(BOYLE LAW)(sometimes referred to as the Boyle-Mariotte law) is one of many gas laws and a special case of the ideal gas law. Boyle's law describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system.^[1][2] The law was named after chemist and physicist Robert Boyle, who published the original law in 1662.^[3] The law itself can be stated as follows:

A gas consists of a collection of small particles traveling in straight-line motion and obeying Newton's Laws.

• The molecules in a gas occupy no volume (that is, they are points).
• Collisions between molecules are perfectly elastic (that is, no energy is gained or lost during the collision).
• There are no attractive or repulsive forces between the molecules.

The average kinetic energy of a molecule is 3kT/2. (T is the absolute temperature and k is the Boltzmann constant.)
CHARLES LAW)( (also known as the law of volumes) is an experimental gas law which describes how gases tend to expand when heated. It was first published by French natural philosopher Joseph Louis Gay-Lussac in 1802,^[1] although he credited the discovery to unpublished work from the 1780s by Jacques Charles. The law was independently discovered by British natural philosopher John Dalton by 1801, although Dalton's description was less thorough than Gay-Lussac's.^[2] The basic principles had already been described a century earlier by Guillaume Amontons.
Taylor Buchanan was the first to demonstrate that the law applied generally to all gases, and also to the vapours of volatile liquids if the temperature was more than a few degrees above the boiling point.^{[citation needed]} His statement of the law can be expressed mathematically as:

where V₁₀₀ is the volume occupied by a given sample of gas at 100 °C; V₀ is the volume occupied by the same sample of gas at 0 °C; and k is a constant which is the same for all gases at constant pressure. Gay-Lussac's value for k was ¹⁄_2.6666, remarkably close to the present-day value of ¹⁄_2.7315.
A modern statement of Charles' law is:

At constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature on the absolute temperature scale (i.e. the gas expands as the temperature increases).^[3]

which can be written as:

where V is the volume of the gas; and T is the absolute temperature. The law can also be usefully expressed as follows:

• Gay-Lussac's name is also associated — erroneously — with another gas law, the so-called pressure law, which states that:
  

  The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas' absolute temperature.

  Simply put, if a gas' temperature increases then so does its pressure, if the mass and volume of the gas are held constant. The law has a particularly simple mathematical form if the temperature is measured on an absolute scale, such as in kelvins. The law can then be expressed mathematically as:
  

  

  or
  

  

  where:
  

  P is the pressure of the gas (measured in ATM).

  T is the temperature of the gas (measured in Kelvin).

  k is a constant.

  This law holds true because temperature is a measure of the average kinetic energy of a substance; as the kinetic energy of a gas increases, its particles collide with the container walls more rapidly, thereby exerting increased pressure.
  For comparing the same substance under two different sets of conditions, the law can be written as:
  

  

  Amontons' Law of Pressure-Temperature: The pressure law described above should actually be attributed to Guillaume Amontons, who, in the late 17th century (more accurately between 1700 and 1702^[3][4]), discovered that the pressure of a fixed mass of gas kept at a constant volume is proportional to the temperature. Amontons discovered this while building an "air thermometer". Calling it Gay-Lussac's law is simply incorrect as Gay-Lussac investigated the relationship between volume and temperature (i.e. Charles' Law), not pressure and temperature.
  Charles' Law was also known as the Law of Charles and Gay-Lussac, because Gay-Lussac published it in 1802 using much of Charles's unpublished data from 1787. However, in recent years the term has fallen out of favor, and Gay-Lussac's name is now generally associated with the law of combining volumes. Amontons' Law, Charles' Law, and Boyle's law form the combined gas law. The three gas laws in combination with Avogadro's Law can be generalized by the ideal gas law.
  The expression Gay-Lussac's law is used for each of the two relationships named after the French chemist Joseph Louis Gay-Lussac and which concern the properties of gases, though it is more usually applied to his law of combining volumes, the first listed here. One law relates to volumes before and after a chemical reaction while the other concerns the pressure and temperature relationship for a sample of gas.



• Behavior of Molecules in a Gas

To illustrate the significance of these postulates, consider the box containing a single molecule shown below. Start the animation and observe the molecule, represented by the blue ball, bouncing and traveling back and forth across the box. The collisions with the walls are perfectly elastic. Energy is neither gained nor lost from the collision. Because the walls do not move, the molecule's speed is unaffected by the collision. The graph plots the particle speed as a function of time. Observe that the speed has a constant value.A third gas law may be derived as a corollary to Boyle's and Charles's laws. Suppose we double the thermodynamic temperature of a sample of gas. According to Charles’s law, the volume should double. Now, how much pressure would be required at the higher temperature to return the gas to its original volume? According to Boyle’s law, we would have to double the pressure to halve the volume. Thus, if the volume of gas is to remain the same, doubling the temperature will require doubling the pressure.This law was first stated by the Frenchman Joseph Gay-Lussac (1778 to 1850). According to Gay-Lussac’s law, for a given amount of gas held at constant volume, the pressure is proportional to the absolute temperature. Mathematically,



where k_G is the appropriate proportionality constant.
Gay-Lussac’s law tells us that it may be dangerous to heat a gas in a closed container. The increased pressure might cause the container to explode.

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EXAMPLE 1 A container is designed to hold a pressure of 2.5 atm. The volume of the container is 20.0 cm³, and it is filled with air at room temperature (20°C) and normal atmospheric pressure. Would it be safe to throw the container into a fire where temperatures of 600°C would be reached?

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Solution Using the common-sense method, we realize that the pressure will increase at the higher temperature, and so



This would exceed the safe strength of the container. Note that the volume of the container was not needed to solve the problem.

This concept works in reverse, as well. For instance, if we subject a gas to lower temperatures than their initial state, the external atmosphere can actually force the container to shrink. The following video demonstrates how a sample of hot gas, when cooled will collapse a container. A syringe barrel is filled with hot steam (vaporized water) and a plunger placed to cap off the end. The syringe is then placed in a beaker of ice water to cool the internal gas. When the temperature of the water vapor decreases, the pressure exerted by the vapor decreases as well. This leads to a difference in pressure between the vapor inside the barrel and the atmosphere. Atmospheric pressure then pushes the plunger into the barrel.

Define molar volume for a gas at STP.?

Part A:
a.) The molar volume of an ideal gas is the volume occupied by one mole of gas at T = 0 C (298 K) and P=1.00 atm.
b.) The molar volume of an ideal gas is the volume occupied by one mole of gas at T = 25 C (298 K) and P =1.00 atm.
c.) The molar volume of an ideal gas is the volume occupied by one mole of gas at T = 0 C (273 K) and P = 1.00 atm.
d.) The molar volume of an ideal gas is the volume occupied by one mole of gas at T = 25 C (273 K) and = 1.00 atm.

Part B:
Give molar volume value for a gas at STP.

• The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units (SI) and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin is defined as the fraction ¹⁄_273.16 of the thermodynamic temperature of the triple point of water (273.16 K (0.01 °C; 32.02 °F)). ^[1]

The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907), who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or typeset as a degree. The kelvin is the primary unit of measurement in the physical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. Absolute zero at 0 K is −273.15 °C (−459.67 °F).