Pressure Pressure: Force applied per unit area. Barometer: A device that measures atmospheric pressure. Manometer: A device for measuring the pressure of a gas in a container.

Pressure Units of Pressure Pascal: (abbrev. Pa) The SI unit for pressure. 1 standard atmosphere = atm = mm Hg = torr 1 standard atmosphere = 101,325 Pa = kPa atm = psi

Pressure and Volume: Boyle’s Law Boyle’s Law: Pressure times Volume equals a constant. PV=k where k is a constant at a specific temperature for a given amount of gas. If we know the volume of a gas at a given pressure, we can predict the new volume if the pressure is changed, provided that neither the temperature nor the amount of gas is changed.

Pressure and Volume: Boyle’s Law Example A sample has a volume of 1.51 L at a pressure of 635 torr. Calculate the final volume of the gas if the final pressure is 785 torr.

Volume and Temperature: Charles’s Law Charles’s Law: Proportionality constant times temperature is equal to volume. V = bT where T is in Kelvins and b is the proportionality constant. Charles’s Law implies that the amount of gas (moles) and pressure are constant. The volume of the gas is directly proportional to temperature on the Kelvin scale.

Volume and Temperature: Charles’s Law Example A sample has a temperature of 28 o C and a volume of 23 cm 3 at 1 atm. The final temperature was found to be 18 o C, assuming no change in pressure. Calculate the final volume.

Volume and Moles: Avogadro’s Law Avogadro’s Law: For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas. V = an or V = a n where V is the volume of the gas N is the number of moles a is the proportionality constant.

Volume and Moles: Avogadro’s Law Example 3H 2(g) + N 2(g)  2NH 3(g) If one has 15.0 L of H 2(g), what volume of N 2(g) is required for a complete reaction, given that both gases are at the same temperature and pressure?

The combined gas law Combined Gas Law: The following equation is called the combined gas law. It holds when the amount of gas (moles) is held constant. P 1 V 1 = P 2 V 2 T 1 T 2

The combined gas law Example A sample has a volume of 11.0 L at a temperature of 13 o C and a pressure of atm. The sample is heated to 56 o C at a final pressure of 1.18 atm. Calculate the final volume.

Standard (STD) molar volume Lets define the volume occupied by 1 mol of a gas under specified conditions. For 1 mol of an ideal gas at K and 1.0 atm, the volume of the gas is L, regardless of gas. 0 o C ( K) and 1.0 atm = standard temperature and pressure (STP)

The Ideal Gas Law Ideal gas Law: The equation for the ideal gas law is PV=nRT where R= L atm/mol K (universal gas constant). Derived from STP and standard molar volume

The Ideal Gas Law Example A 1.5 mol of a sample of gas has a volume of 21.0 L at 33 o C. What is the pressure of the gas.

Density of Gases  = m/V PV = nRT n = m/MM  PV = (m/MM)RT m/V = P  MM/RT = 

Dalton’s Law of Partial Pressures Partial Pressure: The pressure that the gas exerts if it were above in the container. For a mixture of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present. This can be expressed as P total = P 1 + P 2 + P where the subscripts refer to the individual gases. The pressures P 1, P 2, and P 3 are the partial pressures. Important Points 1. The volume of the individual gas particles must not be very important. 2. The forces among the particles must not be very important.

Dalton’s Law of Partial Pressures For a mixture of ideal gases, it is the total number of moles of particles that is important, not the identity of the individual gas particles. We can calculate the partial pressure of each gas from the ideal gas law.

Dalton’s Law of Partial Pressures Example A 2.0 L flask contains a mixture of N 2 and O 2 gas 25 o C. The total pressure of the mixture is 0.91 atm. The mixture is known to contain mol of N 2. Calculate the partial pressure of O 2 and the number of moles of O 2 present.

Dalton’s Law of Partial Pressures Pressure of gas in mixture of gases = product of its mole fraction and total pressure of mixture P A = X A P tot Ex: X nitrogen gas = What’s its partial pressure at STP?

The Kinetic Molecular Theory of Gases Kinetic Molecular Theory: The behavior of individual particles (atoms or molecules) in a gas. Postulates of the Kinetic Molecular Theory of Gases 1. Gases consist of tiny particles (atoms or molecules). 2. These particles are continually in rapid and random motion. 3. The particles are assumed not to attract or to repel each other. 4. All gases, regardless of MM, have = average = temp.

The Implications of the Kinetic Molecular Theory Gas speed  u 2 =  (3RT/MM) Maxwell’s equation = gas molecule speeds  temperature Same av. same temp BUT, different av. Speeds! Smaller MM molecules go faster

The Implications of the Kinetic Molecular Theory Diffusion = random mixing of gases Effusion = gas movt through a small opening in a container into another container with lower pressure Graham’s Law: Effusion rate 1 /effusion rate 2 =  (MM 2 /MM 1 ) Gas effusion used initially for 235 UF 6 / 238 UF 6 separation

Gas Stoichiometry Example Calculate the volume of H 2 produced at 1.50 atm and 19 o C by the reaction of 26.5 g of Zn with excess HCl. Zn (s) + 2HCl (aq)  ZnCl 2(aq) + H 2(g)

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