The Gaseous State.pdf 455ny

THE GASEOUS STATE PRESSURE 1 atm = 101,325 Pa = 101 kPa

BOYLE’S LAW At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure. V=k

𝟏 𝑷

, where k is a constant. OR

pV = constant and P1V1 = P2V2 when temperature is constant.

CHARLES’ LAW At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. V = mT, where m is a constant. OR 𝑽 𝑻

= constant and

𝐕𝟏 𝐓𝟏

=

𝐕𝟐 𝐓𝟐

when pressure is constant.

AVOGADRO’S LAW At any given temperature and pressure, the volume of a gas is directly proportional to the number of molecules present. V = k n, where k is a constant. OR 𝑽 𝒏

= constant and

𝐕𝟏 𝐧𝟏

=

𝐕𝟐 𝐧𝟐

when temperature and pressure are constant.

COMBINED GAS EQUATION 𝐏𝟏𝐕𝟏 𝐓𝟏

=

𝐏𝟐𝐕𝟐 𝐓𝟐

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IDEAL GAS An ideal gas is a hypothetical gas whose pressure – volume – temperature behaviour can be completely ed for by the ideal gas equation pV = nRT. pV = nRT     

T must always be expressed in Kelvin. n is usually expressed in moles. R = 8.31 J K-1 mol-1 1 cm3 = 1 × 10-6 m3 1 dm3 = 1 × 10-3 m3

GAS MIXTURES & PARTIAL PRESSUES In a mixture of gases, the pressure exerted by any individual gas on the sides of a container is known as the partial pressure of the gas. Dalton’s law of partial pressure states that the total pressure of a mixture of gases is the sum of the partial pressure of the constituent gases. Ptotal = PA + PB + Pc …

𝒏 (𝒂)

Pa = (𝒏 (𝒕𝒐𝒕𝒂𝒍)) Ptotal where

𝒏 (𝒂) 𝒏 (𝒕𝒐𝒕𝒂𝒍)

is called the mole fraction.

In a gas mixture, the partial pressure of any individual gas is proportional to its mole fraction in the mixture. In a mixture of gases, the amount (or number of moles) of any individual gas in proportion to the total amount of gas is called its mole fraction.

KINETIC MOLECULAR THEORY OF GASES The kinetic molecular theory is based on the following assumptions, as applied to an ideal gas whose particles are in continuous, random motion: 1. Gas particles behave as rigid spheres. 2. The size of the gas particles is so small compared to the space between them that we can assume that the particles themselves have negligible volume. The gas particles have negligible volume compared to the volume of their container. 3. The intermolecular forces between gas particles are negligible. 2

4. Collision between gas particles, and their collisions with the walls of the container, are perfectly elastic; there is no net loss or gain of kinetic energy during collision. 5. The average kinetic energy of the gas particles is directly proportional to the absolute temperature. So at a particular temperature, all types of gaseous particles have the same average kinetic energy.

MAXWELL-BOLTZMANN DISTRIBUTION CURVE

 

Although collectively the molecules in a gas sample have the same average kinetic energy, the individual molecules are moving at different speeds. At a given temperature heavier gases travel slower while lighter gases travel faster. 𝟏

(KE=𝟐mv2)





Given a gas sample at different temperatures, the speed distribution of the molecules shifts toward higher speeds and becomes less sharply peaked as the temperature (and kinetic energy) of the gas sample is increased. Even at low temperatures, there is small number of molecules having high speed and kinetic energy. This number of molecules increases with temperature, while the number of molecules with low speed and KE becomes smaller but does not vanish. 3

Important features: 1. Graph would have the same shape when either speed or kinetic energy is used as the x-axis. 2. Labels for vertical (y) axis include number of (gas) particles (or molecules), proportion of particles, or fraction of particles. 3. The area under the curve generally represents the total number of particles in the sample. For a fixed sample and different temperatures, the area should remain the same even when the curve shifts. 4. The peak of each curve represents the most probable speed (or KE). As the temperature increases, the peak decreases in height and shifts to the right as the distribution of molecular speeds becomes more spread out. 5. All curves start at the origin (0,0) because in a gas sample there are no particles with zero speed (or KE) and all particles must be moving. 6. The curves do not show a maximum speed (or KE) value. The curves do not intersect the x-axis again as there is theoretically no limit to the amount of speed (or KE) a particle can have.

