ideal gas

•Definition of Ideal Gases: An ideal gas is a

theoretical gas composed of many randomly

moving point particles that interact only when

they collide elastically. The concept of an ideal

gas helps in understanding the behavior of real

gases under various conditions and forms the

basis for the ideal gas law.

•Purpose of the Ideal Gas Model: The ideal

gas model simplifies the complex behavior of

real gases and provides a foundation for

understanding gas laws. It is particularly

accurate for gases at high temperatures and

low pressures where the behavior of real gases

closely approximates that of ideal gases.

•Definition of Ideal Gases: An ideal gas is a

theoretical gas composed of many randomly

moving point particles that interact only when

they collide elastically. The concept of an ideal

gas helps in understanding the behavior of real

gases under various conditions and forms the

basis for the ideal gas law.

•Purpose of the Ideal Gas Model: The ideal•Definition: Boyle’s Law states that the pressure of a given amount of

gas is inversely proportional to its volume when the temperature and

the number of particles are held constant.

•Mathematical Expression: P1V1=P2V2P1 V1 =P2 V2 Where:

•P1P1 and P2P2 are the initial and final pressures of the gas.

•V1V1 and V2V2 are the initial and final volumes of the gas.

•Explanation:

•If the volume of a gas decreases, the pressure increases, provided the

temperature and the number of gas particles remain constant.

•Conversely, if the volume increases, the pressure decreases.

•Graphical Representation:

•A graph of pressure (P) versus volume (V) for a gas at constant

temperature is a hyperbola. This illustrates the inverse relationship

between pressure and volume.

•Example:

•If a gas at 1.0 atm pressure occupies a volume of 2.0 liters, and the

volume is reduced to 1.0 liter while keeping the temperature constant,

the pressure will increase to 2.0 atm.

•Real-World Application:

•Boyle’s Law is applied in various real-life scenarios, such as in the

functioning of syringes, where pulling the plunger increases volume,

reducing pressure, and drawing fluid into the barrel.

gas model simplifies the complex behavior of

real gases and provides a foundation for

understanding gas laws. It is particularly

accurate for gases at high temperatures and

low pressures where the behavior of real gases

closely approximates that of ideal gases.

•Definition: Charles's Law states that the volume of a given amount of gas is directly

proportional to its absolute temperature, provided the pressure and the number of gas

particles remain constant.

•Mathematical Expression: V1T1=V2T2T1 V1 =T2 V2 Where:

•V1V1 and V2V2 are the initial and final volumes of the gas.

•T1T1 and T2T2 are the initial and final temperatures of the gas in Kelvin.

•Explanation:

•As the temperature of a gas increases, its volume increases, assuming constant

pressure.

•Conversely, when the temperature decreases, the volume decreases.

•Graphical Representation:

•A graph of volume (V) versus temperature (T) for a gas at constant pressure is a

straight line, showing the direct proportionality.

•Example:

•If a gas occupies a volume of 3.0 liters at 300 K, and the temperature is increased to

600 K while keeping the pressure constant, the volume will increase to 6.0 liters.

•Real-World Application:

•Charles's Law can be observed in hot air balloons, where heating the air inside the

balloon increases its volume, causing the balloon to rise.

•Definition: Avogadro’s Law states that the volume of a gas is directly proportional to the

number of moles (n) of gas present, provided the pressure and temperature are constant.

•Mathematical Expression: V1n1=V2n2n1 V1 =n2 V2 Where:

•V1V1 and V2V2 are the initial and final volumes of the gas.

•n1n1 and n2n2 are the initial and final number of moles of the gas.

•Explanation:

•Increasing the number of gas particles while keeping pressure and temperature constant will

increase the volume.

•Decreasing the number of gas particles will decrease the volume.

•Example:

•If 1 mole of gas occupies 2 liters, then 2 moles of the same gas at the same conditions will

occupy 4 liters.

•Application:

•Avogadro’s Law helps explain the relationship between the number of particles and the

volume of gases, which is essential in stoichiometry and chemical reactions involving gases.

•Definition: Gay-Lussac’s Law states that the pressure of a

gas is directly proportional to its absolute temperature when

the volume and the number of gas particles are constant.

•Mathematical Expression: P1T1=P2T2T1 P1 =T2 P2

Where:

•P1P1 and P2P2 are the initial and final pressures of the gas.

•T1T1 and T2T2 are the initial and final temperatures of the

gas in Kelvin.

•Explanation:

•As the temperature of a gas increases, the pressure

increases, assuming constant volume.

•Conversely, a decrease in temperature leads to a decrease

in pressure.

•Example:

•If a gas at 300 K exerts a pressure of 2 atm, raising the

temperature to 600 K will increase the pressure to 4 atm.

•Application:

•This law is observed in pressure cookers, where increasing

the temperature increases the pressure, cooking food faster.

•Definition: The Combined Gas Law combines Boyle’s, Charles’s, and Gay-

Lussac’s laws into a single equation, showing the relationship between

pressure, volume, and temperature when the number of particles is

constant.

•Mathematical Expression: P1V1T1=P2V2T2T1 P1 V1 =T2 P2 V2 Where:

•P1P1 , V1V1 , and T1T1 are the initial pressure, volume, and temperature.

•P2P2 , V2V2 , and T2T2 are the final pressure, volume, and temperature.

•Explanation:

•The combined gas law allows for the calculation of changes in one variable

when the other two are changed.

•Example:

•If a gas has a pressure of 1 atm, volume of 2 liters, and temperature of

300 K, and the volume changes to 1 liter at 400 K, the new pressure can be

calculated using the combined gas law.

•Application:

•This law is useful in situations where multiple variables change, such as in

weather balloons or HVAC systems.

•Definition: The Combined Gas Law combines Boyle’s, Charles’s, and Gay-

Lussac’s laws into a single equation, showing the relationship between

pressure, volume, and temperature when the number of particles is

constant.

•Mathematical Expression: P1V1T1=P2V2T2T1 P1 V1 =T2 P2 V2 Where:

•P1P1 , V1V1 , and T1T1 are the initial pressure, volume, and temperature.

•P2P2 , V2V2 , and T2T2 are the final pressure, volume, and temperature.

•Explanation:

•The combined gas law allows for the calculation of changes in one variable

when the other two are changed.

•Example:

•If a gas has a pressure of 1 atm, volume of 2 liters, and temperature of

300 K, and the volume changes to 1 liter at 400 K, the new pressure can be

calculated using the combined gas law.

•Application:

•This law is useful in situations where multiple variables change, such as in

weather balloons or HVAC systems.

•The Ideal Gas Law is a fundamental equation in chemistry that relates the

pressure, volume, temperature, and number of moles of an ideal gas. The equation

is:

•PV=nRTPV=nRT

•Where:

•PP is the pressure of the gas (in units like atm or Pa),

•VV is the volume of the gas (in liters or cubic meters),

•nn is the number of moles of the gas,

•RR is the ideal gas constant, which is typically 0.0821 L·atm/mol·K or 8.314 J/mol·K

depending on the units,

•TT is the temperature of the gas (in Kelvin).

•To determine molar quantities (like the number of moles, nn) using the Ideal Gas

Law, you can rearrange the equation:

•n=PVRTn=RTPV This formula can be used in various situations where you know

three of the variables (P, V, T, or n) and need to calculate the fourth.

•Example:

•Suppose you have a gas with a pressure of 2.00 atm, a volume of 10.0 L, and a

temperature of 300 K. To calculate the number of moles of the gas, use the Ideal

Gas Law: