StudySmarter - The all-in-one study app.

4.8 • +11k Ratings

More than 3 Million Downloads

Free

Suggested languages for you:

Americas

Europe

Graham's Law

- Chemical Analysis
- Formulations
- Instrumental Analysis
- Pure Substances
- Sodium Hydroxide Test
- Test for Anions
- Test for Metal Ions
- Testing for Gases
- Testing for Ions
- Chemical Reactions
- Acid-Base Reactions
- Acid-Base Titration
- Bond Energy Calculations
- Decomposition Reaction
- Displacement Reactions
- Electrolysis of Aqueous Solutions
- Electrolysis of Ionic Compounds
- Energy Changes
- Extraction of Aluminium
- Fuel Cells
- Hydrates
- Making Salts
- Net Ionic Equations
- Percent Composition
- Physical and Chemical Changes
- Precipitation Reaction
- Reactions of Acids
- Reactivity Series
- Redox Reactions
- Redox Titration
- Representing Chemical Reactions
- Single and Double Replacement Reactions
- Skeleton Equation
- Stoichiometric Calculations
- Stoichiometry
- Synthesis Reaction
- Types of Chemical Reactions
- Chemistry Branches
- Inorganic Chemistry
- Catalysts
- Chlorine Reactions
- Group 1
- Group 2
- Group 2 Compounds
- Group 2 Reactivity
- Halogens
- Ion Colours
- Nitrogen
- Nitrous Oxide
- Period 3 Elements
- Period 3 Oxides
- Periodic Table
- Periodic Trends
- Properties of Halogens
- Properties of Transition Metals
- Reactions of Halides
- Reactions of Halogens
- Redox Potential Of Transition Metals
- Shapes of Complex Ions
- Stability Constant
- Test Tube Reactions
- Titrations
- Transition Metal Ions in Aqueous Solution
- Transition Metals
- Variable Oxidation State of Transition Elements
- Ionic and Molecular Compounds
- Bond Hybridization
- Bond Length
- Bonding and Elemental Properties
- Coulomb Force
- Formal Charge
- Interstitial and Substitutional Alloys
- Intramolecular Force and Potential Energy
- Lattice Energy
- Lewis Dot Diagrams
- Limitations of Lewis Dot Structure
- Naming Ionic Compounds
- Polar and Non-Polar Covalent Bonds
- Potential Energy Diagram
- Properties of Covalent Compounds
- Resonance Chemistry
- Saturated Bond
- Sigma and Pi Bonds
- Structure of Ionic Solids
- Structure of Metals and Alloys
- The Octet Rule
- Types of Chemical Bonds
- VSEPR
- Kinetics
- Activation Energy
- Catalysis
- Concentration
- Energy Profile
- First Order Reaction
- Multistep Reaction
- Pre-equilibrium Approximation
- Rate Constant
- Rate Law
- Reaction Rates
- Second Order Reactions
- Steady State Approximation
- Steady State Approximation Example
- The Change of Concentration with Time
- Zero Order Reaction
- Making Measurements
- Accuracy and Precision
- Analytical Chemistry
- Chemistry Lab Equipment
- Lab Safety
- Lab Temperature Monitoring
- Nuclear Chemistry
- Balancing Nuclear Equations
- Carbon Dating
- Mass Energy Conversion
- Radioactive Dating
- Radioactive Isotopes
- Spontaneous Decay
- Transmutation
- Organic Chemistry
- Acylation
- Alcohol Elimination Reaction
- Alcohols
- Aldehydes and Ketones
- Alkanes
- Alkenes
- Amide
- Amines
- Amines Basicity
- Amino Acids
- Anti-Cancer Drugs
- Aromatic Chemistry
- Aryl Halide
- Benzene Structure
- Biodegradability
- Carbon
- Carbon -13 NMR
- Carbonyl Group
- Carboxylic Acid Derivatives
- Carboxylic Acids
- Chlorination
- Chromatography
- Column Chromatography
- Combustion
- Condensation Polymers
- Cracking (Chemistry)
- Drawing Reaction Mechanisms
- Electrophilic Addition
- Electrophilic Substitution of Benzene
- Elimination Reactions
- Esterification
- Esters
- Fractional Distillation
- Functional Groups
- Gas Chromatography
- Halogenation of Alcohols
- Halogenoalkanes
- Hydrogen -1 NMR
- Hydrolysis of Halogenoalkanes
- IUPAC Nomenclature
- Infrared Spectroscopy
- Isomerism
- NMR Spectroscopy
- Natural Polymers
- Nitriles
- Nucleophiles and Electrophiles
- Nucleophilic Substitution Reactions
- Optical Isomerism
- Organic Analysis
- Organic Chemistry Reactions
- Organic Compounds
- Organic Synthesis
- Oxidation of Alcohols
- Ozone Depletion
- Paper Chromatography
- Phenol
- Polymerisation Reactions
- Preparation of Amines
- Production of Ethanol
- Properties of Polymers
- Purification
- R-Groups
- Reaction Mechanism
- Reactions of Aldehydes and Ketones
- Reactions of Alkenes
- Reactions of Benzene
- Reactions of Carboxylic Acids
- Reactions of Esters
- Structure of Organic Molecules
- Thin Layer Chromatography Practical
- Thin-Layer Chromatography
- Understanding NMR
- Uses of Amines
- Physical Chemistry
- Absolute Entropy and Entropy Change
- Acid Dissociation Constant
- Acid-Base Indicators
- Acid-Base Reactions and Buffers
- Acids and Bases
- Alkali Metals
- Allotropes of Carbon
- Amorphous Polymer
- Amount of Substance
- Application of Le Chatelier's Principle
- Arrhenius Equation
- Arrhenius Theory
- Atom Economy
- Atomic Structure
- Autoionization of Water
- Avogadro Constant
- Avogadro's Number and the Mole
- Beer-Lambert Law
- Bond Enthalpy
- Bonding
- Born Haber Cycles
- Born-Haber Cycles Calculations
- Boyle's Law
- Brønsted-Lowry Acids and Bases
- Buffer Capacity
- Buffer Solutions
- Buffers
- Buffers Preparation
- Calculating Enthalpy Change
- Calculating Equilibrium Constant
- Calorimetry
- Carbon Structures
- Cell Potential
- Cell Potential and Free Energy
- Chalcogens
- Chemical Calculations
- Chemical Equations
- Chemical Equilibrium
- Chemical Thermodynamics
- Closed Systems
- Colligative Properties
- Collision Theory
- Common-Ion Effect
- Composite Materials
- Composition of Mixture
- Constant Pressure Calorimetry
- Constant-Volume Calorimetry
- Coordination Compounds
- Coupling Reactions
- Covalent Bond
- Covalent Network Solid
- Crystalline Polymer
- De Broglie Wavelength
- Determining Rate Constant
- Deviation From Ideal Gas Law
- Diagonal Relationship
- Diamond
- Dilution
- Dipole Chemistry
- Dipole Moment
- Dissociation Constant
- Distillation
- Dynamic Equilibrium
- Electric Fields Chemistry
- Electrochemical Cell
- Electrochemical Series
- Electrochemistry
- Electrode Potential
- Electrolysis
- Electrolytes
- Electromagnetic Spectrum
- Electron Affinity
- Electron Configuration
- Electron Shells
- Electronegativity
- Electronic Transitions
- Elemental Analysis
- Elemental Composition of Pure Substances
- Empirical and Molecular Formula
- Endothermic and Exothermic Processes
- Energetics
- Energy Diagrams
- Enthalpy Changes
- Enthalpy for Phase Changes
- Enthalpy of Formation
- Enthalpy of Reaction
- Enthalpy of Solution and Hydration
- Entropy
- Entropy Change
- Equilibrium Concentrations
- Equilibrium Constant Kp
- Equilibrium Constants
- Examples of Covalent Bonding
- Factors Affecting Reaction Rates
- Finding Ka
- Free Energy
- Free Energy and Equilibrium
- Free Energy of Dissolution
- Free Energy of Formation
- Fullerenes
- Fundamental Particles
- Galvanic and Electrolytic Cells
- Gas Constant
- Gas Solubility
- Gay-Lussac's Law
- Giant Covalent Structures
- Graham's Law
- Graphite
- Ground State
- Group 3A
- Group 4A
- Group 5A
- Half Equations
- Heating Curve for Water
- Heisenberg Uncertainty Principle
- Henderson-Hasselbalch Equation
- Hess' Law
- Hybrid Orbitals
- Hydrogen Bonds
- Ideal Gas Law
- Ideal and Real Gases
- Intermolecular Forces
- Introduction to Acids and Bases
- Ion and Atom Photoelectron Spectroscopy
- Ion dipole Forces
- Ionic Bonding
- Ionic Product of Water
- Ionic Solids
- Ionisation Energy
- Ions: Anions and Cations
- Isotopes
- Kinetic Molecular Theory
- Lattice Structures
- Law of Definite Proportions
- Le Chatelier's Principle
- Lewis Acid and Bases
- London Dispersion Forces
- Magnitude of Equilibrium Constant
- Mass Spectrometry
- Mass Spectrometry of Elements
- Maxwell-Boltzmann Distribution
- Measuring EMF
- Mechanisms of Chemical Bonding
- Melting and Boiling Point
- Metallic Bonding
- Metallic Solids
- Metals Non-Metals and Metalloids
- Mixtures and Solutions
- Molar Mass Calculations
- Molarity
- Molecular Orbital Theory
- Molecular Solid
- Molecular Structures of Acids and Bases
- Moles and Molar Mass
- Nanoparticles
- Neutralisation Reaction
- Oxidation Number
- Partial Pressure
- Particulate Model
- Partition Coefficient
- Percentage Yield
- Periodic Table Organization
- Phase Changes
- Phase Diagram of Water
- Photoelectric Effect
- Photoelectron Spectroscopy
- Physical Properties
- Polarity
- Polyatomic Ions
- Polyprotic Acid Titration
- Prediction of Element Properties Based on Periodic Trends
- Pressure and Density
- Properties of Buffers
- Properties of Equilibrium Constant
- Properties of Solids
- Properties of Water
- Quantitative Electrolysis
- Quantum Energy
- Quantum Numbers
- RICE Tables
- Rate Equations
- Rate of Reaction and Temperature
- Reacting Masses
- Reaction Quotient
- Reaction Quotient and Le Chatelier's Principle
- Real Gas
- Redox
- Relative Atomic Mass
- Representations of Equilibrium
- Reversible Reaction
- SI units chemistry
- Saturated Unsaturated and Supersaturated
- Shapes of Molecules
- Shielding Effect
- Simple Molecules
- Solids Liquids and Gases
- Solubility
- Solubility Curve
- Solubility Equilibria
- Solubility Product
- Solubility Product Calculations
- Solutes Solvents and Solutions
- Solution Representations
- Solutions and Mixtures
- Specific Heat
- Spectroscopy
- Standard Potential
- States of Matter
- Stoichiometry in Reactions
- Strength of Intermolecular Forces
- The Laws of Thermodynamics
- The Molar Volume of a Gas
- Thermodynamically Favored
- Trends in Ionic Charge
- Trends in Ionisation Energy
- Types of Mixtures
- VSEPR Theory
- Valence Electrons
- Van der Waals Forces
- Vapor Pressure
- Water in Chemical Reactions
- Wave Mechanical Model
- Weak Acid and Base Equilibria
- Weak Acids and Bases
- Writing Chemical Formulae
- pH
- pH Change
- pH Curves and Titrations
- pH Scale
- pH and Solubility
- pH and pKa
- pH and pOH
- The Earths Atmosphere

Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmeldenNie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmeldenHave you ever sprayed an air freshener in a room? At first, you can only smell it directly where you sprayed, but eventually, the particles will spread across the room and can be smelt anywhere.

Now, what would happen if you sprayed two different air fresheners at the same time in the same general place? While the scents will be mixed, one will be smelt on the opposite end of the room earlier than the other. Why is this? Well, **Graham's law** has the answer, continue reading to find out!

- This article covers
**Graham's law.** - First, we will define Graham's law.
- Next, we will look at Graham's law equation.
- Then we will look at the two parts of Graham's law: Graham's law of
**diffusion**and Graham's law of**effusion.** - Lastly, we will work on some examples using Graham's law.

Let's start by looking at the definition of Graham's law.

**Graham's law **states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of the molar masses of its particles.

**Diffusion **is the process of particles moving from an area of high density to one of low density

**Effusion **is the process of gas particles escaping their container into another container through a small hole. This hole's diameter is much smaller than the particle's **mean free path, **which is the distance a particle travels before it collides with something. Essentially, this means that only one particle can travel through the hole at a time.

Now, this is a bit of a tricky definition. To help us out, we are first going to look at the equation.

The equation for graham's law is:$$\frac{Rate_A}{Rate_B}=\sqrt{\frac{M_B}{M_A}}$$

Where,

- M
_{A }and Rate_{A }are the molar mass and rate of effusion/diffusion of gas, A respectively. - M
_{B }and Rate_{B }are the respective molar mass and rate of effusion/diffusion of gas, B.

