GEN CHEM 2 | ETA Reviewer

Energy

• the capacity to do work or transfers heat

• in chemistry, it is defined as directed energy change resulting from a process

Examples of Energy Relevant to Chemistry

• radiant

• thermal

• chemical

• potential

Radiant Energy

• comes from the sun and is Earth’s primary energy source.

• heats the atmosphere and Earth’s surface, stimulates the growth of vegetation through photosynthesis, and influences global climate patterns.

Thermal Energy

• associated with random movement of atoms and molecules

• calculated through temperature

• the more vigorous the motion, the hotter the sample and the greater the thermal energy

• is also dependent on the sample’s volume and mass

Chemical Energy

• stored within structural units of chemical substances

• determined by the type and arrangement of the molecule’s constituent atoms

• it is released, stored, or converted during chemical reaction

Potential Energy

• energy available by virtue of an object’s position

• chemical energy is a form of this as it is associated with the relevant positions of atoms in a substance

Law of Conservation of Energy

• all of forms of energy can be converted to another of equal magnitude

• the total quantity of energy in the universe is assumed constant

Thermodynamics

studies all forms of energy transfer (heat and work) and predicts whether processes are possible based on energy principles

Zeroth Law of Thermodynamics

If A is in thermal equilibrium with both B and C, then B and C are in thermal equilibrium with each other

First Law of Thermodynamics

• Energy cannot be created nor destroyed, merely converted

• ∆U = Q - W wherein

  • ∆U = change in internal energy of a system

  • Q = heat added to the system

  • W = work done by the system

• If heat is added, energy increases

• If system does work on surroundings, energy decreases

Thermochemistry

study of energy/heat changes occurring during chemical reactions and physical changes

Heat

transfer of thermal energy between two systems that have different temperatures

System

the specific part of the universe that is of interest to the relevant scenario or reaction

Surrounding

rest of the universe outside the system

Open System

allows for the exchange of mass and energy, usually in the form of heat with its surroundings

Closed System

allows the transfer of energy (heat) but not mass; created by fully encasing the substances in the system

Isolated System

does not allow the transfer of either mass or energy; created by fully insulating the substances in the system

First Law of Thermodyanmics

• Energy is transferred between system and surroundings.

• E_system + E_surroundings = 0

• E_system = -E_surroundings

Exothermic Reaction

• any process that gives off heat

• transfers thermal energy from system to surroundings

• E_reactants > E_products

• reaction led to a decrease in temperature

• ∆H < 0, negative

• heat flow (q) is less than 0 (q < 0)

Endothermic Reaction

• any process that absorbs heat

• transfers thermal energy from surroundings to system

• E_reactants < E_products

• reaction led to an increase in temperature or requires heating

• ∆H > 0, positive

• heat flow (q) is greater than 0 (q > 0)

Bond Energy

• average energy required to form or break 1 mole of a specific bond in the gas phase

• how “strong” a bond is

• Unit is kJ/mol

Bond Breaking

• energy is required to break the bonds in the reactants

• endothermic reaction

• BE > 0, positive

Bond Formation

• energy is released to form the bonds in the products

• exothermic reaction

• BE < 0, negative

Reaction Profile

• The energy increases after the bonds of the reactants break.

• The energy decreases after the products’ bonds are formed

Overall Energy Change

• difference in the energies absorbed during bond breaking and released during bond formation

• ∆H = ∑BE(reactants) - ∑BE(products)

Calculating Overall Energy Change of a Chemical Reaction

1. Balance the chemical reaction.

2. Count the number of bonds broken and formed, alongside their bond energies.

3. Add all the bond energies of the reactant bonds (∑BE(reactants)) as the energy input and add all the bond energies of the product bonds (∑BE(products))

4. Calculate the overall energy change (∆H) by subtracting the BE products from the BE reactants [∑BE(reactants) - ∑BE(products)]

5. Interpret if the ∆H entails the reaction is endothermic or exothermic.

When is the reaction endothermic?

• the ∆H > 0 or is positive

• the energy of the system is higher after the reaction

• on the profile graph, the reactants start at a lower energy level than the products

• BE(reactants) > BE(products)

When is the reaction exothermic?

