There are 3 experimental gas laws used to describe the way in which gases behave. If these laws are combined with Avogadro’s principle the ideal gas equation is formed. This is an example of an energy balance equation.
Some conditions will need to be known such as standard ambient temperature and pressure.
If 2 gases are mixed together Dalton’s law can be used to calculate the pressure of each of the gases.
- What are the 3 experimental gas laws?
- What is Avogadro’s principle?
- State the ideal gas equation?
- What are the values for the standard ambient temperature and pressure?
- What is Dalton’s Law and how can it be used to calculate the partial pressure of a gas in a mixture?
Boyle's law states for a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume.
Charles law states for a fixed mass of gas at contstant pressure, the volume is directly proportional to the temperature.
Pressure law states for a fixed mass of gas at constant volume, the pressure is direstly proportional to the temperature.
Avogadro's principle states that the volume of a gas is proportional to the number of moles at a constant temperature and pressure.
Standard ambient temperature and pressure is 298.15K and 100kPa.
Dalton's law states for a mixture of gases the total pressure is directly proportional to the sum of the partial pressures exterted by each gas.
Kinetic Theory of Gases
Gas molecules in a container are always moving. Therefore they have kinetic energy. This is related using the kinetic theory equation and uses the root mean square speed of the gas molecules.
However using this equation requires some assumptions to be made.
The distribution of speeds and energies is related using the Maxwell-Boltzmann Distribution.
Kinetic theory can be proved using effusion.
- State the kinetic theory equation?
- What is the root mean square speed?
- State the 3 assumptions for kinetic theory?
- Draw the Maxwell-Boltzmann Distribution Curve and what is shown by the integral of the curve?
The root mean square speed is statistical value based on the idea that gas molecules have a continous range of speeds. The root mean square speed takes an average of these speeds.
There are 3 main assumptions for kinetic theory:
- Gas molecules move in a random, ceaseless, constant motion.
- They undergo no interactions, except brief elastic collisions.
- The size of the particle is negligible when compared to the distance over which it moves between collisions.
The Maxwell-Boltzmann distribution shows the relation between the energy of a molecule and the number of molecules with that energy in a container. The integral of the curve therefore gives the total number of molecules.
Intermolecular Forces and the Joule-Thompson Effec
In reality intermolecular forces act in between molecules of gases. This would change the pressure and volume of a gas. This can be shown using the Van der Waals equation. Changes to the pressure and volume are denoted by the letters “a” and “b” respectively.
When a gas liquidises the Joule-Thompson effect occurs. This states that the energy needed to oppose attractive forces in between molecules is taken away from the kinetic energy. As a result different types of forces can cause different things to happen when a gas expands.
- State the Van der Waals equation and what do the constants “a” and “b” mean?
- When a gas liquefies, if attractive forces dominate does the gas cool or heat on expansion?
- When a gas liquefies, if repulsive forces dominate does the gas cool or heat on expansion?
In the Van der Waals equation "a" takes into account the attractive interactions in between the molecules and "b" is a measure of the size of the gas molecules.
When a gas liquefies...
- If attractive force dominate, the gas cools on expansion.
- If repulsive forces dominate, the gas heats on expansion.
Types of Systems, Boundaries and Work, Energy and
There are 3 types of system. These are open, closed and isolated.
Work, energy and heat are all related.
There are 2 types of boundaries - Diathermic and Adiabatic. The temperature changes in different ways changes depending on what reaction is happening.
- What is an open, closed and isolated system?
- When is work done?
- What is energy?
- What is heat and what is it caused by?
- What is a diathermic boundary and what temperature changes occur when exothermic and endothermic reactions take place in this system?
- What is an adiabatic boundary and what temperature changes occur when an exothermic reaction takes place in this system?
- An open system can exchange energy and matter with its surroundings.
- An closed system can exchange energy but not matter with its surroundings.
- An isolated system cannot exchange energy or matter with its surrounding.
Work is done when an object is moved against an opposing force. If the force isn't opposing but helps the object move, the energy of the system decreases.
Energy is the capacity to do work.
Heat is a form of energy which is caused by molecular vibrations.
Diathermic boundaries allow the transfer of heat energy.
- Exothermic reactions-------temperature remains the same.
- Endothermic reactions-------temperature remains the same.
