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Gas Laws Boyles Law Charless Law Gay-Lussac Combined Gas Law

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Properties of Gases V = volume of the gas (liters, L) T = temperature (Kelvin, K) P = pressure (atmospheres, atm) n = amount (moles, mol) Gas properties can be modeled using math. Model depends on:

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Pressure - Temperature - Volume Relationship P T V Gay-Lussacs P T CharlesV T P T V Boyles P 1V1V

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Pressure - Temperature - Volume Relationship P T V Gay-Lussacs P T CharlesV T Boyles P 1V1V ___ P n V

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Pressure and Balloons A B = pressure exerted ON balloon A = pressure exerted BY balloon B When balloon is being filled: P A > P B When balloon is filled and tied: P A = P B When balloon deflates: P A < P B

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When the balloons are untied, will the large balloon (A) inflate the small balloon (B); will they end up the same size or will the small balloon inflate the large balloon? Why? Balloon Riddle A B C

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Robert Boyle Robert Boyle, an Irish chemist (1627-1691), performed the first quantitative experiments on gases used a j- shaped tube to study the relationship between the pressure of the trapped gas and its volume.

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Boyles Law Boyles Law states that at constant temperature (and constant number of gas molecules) the volume of a fixed amount of gas is inversely proportional to its pressure. Boyles Law: P 1 V 1 = P 2 V 2

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Boyle Proves Changes in Pressure cause Changes in Volume As the pressure in a closed system (like a piston) decreases, the volume of the gas inside the system increases. The pressure in the system decreases exponentially. Proving an indirect relationship.

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Example: Sulfur dioxide (SO 2 ), a gas, that plays a central role in the formation of acid rain, is found in the exhaust of automobiles and power plants. Consider a 1.53 L sample of gaseous SO 2 at a pressure of 5.6 kPa. If the pressure is changed to 15 kPa at a constant temperature, what will be the new volume of the gas?

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Solution: P 1 V 1 = P 2 V 2 P 1 = 5.6 kPaP 2 = 15 kPa V 1 = 1.53 LV 2 = ? Rearrange the formula to isolate V 2. P 1 V 1 = (5.6 kPa)(1.53 L) = O.571 L P 2 (15 kPa)

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Does Boyles law really work? Since Boyles experiments (only three centuries of technological advances!) we have found that his law only holds precisely at very low pressures. We describe a gas that strictly follows Boyles law an ideal gas.

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Jacques Charles In the century following Boyle, a French physicist, Jacques Charles (1746- 1823), was the first person to fill a balloon with hydrogen gas and who made the first solo balloon flight.

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Charless Law Charless Law states that at constant pressure (and constant number of gas molecules) the volume of a fixed amount of gas is directly proportional to its absolute temperature. *All gas laws must be calculated with Kelvin temperature!

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Volume vs. Temperature: Charles Law Notice the linear relationship. This relationship between temperature and volume describes a direct relationship. This means when temperature increases, so does the volume.

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The importance of 0 Kelvin At temperatures below 0 K, the extrapolated volume of gases would be negative. The fact that a gas cant have a negative volume tells us 0 K has a special significance. Absolute temperature is measured in Kelvins. At 0 K, all motion of any atom or bond ceases, therefore producing no energy. Temperatures of approximately 0.000001K have been produced in laboratories, but 0 K has never been reached.

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Example: A sample of a gas at 15°C and 1 atm has a volume of 2.58 L. What volume will the gas occupy at 38°C and 1 atm? (NOTE: The pressure did not change. So you do not need to worry about it!)

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Solution: V 1 = V 2 Dont forget to convert °C to K T 1 T 2 V 1 = 2.58LV 2 =? T 1 = 15°C=288K T 2 = 38°C=311K Rearrange to solve for V 2. V 1 T 2 = (2.58L)(311K) = 2.79 L T 1 (288K)

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Gay-Lussac Joseph Louis Gay-Lussac was a French chemist and physicist. He is known mostly for two laws related to gases, and for his work on alcohol-water mixtures, which led to the degrees Gay-Lussac used to measure alcoholic beverages in many countries. 1778 – 1850 Charles's law, describing how gases tend to expand when heated, was formulated by Joseph Louis Gay-Lussac in 1802, but he credited it to unpublished work by Jacques Charles.

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Gay-Lussacs Gas Law The pressure of a fixed mass and fixed volume of a gas is directly proportional to the gas's temperature. *All gas laws must be calculated with Kelvin temperature!

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The Combined Gas Law The combined gas law was derived from Boyles and Charless work. A direct relationship was observed. As temperature increased, volume increased. As volume increased pressure increased. This resulted in a combined formula to calculate changes observed in a gas due to changes in either temperature, pressure or volume.

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Combined Gas Law Equation By combining the equation for Boyles Law and Charless Law. We derive the Combined Gas Law Equation where:

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Example: A sample of a gas at 15°C and 2.0 atm has a volume of 2 mL. What volume will the gas occupy at 38°C and 1 atm?

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Solution P 1 V 1 = P 2 V 2 Dont forget to convert Temperatures! T 1 T 2 P 1 = 2 atmP 2 = 1 atm V 1 =2 mLV 2 =? T 1 =15 °C=288K T 2 =38°C=311K Rearrange to solve for V 2 ! V 2 = P 1 V 1 T 2 = (2 atm)(2 mL)(311K) = 4.32 mL T 1 P 2 (288K)(1 atm)

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Summary: Boyles Law – Inverse relationship when P V and if P V Charless Law -- Direct relationship When V T and if V T Gay-Lussac Law -- Direct relationship When P T and if P T

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