• the ∆H < 0 or is negative

• the energy of the system is lower after the reaction

• on the profile graph, the reactants start at a higher energy level than the products

• BE(reactants) < BE(products)

Enthalpy

• represented as H

• energy change

• quantifies as the heat flow into or out of the system in a process that occurs at constant pressure

• tells us about the “heat content of a system”

• state function (path independent)

• depends only on reactants and products

Enthalpy of Reactions

• represented as ∆H_rxn

• heat transferred in a chemical reaction held at constant pressure

• the difference between the enthalpies of the products and enthalpies of the reactants

• ∆H = H(products) - H(reactants)

Enthalpy of Endothermic Processes

• H(products) > H (reactants)

• ∆H is positive

Enthalpy of Exothermic Processes

• H(products) < H (reactants)

• ∆H is negative

Thermochemical Equations

equations that show the mass relationships between the substances involved in a reaction, alongside its corresponding enthalpy change

Rules in Interpreting Thermochemical Equations

1. Specify the physical states of all reactants and products as they can influence the resulting enthalpy

2. Reversing a reaction entails that the sign of ∆H reverses as well

3. If you multiply both sides of the equation by a factor of n, then multiply ∆H by the same factor of n.

4. The stochiometric coefficients, which are the numbers beside each reactant and product, refer to the number of moles of a substance.

Standard Enthalpy (∆Hº_rxn or ∆Hº_f)

• enthalpy of a reaction carried out at 1 atm, as substances are said to be at the standard state at this point

• ∆Hº_f of any element in its standard state is therefore 0

Formulas for Standard Enthalpy of Reaction (Summation)

∆Hº_rxn = ∑(n∆Hº_f products) - ∑(n∆Hº_f reactants)

or

In formula [aA + bB → cC + dD]

where a, b, c, d = stoichiometric coefficients and A, B, C, D = reactants/products

∆Hº_rxn = [c∆Hº_f (C) + d∆Hº_f (D)] - [a∆Hº_f (A) + b∆Hº_f (B)]

Hess’ Law

• The overall enthalpy change in converting reactants to products is the same, regardless if the reaction took place in one step or in a series of steps

• The sum of the ∆Hº_rxn of the sub-processes is the sum of the overall reaction

Calculating ∆Hº_rxn with Hess’ Law

1. Balance the chemical reaction

2. Manipulate the sub-step processes to ensure that the products and reactants are the same with the 1-step process. Reverse the sub-step processes if necessary,

3. Maipulate the coefficients to ensure it is the same with the 1-step process.

4. Cancel the substances found in both reactants and products.

5. Cancel the substances in both reactants and products.

6. Add the ∆Hº_rxn of the sub-step processes to get ∆Hº_rxn of the 1-step process.

Spontaneous Reactions

• A reaction that occurs under specific conditions.

• Product-favored

• Gives substantial amounts of products at equilibrium.

• Releases free energy

• mostly exothermic but not all

• based on entropy

Non-spontaneous Reaction

• does not occur under specified conditions

Entropy

• Indicated as S

• measure of randomness/disorder or energy dispersal of a system

• as this quality of a system increases, it has a higher probability of occurring

• the number of microscopic arrangement consistent with the observed state

Signs of High Entropy

• particles are more spread out (gas > liquid > solid)

  • As the substance goes from solid to gas, the particle’s position become less rigid. This leads to more possible positions and therefore microstates.

• more particles/more moles of gas

• mixing occurs (possible arrangement)

Signs of Positive Entropy Change

• phase change from: solid → liquid → gas

• moles of gas increase (more moles in the products than reactants)

• mixing or dissolving increases particle freedom

Signs of Negative Entropy Change

• phase change from: gas → liquid → solid

• moles of gas decrease (more moles in the reactants than products)

• particles become more ordered (e.g. crystallization)

Boltzman’s constant

• used to calculate a system’s entropy based on its microtates

• 1.38 × 10^-23 J/K

Microstates

• possible ways of distributing molecules

• Distribution I (usually when molecules are all grouped up) is the least probable while the last distribution (usually when molecules are all separated) is the most probable

• probability of occurrence of a particular distribution (state) depends on the number of ways in which the distribution can be achieved

Microstates and Entropy

• the entropy of a system is related to the natural logarithm of the number of microstates (W)

• S = k ln W

  • k = Boltzman’s constant

• the no. of microstates and entropy have a direct relationship, i.e the more microstates, the greater the entropy

Second Law of Thermodynamics

The entropy of the universe

• increases in a spontaneous process (∆S_univ = ∆S_sys + ∆S_surr > 0)

• remains unchanged in an equilibrium process (∆S_univ = ∆S_sys + ∆S_surr = 0)

Formula for Entropy Changes in the System

∆Sº_rxn = ∑(n∆S products) - ∑(n∆s reactants)

or

In formula [aA + bB → cC + dD]

where a, b, c, d = stoichiometric coefficients and A, B, C, D = reactants/products

∆Sº_rxn = [c∆S (C) + d∆S (D)] - [a∆S (A) + b∆S (B)]

What happens if the entropy change is greater than zero?

It entails that the reaction leads to more disorder and is product-favored.

What happens if the entropy change is less than zero?

It entails that the reaction leads to less disorder and is reactant-favored.

