Chemistry: Lattice Energy, Thermodynamics, and Gas Laws

What is lattice energy?

The energy required to completely separate one mole of an ionic solid into gaseous ions. Always POSITIVE (endothermic).

What factors affect lattice energy?

1. Charge - higher charges = higher lattice energy, 2. Size - smaller ions = higher lattice energy

Rank by lattice energy: NaCl, MgO, KBr

MgO > NaCl > KBr (higher charges and smaller ions = higher lattice energy)

What is a state function?

A property that depends only on the current state, NOT the path taken. Examples: H, U, S, G, T, P, V

What is a path function?

A property that depends on the path taken. Examples: heat (q) and work (w)

First Law of Thermodynamics

ΔU = q + w (change in internal energy = heat + work)

Sign of q for endothermic reaction

Positive (+q) - system absorbs heat

Sign of q for exothermic reaction

Negative (-q) - system releases heat

What is enthalpy (H)?

Heat transferred at constant pressure. ΔH = q at constant pressure

Exothermic reaction ΔH sign

ΔH < 0 (negative) - releases heat

Endothermic reaction ΔH sign

ΔH > 0 (positive) - absorbs heat

Hess's Law

If a reaction occurs in multiple steps, total ΔH equals the sum of ΔH for each step. Enthalpy is a state function.

Reverse a reaction in Hess's Law

Change the sign of ΔH

Multiply coefficients in Hess's Law

Multiply ΔH by the same factor

Calorimetry equation

q = mcΔT where q=heat, m=mass, c=specific heat, ΔT=temperature change

Specific heat of water

4.184 J/g·°C

Coffee cup calorimeter measures

qp = ΔH (constant pressure), used for solution reactions

Bomb calorimeter measures

qv = ΔU (constant volume), used for combustion reactions, q = CcalΔT

Energy conservation in calorimetry

qreaction + qwater + qcalorimeter = 0 OR -qreaction = qwater + qcalorimeter

Standard enthalpy of formation (ΔH°f)

Enthalpy change when 1 mole of compound forms from elements in their standard states

ΔH°f of elements in standard state

Zero (0). Examples: O₂(g), N₂(g), H₂(g), C(graphite) all = 0

Standard conditions

25°C (298 K), 1 atm pressure, elements in most stable form

Heat of formation formula

ΔH°rxn = Σ npΔH°f(products) - Σ nrΔH°f(reactants)

Breaking bonds (energy)

Requires energy - endothermic, POSITIVE

Forming bonds (energy)

Releases energy - exothermic, NEGATIVE

Bond energy formula

ΔH°rxn ≈ Σ BE(broken) - Σ BE(formed)

H-H bond energy

436 kJ/mol

C-H bond energy

413 kJ/mol

O=O bond energy

498 kJ/mol

C=O bond energy

799 kJ/mol

O-H bond energy

463 kJ/mol

Ideal Gas Law

PV = nRT where P=pressure, V=volume, n=moles, R=gas constant, T=temperature (KELVIN!)

Gas constant R (atm)

0.0821 L·atm/(mol·K)

Gas constant R (J)

8.314 J/(mol·K)

Convert Celsius to Kelvin

K = °C + 273.15

STP conditions

T = 0°C (273 K), P = 1 atm

Volume of 1 mole gas at STP

22.4 L

Density formula (ideal gas)

d = PM/RT where M = molar mass

Molar mass from density

M = dRT/P

Boyle's Law

P₁V₁ = P₂V₂ (constant T and n) - inverse relationship between P and V

Charles's Law

V₁/T₁ = V₂/T₂ (constant P and n) - direct relationship, MUST USE KELVIN

Gay-Lussac's Law

P₁/T₁ = P₂/T₂ (constant V and n) - direct relationship, MUST USE KELVIN

Avogadro's Law

V₁/n₁ = V₂/n₂ (constant P and T) - more moles = larger volume

Combined Gas Law

P₁V₁/T₁ = P₂V₂/T₂

Dalton's Law of Partial Pressures

Ptotal = P₁ + P₂ + P₃ + ... (total pressure = sum of individual pressures)

Mole fraction formula

χA = nA/ntotal

Partial pressure from mole fraction

PA = χA × Ptotal

Gas collected over water

Ptotal = Pgas + PH₂O, so Pgas = Ptotal - PH₂O

van der Waals equation

[P + a(n/V)²](V - nb) = nRT (corrects for real gas behavior)

When do gases deviate from ideal behavior?

High pressure, low temperature, large molecules, polar molecules

Most ideal gases

Small (He, H₂, Ne), high temperature, low pressure, nonpolar

System in thermodynamics

What you're studying (the reaction)

Surroundings in thermodynamics

Everything else besides the system

What does +w mean?

Work done ON the system (system gains energy)

What does -w mean?

Work done BY the system (system loses energy)

C-C bond energy

347 kJ/mol

C=C bond energy

614 kJ/mol

C≡C bond energy

839 kJ/mol

N≡N bond energy

941 kJ/mol

Why is lattice energy always positive?

Breaking ionic bonds requires energy input (endothermic process)

Which has higher lattice energy: LiF or NaF?

LiF (Li⁺ is smaller than Na⁺, so stronger attraction)

Which has higher lattice energy: NaCl or MgO?

MgO (Mg²⁺ and O²⁻ have higher charges than Na⁺ and Cl⁻)

What does the 'a' correct for in van der Waals?

Intermolecular forces (attractive forces between molecules)

What does the 'b' correct for in van der Waals?

Molecular volume (actual space molecules take up)

Why must T be in Kelvin for gas laws?

Gas laws require absolute temperature scale; 0 K = no molecular motion

Specific heat of ice

2.09 J/g·°C

Specific heat of steam

2.01 J/g·°C

When is bond energy method vs ΔH°f used?

Bond energy: when you have BE values and can identify bonds. ΔH°f: when you have formation enthalpies in tables (more accurate)

Phase change and state functions

Phase doesn't matter for state functions (H, U, S, G) but does matter for path

ΔH°f for O₃(g)

NOT zero (O₂ is standard state, not O₃)

ΔH°f for C(diamond)

NOT zero (graphite is standard state, not diamond)

What type of process is melting ice?

Endothermic (ΔH > 0) - absorbs heat

What type of process is freezing water?

Exothermic (ΔH < 0) - releases heat

What type of process is combustion?

Exothermic (ΔH < 0) - releases heat

What type of process is photosynthesis?

Endothermic (ΔH > 0) - absorbs energy from sunlight

R value for torr units

62.4 L·torr/(mol·K)

How to use Hess's Law

1. Reverse reactions (change sign), 2. Multiply reactions (multiply ΔH), 3. Add reactions (add ΔH values)

1 atm equals how many torr?

760 torr (or 760 mmHg)

1 atm equals how many kPa?

101.325 kPa

Why do real gases deviate at high pressure?

Molecules are forced closer together, volume of molecules becomes significant

Why do real gases deviate at low temperature?

Molecules move slower, intermolecular forces become significant

Most common calorimetry mistake

Forgetting that qreaction is opposite sign of qwater (if water heats up, reaction is exothermic)

Most common gas law mistake

Forgetting to convert temperature to Kelvin

Most common Hess's Law mistake

Forgetting to change sign when reversing equation or forgetting to multiply ΔH when multiplying coefficients