What this basically tells us is the ratio of rates based on their masses. In simpler terms, the heavier the gas, the slower it's going to go. Here's an example:

**Calculate the rate of effusion/diffusion for a container of both helium (He) and neon (Ne) gas.**

The molar mass of helium is 4.00 g/mol, and the molar mass of neon is 20.2 g/mol. Plugging this in, we get:

$$\frac{Rate_A}{Rate_B}=\sqrt{\frac{M_B}{M_A}}$$

$$\frac{Rate_{He}}{Rate_{Ne}}=\sqrt{\frac{M_{Ne}}{M_{He}}}$$

$$\frac{Rate_{He}}{Rate_{Ne}}=\sqrt{\frac{20.2\frac{g}{mol}}{4.00\frac{g}{mol}}}$$

$$\frac{Rate_{He}}{Rate_{Ne}}=\sqrt{5.05}$$

$$\frac{Rate_{He}}{Rate_{Ne}} =2.25$$

This means that helium will effuse/diffuse 2.25x times faster than neon

To better understand this concept, let's split this law up into two parts: **diffusion **and **effusion**.

Let's first talk a bit more about what diffusion is. Like we talked about in the introduction when you spray an air freshener the spray will only be smelt in the direct area, but the particles will eventually spread across the room.

Here's a diagram of what's happening:

Fig.1-Particles diffuse across a space

The purpose of diffusion is to create an **equilibrium**. Equilibrium is essentially a state of balance. In this case, equilibrium means a balanced concentration across the whole container.

So, what happens when there are two gases? That's where **Graham's law steps** come in.

Our main assumption is that both gases are at the same temperature, and therefore have the same **kinetic energy**, which is the energy of motion.

In fact, that's where graham's law comes from. Here's the formula for kinetic energy:

$$KE=\frac{1}{2}*M_A*\nu_{rms}^2$$

Where KE is kinetic energy, M_{A }is the molar mass of species A, and ν_{rms }is the **root-mean-square speed**.

**Root-mean-square speed (RMS speed) **is the average speed of a gas. The formula is:

$$\nu_{rms}=\sqrt{3RTM}$$

Where R is the ideal gas constant, T is the temperature, and M is the molar mass of the gas.

You don't really need to worry about the exact definition of RMS speed, so you can just think of it as "speed" for now.

For gases, we don't use normal velocity since the net velocity of a gas is zero, since the gases will move in all directions (i.e. they will cancel each other out since velocity is speed + direction)

Continuing on with our derivation, we are going to set the kinetic energies of our two gases (A and B) equal to each other:

$$KE=\frac{1}{2}*M_A*\nu_{rms,A}^2=\frac{1}{2}*M_B*\nu_{rms,B}^2$$

Next, we can cancel out the 1/2, since it is on both sides:

$$M_A*\nu_{rms,A}^2=M_B*\nu{rms,B}^2$$

Then, we move both of our molar mass terms onto one side and our RMS speed terms onto the other:

$$\frac{M_A}{M_B}=\frac{\nu_rms,B^2}{\nu_rms,A^2}$$

Lastly, we take the square root of both sides:

$$\sqrt\frac{M_A}{M_B}=\frac{\nu_rms,B}{\nu_rms,A}$$

Now that we know how we got our equation, let's see it in action.Earlier, we calculated that helium would diffuse 2.25x faster than neon, below is a diagram showing this process:

Essentially, helium is going to diffuse faster since it is lighter. This means that more helium particles will reach the neon "side".

Think of it like rolling a ping-pong ball versus a soccer ball. If I rolled both balls with the exact same amount of energy, the ping-pong ball will travel farther (i.e. have a greater velocity) than the soccer ball since the ping-pong ball is much lighter.

However, after a certain amount of time, there will be an equilibrium of gases, i.e. the same concentration on both sides.

Now let's talk about **effusion.**

As a reminder, here's the definition of effusion from earlier:

**Effusion** is the process of gas particles escaping their container into another container through a small hole. This hole's diameter is much smaller than the particle's mean free path, which is the distance a particle travels before it collides with something. Essentially, this means that only one particle can travel through the hole at a time.

