Gases: Critical to Our Lives

How do we describe a gas? Does saying “a liter of air” really mean that much? You need to know the conditions at which that liter of air is measured. To describe a gas fully, you need to state four measureable quantities: Volume Temperature Number of Particles Pressure

Gas particles exert pressure when they collide with the walls of their container. For example, if you blow air into a rubber balloon, the collision of particles of air with the inside walls of the balloon will cause it to expand. The collisions cause an outward push, or force, against the inside walls. Pressure: force applied per unit area on a surface Gas Pressure Defined

Equation Defining Pressure force Pressure = ----------------------- area The SI unit for force is the newton, abbreviated N. It is the force that will increase the speed of a one-kilogram mass by one meter per second each second it is applied.

What We Mean By Pressure At Earth’s surface, each kilogram of mass exerts 9.8 N of force, due to gravity. Consider a ballet dancer with a mass of 51 kg. A mass of 51 kg exerts a force of 500 N (51 x 9.8) on Earth’s surface. No matter how the dancer stands, she exerts that much force against the floor. However, the pressure she exerts against the floor depends on the area of contact. Less area of contact means greater pressure on that area.

Atmospheric (Air) Pressure The atmosphere, the blanket of air surrounding earth, extends for hundreds of miles, and exerts pressure in all directions. At sea level, atmospheric pressure is about equal to 1.03 kg per square centimeter of surface, or 10.1 N/cm2. This pressure is caused by the gases that compose the atmosphere, which is composed of about 78% N2, 21% O2, and 1% other gases.

More About Air Pressure Air pressure varies at different points on Earth. The air pressure at higher altitudes is slightly lower than at sea level. Evangelista Torricelli, an Italian physicist, was the first to demonstrate that air exerted pressure. He invented a device called a barometer. Barometer: an instrument that is used to measure atmospheric pressure

Torricelli’s Experiment The mercury in the tube pushes downward because of gravitational force. The column of mercury in the tube is stopped from falling beyond a certain point because the atmosphere exerts a pressure on the surface of the mercury outside the tube. This pressure is transmitted through the fluid mercury and is exerted upward on the column of mercury.

Interpreting Torricelli’s Experiment The mercury in the tube falls only until the pressure exerted by its weight is equal to the pressure exerted by the atmosphere. So we can measure the pressure of the atmosphere directly in terms of the height of the mercury column in the barometer tube. At any given place on earth, the specific atmospheric pressure depends on both the elevation and the weather conditions, which cause changes in humidity and temperature. Greater pressure = higher column. Lower pressure = shorter column.

What is a manometer? A manometer is an instrument used to measure gas pressure in a closed container. We use the difference in the height of the mercury in the two arms to calculate the pressure of the gas in the flask.

Units of Pressure The SI unit of pressure is the pascal (Pa), that is, the force of 1 newton acting on one square meter: 1 Pa = 1 N/m2 An older, traditional unit of pressure is pounds per square inch (psi): 1 psi = 1 lb/in2 For barometers and manometers, we often report pressure in millimeters of mercury (mm Hg). In honor of Torricelli, we can also call it the Torr: 1 torr = 1 mm Hg Finally, we have the atmosphere (atm), often used to measure air pressure: 1 atm = 760 mm Hg

So that leads to a bunch of conversion factors... But here are the critical ones to remember: 1 atm = 760 mm Hg = 760 torr 1 atm = 1.013 x 105 Pa = 101.3 kPa (We assume an unlimited number of significant figures when making conversions in atm, mm Hg, and torr, since they are defined quantities. So use the measured values, not these factors, when deciding how to round off answers.)

A Little Conversion Practice The average atmospheric pressure in Denver, Colorado, is 0.830 atm. Express this pressure (a) in mm Hg and (b) in kPa: Convert a pressure of 570. torr (a) to atmospheres and (b) to kPa:

Standard Temperature and Pressure (STP) As you may recall, to compare volumes of gases, it is necessary to know the temperature and pressure at which the volumes are measured. For purposes of comparison, scientists have agreed on the standard conditions of exactly 1 atm pressure and 0 degrees C. These conditions are called standard temperature and pressure, or STP.

Dalton's Law of Partial Pressures John Dalton found that each gas exerts a pressure independently of the other gases present. Dalton's law of partial pressures: States that the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture. The portion of the total pressure contributed by a single gas is called its partial pressure. Ptotal = P1 + P2 + P3 + ...Pn

An Illustration of Dalton's Law

A Sample Partial Pressure Problem The pressure of a sample of air in a manometer is 102.3 kPa. What is the partial pressure of nitrogen (N2) in the sample if the combined partial pressures of the other gases is 22.4 kPa?

A Common Application of Partial Pressures: Collecting a Gas by Water Displacement Sometimes we carry out a reaction in which a gas is produced. One easy way to collect it is by water displacement. The gas is bubbled into an inverted container of water. As the gas collects, it displaces the water. The gas collected will be a mixture of the gas being produced plus water vapor. The partial pressure of the water vapor can be found at any given temperature and the partial pressure of the gas produced can be calculated from Dalton's law of partial pressures.

Boyle's Law Robert Boyle, an Irish chemist, did experiments to study the relationship between the pressure and the volume of a gas. He found that pressure and volume had an inverse relationship, that is, doubling the pressure decreases the volume by one-half, tripling the pressure decreases the volume by one-third. Conversely, reducing the pressure on a gas by one-third allows the volume of the gas to triple. Boyle's law: States that the volume of a given amount of gas held at a constant temperature varies inversely with the pressure.

Boyle's Law and Kinetic-Molecular Theory Because the pressure is caused by the collisions of moving particles hitting the container walls, so decreasing the volume causes there to be twice as many collisions of the particles with the walls of the container, so pressure will increase proportionately.

Boyle's Law Expressed Mathematically V = k x 1/P or PV = k where V is volume, P is pressure, and k is a constant for each particular gas If we compare a gas at an initial condition with the same gas at its final condition, we get the equation: P1V1 = P2V2

Some Sample Boyle's Law Problems 1. A gas has a pressure of 1.26 atm and occupies a volume of 7.40 L. If the gas is compressed to a volume of 2.93 L, what will its pressure be, assuming constant temperature? 2. A weather balloon with a volume of 1.375 L is released from Earth's surface at sea level. What volume will the balloon occupy at an altitude of 20.0 km, where the air pressure is 10.0 kPa?