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Physical Chemistry I (TKK-2246) 13/14 Semester 2 Instructor: Rama Oktavian Office Hr.: M.13-15, Tu , W , Th , F

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Outlines 1. Ideal gas properties 2. Molar mass of gas 3. Molar mass of volatile component 4. Gas mixture

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Review Learning check A sealed flask with a capacity of 1 dm 3 contains 5 g of ethane. The flask is so weak that it will burst if the pressure exceeds 1 MPa. At what temperature will the pressure of the gas reach the bursting pressure ?

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Review Learning check A perfect gas undergoes isothermal compression, which reduces its volume by 1.80 dm 3. The final pressure and volume of the gas are 1.97 bar and 2.14 dm 3, respectively. Calculate the original pressure of the gas in (a) bar, (b) Torr

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Review Learning check A large cylinder for storing compressed gases has a volume of about m3. If the gas is stored under a pressure of 15 MPa at 300 K, how many moles of gas are contained in the cylinder ? What would be the mass of oxygen in such a cylinder ?

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Review Learning check A manometer consists of a U-shaped tube containing a liquid. One side is connected to the apparatus and the other is open to the atmosphere. The pressure inside the apparatus is then determined from the difference in heights of the liquid. Suppose the liquid is water, the external pressure is 770 Torr, and the open side is 10.0 cm lower than the side connected to the apparatus. What is the pressure in the apparatus? (The density of water at 25°C is g cm −3.)

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Ideal gas and Real gas Ideal gas The ideal gas law is used to describe the behavior of an ideal gas. Ideal gas: hypothetical gas that obeys kinetic molecular theory and the ideal gas law

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Ideal gas and Real gas Ideal gas The ideal gas law was useful in determining the properties of a specific sample of gas at constant T, P, V, and n. We often need to know how a change in one (or more) properties impacts the other properties for a sample of a gas

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Ideal gas and Real gas Real gas deviations from the perfect gas law because molecules interact with one another Repulsive forces are significant only when molecules are almost in contact Attractive intermolecular forces have a relatively long range and are effective over several molecular diameters

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Ideal gas and Real gas Real gas The compression factor For ideal gas P moderate Z < 1

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Ideal gas and Real gas Real gas The compression factor

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Ideal gas and Real gas Equation of state for Real gas Virial equation of state How to describe this P-V behavior?

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Ideal gas and Real gas Equation of state for Real gas Virial equation of state

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Ideal gas and Real gas Equation of state for Real gas Virial equation of state

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Ideal gas and Real gas Equation of state for Real gas Virial equation of state The second virial coefficient B′ can be obtained from measurements of the density ρ of a gas at a series of pressures. Show that the graph of p/ρ against p should be a straight line with slope proportional to B′.

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Molar mass of ideal gas Determination of molar mass for ideal gas Ideal gas equation Intensive properties and measurable

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Molar mass of ideal gas Determination of molar mass for ideal gas Gas density Density is higher 1. for gases with a higher molar mass Gases 2. at higher pressures 3. at lower temperatures

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Molar mass of ideal gas Determination of molar mass for ideal gas Example if chemical analysis of a gas yields an empirical formula (CH 2 )n, then the molar mass must be some multiple of 14 g/mol ; the possibilities are 28, 42, 56, 70, and so on. If a molar mass determination using Eq. (2. 20) yields a value of 54 g/mol, then we may conclude that n = 4 and that the material is one of the butenes.

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Molar mass of ideal gas Determination of molar mass for ideal gas Problem : Calculation of Molecular Weight of a Natural Gas - Methane A sample of natural gas is collected at 25.0 C in a ml flask. If the sample had a mass of g at a pressure of torr, what is the molecular weight of the gas? Use the ideal gas law to calculate n, then calculate the molar mass.

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Molar mass of ideal gas Determination of molar mass for ideal gas Problem At 100°C and 1.60 kPa, the mass density of phosphorus vapour is kg m −3. What is the molecular formula of phosphorus under these conditions?

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Molar mass of ideal gas Determination of molar mass for ideal gas Problem A series of measurements are made in order to determine the molar mass of an unknown gas. First, a large flask is evacuated and found to weigh g. It is then filled with the gas to a pressure of 735 torr at 31°C and reweighed; its mass is now g. Finally, the flask is filled with water at 31°C and found to weigh g. (The density of the water at this temperature is g/mL.) Assuming that the ideal-gas equation applies, calculate the molar mass of the unknown gas.

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Gas mixture Air is an example of an ideal gas mixture and has the following approximate composition. Component % by Volume N O Argon 0.92 CO2 + trace elements 0.03

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Gas mixture Properties of gas mixture k gases T = T m V = V m P = P m m = m m The total mass of the mixture m m and the total moles of mixture N m are defined as

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Gas mixture Properties of gas mixture Volume concentration Unit : mol/m 3 Volume concentration molarity

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Gas mixture Properties of gas mixture The composition of a gas mixture is described by specifying either the mass fraction mf i or the mole fraction y i of each component i. Note that

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