L 3,4,5 - "Properties of Gases" Prof. Gianluigi...

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“Properties of Gases” Prof. GianluigiVeglia
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The physical state of a substance is defined by its physical properties. These properties are linked through the equation of state. The general form of the equation of state is: ( ) n V T f p , , =
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A gas is a substance that is highly compressible, not very dense (~1000 times less dense than a solid or a liquid at room temperature, and atmospheric pressure), able to expand (able to occupy the entire vessel that contains it). At sufficiently low pressures, all gases obey to the same equation of state , which we call ideal gas equation of state : Where P is the pressure, V is the volume, and T is the temperature, and n is the number of moles. Note that this expression is true for P →0(low pressures). nRT PV = nRT PV =
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If we take the ideal gas law and divide both sides for the n, we obtain: Where is the molar volume . Why do we do this? V RT V P =
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Pressure (P) and Temperature (T) are called intensive quantities (or intrinsic quantities). Intensive quantities are independent of the size of a system. For instance, if we divide a 1 L bottle of gas into 1000 “sub-bottles”, the pressure and the temperature of the sub-bottles are the same as those in the whole bottle. In contrast, volume (V) and number of moles (n) are extensive quantities . Their values depend on how much substance is present. In Physical Chemistry, we often have as a goal the development of mathematical descriptions of physical systems and we want the descriptions to be as general as possible. Therefore, the main goal is to develop relationships between intensive quantities rather than extensive quantities.
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Why do we call an equation of state? Because it expresses the relationships between “state variables” of the systems. The state variable of a system are properties that are independent of the history of a substance. That is, for a certain molar volume and temperature, the pressure of a gas can be calculated. It does not matter whether the gas has ever been hot or cold, or compressed into a liquid, etc. In principle, you should be able to determine any state variable (density, entropy, internal energy) given the identity of a system and two of its state variable. RT V P =
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What is the pressure? The pressure of a gas is the total force (F) exerted by a gas on the vessel that contains it divided by the area (A) over which the force is distributed: surface force A F P = = ). 2 1 2 1 1 1 = = s m kg Nm Pa bar atm 01325 . 1 1 = Pa bar 5 10 1 =
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We will see later that the temperature of a gas is related to the translational energy of the molecule in a system. For now, we will employ an operational definition of the T based on the ideal gas law: = R V P T P lim 0 16 . 273 1 1 = K Note that in this definition T is always positive
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Besides the definition of P and T in Chemistry it is important to define the amount of substance that the system contains (rather than its mass). The amount of
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L 3,4,5 - "Properties of Gases" Prof. Gianluigi...

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