Essentially, effusion is the same as diffusion, except the particles are passing through a hole instead of moving through an open space.Here's what this process looks like:

Like with diffusion, during effusion, gases are moving to a less concentrated area. Now let's see what **effusion **looks like with two gases according to Graham's law:

The two balloons are connected by a small hole, which we assumed to be sealed (i.e. no gas can escape besides the exchange between the two balloons). Since the helium moves faster, it will effuse at a faster rate than the neon. This means the neon balloon will inflate as the helium effuses in, while the helium balloon deflates since it is losing that helium.

Now that we better understand the concept of effusion and diffusion, let's work on some examples!

**A sample of nitrogen and oxygen gas is in a container with a small hole leading to another, empty container. Which of the gases will effuse first?**

- The molar mass of nitrogen is 14.00 g/mol and the molar mass of oxygen is 16.00 g/mol.

While we can plug this into our equation, all we really need to do is look at the molar masses. Nitrogen is lighter, so it will effuse faster, and therefore first.

Now let's do an example where we actually calculate something:

**What is the ratio of the rate of diffusion for chlorine (Cl _{2}) gas and krypton (Kr) gas?**

- The molar mass of chlorine is 35.45 g/mol and the molar mass of krypton is 83.80 g/mol.

Since chlorine gas is Cl_{2} and *not *Cl, we need to double the molar mass value when we plug it into our equation:

$$\frac{Rate_A}{Rate_B}=\sqrt{\frac{M_B}{M_A}}$$

$$\frac{Rate_{Cl2}}{Rate_{Kr}}=\sqrt{\frac{M_{Kr}}{M_{Cl2}}}$$

$$\frac{Rate_{Cl2}}{Rate_{Kr}}=\sqrt{\frac{83.80\frac{g}{mol}}{(35.45\frac{g}{mol}*2)}}$$

$$\frac{Rate_{Cl2}}{Rate_{Kr}}=\sqrt{\frac{83.80\frac{g}{mol}}{70.9\frac{g}{mol}}}$$

$$\frac{Rate_{Cl2}}{Rate_{Kr}}=\sqrt{1.18}$$

$$\frac{Rate_{Cl2}}{Rate_{Kr}}=1.09$$

Since chlorine gas and krypton gas are similar in mass, the difference in the rate of diffusion isn't that large. The greater the difference in mass, the greater the ratio of rates will be.

**Graham's law**states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of the molar masses of its particles.- Basically, the heavier gas will move slower than the lighter one

**Diffusion**is the process of particles moving from an area of high density to one of low density**Effusion**is the process of gas particles escaping their container into another container through a small hole. This hole's diameter is much smaller than the particle's**mean free path,**which is the distance a particle travels before it collides with something. Essentially, this means that only one particle can travel through the hole at a time.- The equation for graham's law is:$$\frac{Rate_A}{Rate_B}=\sqrt{\frac{M_B}{M_A}}$$
Where M

_{A }and Rate_{A}are the molar mass and rate of diffusion/effusion of gas A, respectively, and M_{B}and Rate_{B}are the respective molar mass and rate of diffusion/effusion of gas B

**Graham's law **states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of the molar masses of its particles.

Essentially, lighter gases will effuse/diffuse faster than heavier ones.

**Diffusion **is the process of particles moving from an area of high density to one of low density

Graham's law of diffusion states that the lighter gas will diffuse faster than the heavier gas.

**Effusion **is the process of gas particles escaping their container into another container through a small hole. This hole's diameter is much smaller than the particle's **mean free path, **which is the distance a particle travels before it collides with something. Essentially, this means that only one particle can travel through the hole at a time.

Graham's law of effusion states that the lighter gas will effuse faster than the heavier one.

The equation for graham's law is:

$$\frac{Rate_A}{Rate_B}=\sqrt{\frac{M_B}{M_A}}$$

Where M_{A }and Rate_{A} are the molar mass and rate of gas A, respectively, and M_{B} and Rate_{B} are the respective molar mass and rate of gas B

More about Graham's Law

Be perfectly prepared on time with an individual plan.

Test your knowledge with gamified quizzes.

Create and find flashcards in record time.

Create beautiful notes faster than ever before.

Have all your study materials in one place.

Upload unlimited documents and save them online.

Identify your study strength and weaknesses.

Set individual study goals and earn points reaching them.

Stop procrastinating with our study reminders.

Earn points, unlock badges and level up while studying.

Create flashcards in notes completely automatically.

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.

Over 10 million students from across the world are already learning smarter.

Get Started for Free