Chapter 05 - Chapter 5: The Gaseous State Gas Laws Because...

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Chapter 5 05 1 of 11 Chapter 5: The Gaseous State Gas Laws Because light behaves as a wave, we need to understand more about waves . . . 1. Gas Pressure and Its Measurement a. Pressure and Its Units Pressure is defined as the force per unit area of surface. A F P = To find the SI unit for pressure we rely on some physics: F = ma, or w = mg, where g is the acceleration due to gravity. g = 9.81 m/s 2 . The SI unit for mass is kg and for area is m 2 . Pa , Pascal ms kg m s m kg m N , newton A F P = = = = = 2 2 2 2 To estimate the magnitude of a Pascal, we can use this fact: the pressure exerted by a penny is about 100 Pa. The pressure exerted by the atmosphere is about 100,000 Pa. Other units used to measure pressure include the following: 1 atmosphere = 101,325 Pascal, Pa (exact) 760 mmHg = 101,325 Pa (exact) 760 torr = 101,325 Pa (exact) b. Measuring Pressure Pressure from the atmosphere is measured using a barometer. (See figure on the far left.) Pressure in a closed vessel is measured using a manometer. (See figure on the far right right.) In each case a liquid is used on which pressure is exerted causing it to rise in a tube. The height of that column is a measure of pressure. The pressure of the atmosphere is illustrated in the center figure.
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Chapter 5 05 2 of 11 To relate this to our previous work and equation, we return to physics and a different expression for pressure: gdh P = where g is given above, d is the density of the liquid in kg/m 3 and h is the height of the liquid column in m. The pressure is then in Pa. However, we can also use this equation to compare different liquids in the column measuring the same pressure: 2 2 1 1 h gd h gd = 2 2 1 1 h d h d = This means that density and the height of the column are inversely related. Thus, the more dense the liquid, the shorter the column, and vice versa. 2. Empirical Gas Laws What follows are relationships between two of the four gas variables. These were determined experimentally and, thus, are empirical. Gas Variables Amount, n, in moles Pressure, P, usually in atm Volume, V, usually in L Temperature, T, in K a. Boyle’s Law: Relating Volume and Pressure Boyle s Law is illustrated in the diagram to the right. As mercury is added to the J-tube, increasing the pressure, the volume of the gas in the tip of the “J” decreases. We can even look at this more quantitatively. The J-tube on the left shows the gas at atmospheric pressure, 760 mmHg or 1 atm, where the volume is 100 mL. In the J-tube in the center, the pressure in the tube is atmospheric plus 760 mmHg for a total of 2 atm. Thus, the pressure has been doubled. The volume is now 50 mL or one-half the original volume. In the J-tube on the right, the pressure is now atmospheric plus 1560 mmHg or a total of 3 atm. The volume is now 33 mL or one-third the original volume. The same relationship is illustrated to the left.
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Chapter 05 - Chapter 5: The Gaseous State Gas Laws Because...

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