Entropy Changes in the Surroundings

• ∆S_surr = [-∆H_sys/T]

  • ∆H = enthalpy change of the system

  • T = temperature in Kelvin

Effect of Enthalpy Change of the Surrounding’s Entropy

• When an exothermic process occurs in the system, the heat transferred to the surroundings enhances the motion of its molecules.

  • This increases the no. of microstates and therefore entropy of the surroundings increases.

• When an endothermic process absorbs heat from the surroundings, the surrounding’s entropy decreases because the molecular motion decreases.

Effect of Temperature of the Surrounding’s Entropy

• If the temperature of the surroundings is high, the molecules are already quite energetic. Therefore, the absorption of heat from an exothermic process in the system will have relatively little impact on the molecular motion. The entropy of the surroundings will still increase, but it will be small.

• If the temperature of the surroundings is low, then the addition of the same amount of heat will cause a more drastic increase in molecular motion and hence a larger increase in entropy.

Gibbs Free Energy

• denoted as G

• combines enthalpy and entropy in a single value

• predicts the direction of the chemical reaction under constant temperature and pressure

Formula for Change in Free Energy (∆G)

• ∆G = ∆H - T∆S

Interpreting Gibbs Free Energy

• ∆G > 0, nonspontaneous reaction

• ∆G < 0, spontaneous reaction

• ∆G = 0, at equilibrium

Based on Gibbs Free Energy, what does it mean if ∆H is positive while ∆S is negative?

The reaction is nonspontaneous at all temperatures.

Based on Gibbs Free Energy, what does it mean if ∆H is negative while ∆S is positive?

The reaction is spontaneous at all temperatures.

Based on Gibbs Free Energy, what does it mean if ∆H and ∆S is positive?

The reaction is spontaneous at high temperatures.

Based on Gibbs Free Energy, what does it mean if ∆H and ∆S is negative?

The reaction is spontaneous at low temperatures.

Standard State Gibbs Free Energy of Formation

• The partial pressure of any gas in the reaction is 1 atm.

• The concentration of all aqueous solutions is 1 M

• Measurements are taken at temperatures of 25º C/298 K

• change in free energy that occurs when a compound is formed from its elements in their most thermodynamically stable states

Formula for Free Energy Change

∆Gº_rxn = ∑(n∆Gº_f products) - ∑(n∆Gº_f reactants)

or

In formula [aA + bB → cC + dD]

where a, b, c, d = stoichiometric coefficients and A, B, C, D = reactants/products

∆Gº_rxn = [c∆Gº_f (C) + d∆Gº_f (D)] - [a∆Gº_f A) + b∆Gº_f (B)]

Extent of a Reaction

how far a reaction has progressed to completion

Reaction Rate

• the change in the concentration of reactants with respect to time, or how quickly the reaction is progressing to completion

• determined by measuring the amount of a reactant used up, or the amount of a product formed, in a certain period of time

Chemical Kinetics

the study of the reaction rate, the extent of the reaction, the factors affecting reaction rates, the rearrangement of atoms, and the formation of intermediate product

Collision Theory

A chemical reaction occurs if

• the reactants collide

• the reactants align properly

• the energy of the reaction must overcome the activation energy

Activation Energy

• the minimum amount of energy required to break the bonds between atoms of the reactants

• represented by the hill-shape in reaction profiles

• the larger the activation energy, the slower the reaction as less reactants can provide sufficient energy

Surface Area

area of the reactant particles that are exposed to collisions

Effect of Surface Area on Chemical Reactions

As the surface area is where the collisions occur, increasing the surface area leads to more collisions and a faster chemical reaction. This can be done by dividing the reactants into smaller pieces.

Concentration

• number of particles of a substance dissolved in a given amount of solvent

• expressed as []

• expressed in molarity

Effect of Concentration on Chemical Reactions

Since the reactant concentration refer to the number of particles inside the solvent, a higher concentration means more particles could be available for collision, entailing a faster chemical reaction.

Temperature

the average kinetic energies of the moving particles inside a given substance

Effect of Temperature on Chemical Reactions

As the temperature would entail faster moving particles, they would collide more frequently, leading to a faster reaction.

Catalyst

• an inert chemical substance added to chemical reaction to fasten up its reaction rate by lowering the reaction's activation energy

• do not get consumed in a reaction and actually still remains afterwards

Effect of Catalyst on Chemical Reactions

As catalysts lower the activation energy, there are more fractions of collisions as the reactant particles move faster at a lower energy cost. This entails a faster reaction.

Rate Expressions

In a reaction where A molecules is converted into B molecules or

A → B.