DEVIATION FROM IDEAL BEHAVIOUR 

In practice, a real gas behave almost like an ideal gas and obeys the ideal gas equation closely and under the following conditions: At Low Pressure  



At low pressure, the gas molecules are relatively far apart. Intermolecular forces are negligible and observed pressure is close to that predicted by the ideal gas equation.

At High Temperature 

At high temperature, the gas molecules possess sufficiently high kinetic energy to overcome the intermolecular attractive forces. Hence the intermolecular forces are considered negligible.

The volume of the molecules themselves is negligible compared to the volume of the container. Real gas molecules a low pressure can be approximated to have negligible molecular size, and their behaviour would approach that of an ideal gas.

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

Conversely, a real gas behaves least like an ideal gas under the following conditions At High Pressure 

At high pressures, intermolecular distances become shorter and intermolecular forces become more significant. This lowers the impact of molecules colliding the container wall. Thus the observed pressure is less than that expected of an ideal gas.



The molecules take up a large portion of the volume of the container, resulting in a considerably smaller space in which the molecules can move. Thus it is no longer valid to assume that molecular size is negligible, as the total volume occupied by a real gas is actually greater than the volume predicted by the ideal gas equation.

At Low Temperature 

The kinetic energy of the gas particles decreases and this causes them to move more slowly and intermolecular forces become more significant. This also causes the collision to be inelastic. Eventually, it reaches a point where the particles can no longer overcome the intermolecular attractive forces, at which point real gases liquefy (condense to form a liquid).

Comparing the Behaviour of Different Real Gases 



Large molecules, which have large electron clouds, occupy more space and have stronger intermolecular forces between molecules, Hence they deviate more from ideal behaviour than molecules of smaller size. Polar molecules tend to have stronger intermolecular forces of attraction (e.g. permanent diploe – permanent dipole interactions or hydrogen bonding). Hence they would deviate more from ideal behaviour than non-polar molecules of similar size.

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MISCONCEPTIONS & REMARKS  

 

   



When water (or other molecule) boils, take note that the number of gaseous particles increases and this in turn increases pressure (if the container is enclosed). [T4 Q1] When the question states "explain … in of the behaviour of gas molecules" or "explain … in molecular ", you are not allowed to explain using the pV=nRT equation. [T4 Q1] Note that average kinetic energy is constant as long as the temperature is constant. Do not state that “ideal gases have negligible volume compared to the container”, the correct statement is that “particles of ideal gases have negligible volume compared to the container” or “molecular volume of the gas is insignificant with respect to the volume of the container” [T4 Q1] For an ideal gas, the volume of the container is the volume of the gas. When a gas dimerizes completely, the number of moles decreases by half. Note a constant temperature, pV = constant if the gas behaves ideally. [Class Test Q1] ing for the discrepancies in the volume occupied by gas under high pressure: Under conditions of high pressure, significant IMF (depends on different gases) exist between the gas molecules. Hence they are pulled closer together, which causes the actual volume of the gas to be smaller than that predicted by ideal gas equation. [Class Test Q1] Note if 2 or more variables are constant throughout the question, e.g. volume and constant R, it is possible to combine them into a single constant. E.g. 𝑝𝑉 𝑅𝑇

𝑅 𝑉

= k [TP4 Section B Q5]



For



to infinity, hence pV will NOT approach 0 (but 1). [TP4 Section A Q15] At a given temperature heavier gases travel slower while lighter gases travel faster. 𝟏 𝟐

(compressibility factor of one mole of any real gas), when p approaches 0, v increases

(KE= mv2) but their average kinetic energy are the same. 



[2012 BT1 Paper 1 Q17]

Take note of the number of atoms as well as the type of atoms in a molecule in determining its electron cloud size. CO2 has a bigger electron cloud than O2. Take note that there is an additional C atom is carbon dioxide, and hence the dispersion forces in carbon dioxide is stronger and it deviates more from an ideal gas. [2012 BT1 Paper 3 Q2] When a higher pressure is applied, the gas molecules are forced closer together, and the intermolecular forces becomes more significant. [2013 BT1 Paper 3 Q1]

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