Adiabatic boundaries don't allow the transfer of heat energy.
- Exothermic reactions-------temperature increases.
Heat Transfer, Zeroth's Law, Internal Energy, 1st
Heat can be transferred between 2 objects. If they are not at the same temperature heat energy will be transferred between the 2 objects until they are at thermal equilibrium.
Zeroth's can be used to relate the temperature/thermal equilibrium between 3 objects- A, B and C.
The first law of thermodynamics can be used to describe the internal energy of a system.
Internal energy for a system can change.
- State Zeroth’s Law.
- What is meant by the term internal energy and what type of function is it, what does this mean?
- State the 1st law of thermodynamics.
- Most changes in internal energy are small. Write 2 equations the difference between small and large changes in internal energy of a system?
Zeroth's law states that if object A is in thermal equilibrium with B and object B is in thermal equilibrium with C, then object A is in thermal equilibrium with C.
The internal energy of a system is the total energy a system has. It is a state function which means it doesn't matter which route is taken from the start to the end point, the change in internal energy is still the same.
The first law of thermodynamics states that the internal energy of a system remains constant and can be increased by doing work on the system or by heating it.
This can also be re-written as the work needed to change an adiabatic system from one state to another remains the same.
Expanding Gases and Heat Transactions
When a gas expands work is done by the gas and its internal energy decreases.
Gases can expand in different conditions.
- Free expansion – No opposing force, therefore no work is done.
- Expansion at constant pressure.
- Reversible expansion results in small changes in internal energy. Therefore there is no motion.
- Isothermal reversible expansions.
- Write an equation for work done?
- How is this equation related to the work done by an expanding gas? (Show using an integral)
- What is the work done by an expanding gas at constant pressure?
- What is the work done by a gas expanding isothermally and reversibly?
- If the work done by a gas is zero what can be said about the internal energy and the heat energy?
Equation for Work Done
Intergral for Work Done by an Expanding Gas
Work done by an expanding gas at constant pressure
Work done by a gas expanding isothermally and reversibly
If the work done is zero the internal energy is equal to the heat energy.
Heat Capacities and Enthalpies
Heat capacity is the change in internal energy with temperature at a constant volume. The molar heat capacity is the heat capacity per mole of a substance. It is different for different types of gases
For a solid/liquid to gas reaction the change in volume is very large. This can change the equation defining enthalpy. The enthalpy of a system increases as a system heats up. This can be related using the heat capacity at constant pressure. For larger changes in temperature the heat capacity at constant pressure changes.
- What is the definition of heat capacity? Is it an extensive or intensive property?
- Are molar heat capacity values extensive or intensive properties?
- What is the molar heat capacity for monoatomic gases?
- What is the molar heat capacity for diatomic and linear triatomic gases?
- What is the definition of enthalpy?
- Write an integral defining the change in enthalpy as a system is heated up.
- How does the heat capacity at constant pressure vary at high temperature?
- Write equations showing the heat change at constant volume and at constant pressure.
Heat capacity is the change in internal energy with temperature at a constant volume. It is an extensive property which means it depends on how much of something you have. Molar heat capacities are examples of intensive properties. This value varies for different gases:
- For monoatomic gases it's 3R/2.
- For diatomic and linear triatomic gases it's 5R/2.
Enthalpy can be defined using an equation.
Enthalpy increases as a system is heated up. This can be related to the heat capacity at constant pressure using an intergral.
For large changes in temperature the heat capacity at constant pressure varies as shown in the equation.
The heat energy constant pressure and at constant volume can be calculated as shown below.
Enthalpy values are different for different reactions. As they are state functions they can be added together.
Hess’s law can be used to calculate the enthalpy change for a reaction at standard conditions.
Sometimes reactions don’t happen at 298K. This results in a new change in enthalpy value, therefore we need to use Kirchhoff’s Laws. Remember to write chemical equations.
Are enthalpy changes for endothermic reactions negative or positive?
Are enthalpy changes for exothermic reactions negative or positive?
State Hess’s Law.
State Kirchhoff’s Law and all components.
Enthalpy changes for exothermic reactions are negative and for endothermic reactions they are positive.
Hess's law states that the standard enthalpy change of an overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided into.
Kirchhoff's laws can be used to calculate enthalpy changes at different temperatures.
Some More Equations?????