∆[A] (including other reactant quantities) is a negative quantity while ∆[B] (including other product quantities) is a positive quantity.

rate = -(∆[A] /∆t) = ∆[B]/∆t

Formula for Average Rate

Let [B] be the molarity of a product

average rate = ∆[B]/∆t = ([B]_final - [B]_initial)/(T_final - T_initial)

Solving for Instantaneous Rate

• By calculating the average reaction rate over shorter and shorter intervals, we can obtain the rate for a specific instant in time, which gives us the instantaneous rate of the reaction at that time

• is given by the slope of the tangent to the curve at that instant or the derivative of the function of the curve

Rate Constant

• tells us the relationship between the concentration of the reactant and the reaction rate

• virtually unchanging throughout the course of the reaction

• is equal to rate/[B]

Rate Laws

• mathematical expressions that describe the relationship between the rate of a chemical reaction and the concentration of its reactants

• equations that shows how much the concentration of the reactants affect how fast it proceeds

Formula for Rate Law

Let aA → bB be a chemical reaction, where a and b are stochiometric coefficients.

rate = k[A]^m[B]ⁿ

k = rate constant

m and n = reaction order

Things to Remember about Rate Laws

1. Determined experimentally

2. Use data from early stage of reactants.

3. Always defined in terms of reactants

4. Order is not related to stochiometric coefficients

Determining Rate Law from Experimental Data

1. Write the tentative rate law

2. Determine the order (m) of the first reactant by comparing the experiments where [A] varies but [B] is constant. Use the formula [rate of experiment x/rate of experiment y = rate law of experiment x/rate law of experiment y].

3. Determine the order (n) of the second reactant by comparing the experiments where [B] varies but [A] is constant.

4. Substitute the m and n into the tentative rate law to get the true one

Integrated Rate Laws

helps determine the reactant concentrations at any time during the reaction

Overall Order of Reaction

m + n

First-Order Reactions

• a reaction whose rate depends on the reactant concentrations raised to the first power

• for a reaction “A → product”, rate is expressed as “Rate = -(∆[A]/∆t)”.

• Rate law is “rate = k[A]”, therefore “k[A] = -(∆[A]/∆t)”.

Determining k in First-Order Reactions

k = -(∆[A]/[A])(1/∆t)

ln([A]_t/[A]₀ = -kt) // Equation 1.1

ln[A]_t = -kt +ln [A]₀ // Equation 1.2

where [A]_t is the A concentration at time t and [A]₀ is the A concentration at the start

Using Integrated Rate Laws for First-Order Rwactions

• Use Equation 1.2 to determine the concentration of the reactant after a certain time elapsed.

• Use Equation 1.1 to determine how much time passed to get a certain concentration of the reactant.

Solving First-Order Reaction Problems

1. Write the given quantities and their respective variables

2. Choose which equation is more useful for the problem.

3. Substitute the given values into the chosen equation.

4. Manipulate the equation to solve the problem.

5. Evaluate what the answer means and if it makes sense.

Half-Life (t_1/2)

• Time required for the concentration of a reactant to decrease to half its initial concentration.

• Only depends on the rate constant for first-order reactions

Equations for Half-Life

• t_1/2 = ln 2/k // for half-life

• [A]_t = [A]₀(1/2)ⁿ // for concentration after n half lives

• _t = t_1/2(n) // for elapsed time after n half lives

Second-Order Reactions

• a reaction whose rate depends on the reactant concentrations raised to the second power

• for a reaction “A → product”, rate is expressed as “Rate = -(∆[A]/∆t)”.

• Rate law is “rate = k[A]²”

Determining k in First-Order Reactions

1/[A]_t = 1/[A]₀ + kt // Equation 2.1

1/[A]_t - 1/[A]₀ = kt // Equation 2.2

where [A]_t is the A concentration at time t and [A]₀ is the A concentration at the start

Using Integrated Rate Laws for First-Order Rwactions

• Use Equation 2.1 to determine the concentration of the reactant after a certain time elapsed.

• Use Equation 2.2 to determine how much time passed to get a certain concentration of the reactant.

Solving Second-Order Reaction Problems

1. Write the given quantities and their respective variables

2. Choose which equation is more useful for the problem.

3. Substitute the given values into the chosen equation.

4. Manipulate the equation to solve the problem.

5. Evaluate what the answer means and if it makes sense.

Equations for Second Order Half-Life

• t_1/2 = 1/k[A]₀ // for half-life

• [A]_t = [A]₀(1/2)ⁿ // for concentration after n half lives

• _t = t_1/2(n) // for elapsed time after n half lives

Zero-Order Reactions

• for a reaction “A → product”, rate is expressed as “Rate = k[A]⁰”.

• Rate law is “rate = k”

Zero-Order Reaction Equations

[A]_t = [A]₀ -kt // Equation 0.1

t_1/2 = [A]₀/2k // Equation 0.2

Irreversible Reaction

• goes essentially to completion

• reactants form products and do not significantly reform reactants