2(g) > 2 CO2(g) + 3 H2O(g) ΔH°rxn = -1235 kJ

85.6 °C

What is the specific heat of lead if it takes 96 J to raise the temperature of a 75 g block by 10°C?

96 J = 75g*cs*10°C cs = 96J/75g * 10°C cs = 0.128 J/g°C

An ice cube melting

Endothermic (positive ∆H)

Nail polish remover evaporating after it's spilled on skin

Endothermic rxn (positive ∆H)

Sweat evaporating from skin

Endothermic rxn (positve ∆H)

Gasoline burning within engine

Endothermic rxn (postive ∆H)

Energy exchange

Energy is exchanged between the system and surroundings through either heat exchange or work being done

ΔErxn =

Eproducts - Ereactants

Wood burning in a fire

Exothermic rnx (negative ∆H)

Water freezing in a freezer

Exothermic rxn (negative ∆H)

Give the units of molar heat capacity

J/mole°C

∆T =

T final - T initial

Heat capacity of calorimeter

The heat capacity of the calorimeter is the amount of heat absorbed by the calorimeter for each degree rise in temp. & is called the calorimeter constant. - Ccal, KJ/°C

Diffusion

The spontaneous intermingling of the molecules of one gas with another

Which of the following is TRUE ΔEsys = 423 J? Both the system and the surroundings are gaining 423 J Both the system and the surroundings are losing 423 J The system is gaining 423 J, while the surroundings are losing 423 J The system is losing 423 J, while the surroundings are gaining 423 J None

The system is gaining 423 J, while the surroundings are losing 423 J

Calorimetry

Used to measure thermal energy exchanged between reactions & surroundings

Work

a force acting over a distance - Energy = work = force * distance

State function

a mathematical function whose result only depends on the initial and final conditions, not on the process used

An endothermic reaction has

a positive ∆H, absorbs heat from the surroundings, and feels cold to the touch

Energy

anything that has the capacity to do work

Chemical energy

associated with positions of electrons & nuclei

Thermal energy

associated with temperature

The surrounding area is called a ___ & is usually made of a sealed, insulated container filled with ___

bomb calorimeter water

Potential energy

due to position or composition

Surroundings

everything else with which the system can exchange energy

m

mass of material being heated

Which of the following signs on q and w represent the surroundings that is doing work on the system, as well as gaining heat from the surroundings? q = -, w = - q = -, w = + q = +, w = - q = +, w = + None

q = +, w = +

Which of the following signs on q and w represent a system that is doing work on the surroundings, as well as losing heat to the surroundings q = -, w = + q = +, w = + q = +, w = - q = -, w = - None

q = -, w = -

1.0 kg of H2O 25 °C - 99 °C Takes how much heat input?

q = 1000g*4.18 J/g°C*74°C q = 309,320 J

Exchange of heat energy

q = mass * Cs * ∆T

qrxn = -qrxn=

qrxn = -qsolution -qrxn= qsolution

As the temperature of a gas sample increases, the velocity distribution of the molecules ___

shifts toward higher velocity

cs

specific heat of material (value is a constant & differs with different materials)

If bonds need to be broken to form HIGHER energy bonds in new product molecules...

that excess energy has to be added to the system from the surroundings in an ENDOTHERMIC rxn

If bonds need to be broken to form LOWER energy bonds in new product molecules....

that excess energy has to be released from the system to the surrounding in an EXOTHERMIC rnx

joule (J)

the amount of energy needed to move a 1 kg mass of distance of 1 meter - 1 J = 1 N*m = 1 kg * m2/s2

calorie (cal)

the amount of energy needed to raise the temperature of one gram of water 1 degree celsius

Specific heat capacity

the amount of heat energy required to raise the temperature of one gram of a substance one degree celsius

Molar heat capacity

the amount of heat energy to raise the temperature of one more of a substance 1 degree celsius

Enthalpy

the capacity of a chemical reaction to do non-mechanical work & the capacity to release/absorb heat

Define energy

the capacity to do work

If the final condition has a larger amount of internal energy than the initial condition...

the change in the internal energy will be (+)

If the final condition has a smaller amount of internal energy than the initial condition...

the change in the internal energy will be (-)

Heat

the flow of energy caused by a difference in temperature

Hess's Law

the overall enthalpy change in a reaction is equal to the sum of enthalpy changes for the individual steps in the process

Define work

the result of a force acting through a distance

Internal energy

the total amount of kinetic & potential energy a system possesses

Hess's Law equation

ΔH (rxn) = ∑[ΔH(products)] - ∑[ΔH(reactants)]