Chemistry 141 Wednesday, October 10, 2017 Lecture 16 The Gas Laws Chemistry 11 - Lecture 11 9/30/2009 Chemistry 141 Wednesday, October 10, 2017 Lecture 16 The Gas Laws

Introduction to gases Why learn about gases? They are important in chemistry and to the existence of life! Teach us about the physics of molecules and ensembles of molecules

Pressure An open-ended tube of mercury up-ended in a dish of mercury does not spill out Why not? Copyright © 2002 by Houghton Mifflin Company. All rights reserved.

Atmospheric pressure What is the pressure exerted by the atmosphere on the surface of the earth? m = mass of atmosphere = 5×1018 kg g = acceleration due to gravity = 9.81 m/s A = surface area of Earth = 5×1014 m2

Units of Pressure The pressure exerted by the atmosphere at sea level is: height of barometer mercury column

How much is an atmosphere? Otto von Guericke's vacuum sphere couldn't be separated by the teams of horses (1654).

Measuring pressure: the manometer Allows evaluation of the pressure of a trapped gas compared to that of the atmosphere. Copyright © 2002 by Houghton Mifflin Company. All rights reserved.

Measuring pressure: the manometer In both of the examples shown below, the height of the mercury column is 18 mm. What is the pressure of the trapped gas in each case? (Assume atmospheric pressure of 760 mmHg or 1 atm.) a. 1.18 atm b. 709 mmHg c. 778 mmHg d. 18 mmHg e. 742 mmHg f. 0.82 atm Case 1 Case 2 Copyright © 2002 by Houghton Mifflin Company. All rights reserved.

Boyle’s experiments What happens when mercury is added to the open end of the J tube? Pressure of trapped gas increases Volume of trapped gas decreases Copyright © 2002 by Houghton Mifflin Company. All rights reserved.

Boyle’s measurements (ml) (inHg) (inHg) 48 0.00 29.13 1398 Volume Hg height Ptotal =Patm + PHg PV (ml) (inHg) (inHg) 48 0.00 29.13 1398 44 2.81 31.94 1405 40 6.19 35.31 1413 36 10.19 39.31 1415 32 15.06 44.19 1414 28 21.19 50.31 1409 24 29.69 58.81 1412 20 41.46 70.69 1414 16 58.75 87.88 1406 12 82.44 111.56 1339 -4 +2.81 +3.38 roughly constant -4 +23.69 Need to add more and more Hg to get the same change in volume It gets harder and harder to compress the gas

The volume of a gas is inversely proportional to its pressure Boyle’s Law Volume decreases Pressure increases The volume of a gas is inversely proportional to its pressure Copyright © 2002 by Houghton Mifflin Company. All rights reserved.

Using gas laws 5.00 L of krypton at STP is compressed at constant temperature until a final volume of 2.30 L is reached. What is the final gas pressure?

Concept Question What will happen to the volume of an inflated balloon when it is placed in liquid nitrogen (77 K)? goes up goes down stays constant

Charles’s Law The volume of a gas is proportional to its temperature decrease in T decrease in V V = bT + C Copyright © 2002 by Houghton Mifflin Company. All rights reserved.

Absolute Temperature V = bT + C V = bT We can define a new scale of temperature such that the zero of temperature is the point where the gases have zero volume. This temperature is called absolute zero. Absolute zero = -273.15 °C T(K) = T(°C) + 273.15 Copyright © 2002 by Houghton Mifflin Company. All rights reserved.

Avogadro’s Hypothesis Gay-Lussac noted that the volumes of gases at same T and P that react together are in the ratio of small whole numbers Avogadro concluded that equal volumes of gases contain equal numbers of particles (at same T and P) The volume a gas occupies is proportional to the number of particles n = # of particles in 1 volume a = a constant V = an 2V = a(2n)

Combining the gas laws Boyle’s Law: Charles’s Law: Avogadro’s Law: combine constants into R The ideal gas law