Gaseous State Chapter 9

9.1 The Behavior of Gases

Characteristics of Gas Gases consist of Particles that are relatively far apart Gas particles move very rapidly Gas particles have little interaction until they collide. Gases expand to fill the available space.

Description of Gases Gases can be described in various physical properties. Pressure Temperature Density Volume Number of Particles Changing one physical parameter will change one or more others.

Pressure Pressure (P) = Force/area There are several units for Pressure. Pounds/Sq. Inch (psi) 1 Atmosphere (atm) = 760 mm Hg = 760 torr 1 atm = 101,325 Pa (pascal) 1 atm = 14.7 psi

EXAMPLE Calculate the amount of pressure a 105 lbs. woman exerts by stepping down on a stiletto heel (1/16 sq inch)? Compare this to an Elephant (12,000 lbs., 16 sq. in. foot)?

PROBLEM The depths of the ocean can exceed 380 atm of pressure. How many pascals is this? How many psi?

9.2 Factors That Affect the Properties of Gases

Boyle’s Law For a given mass of gas at a constant temperature, volume varies inversely with pressure. 𝑉= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑃

Implications of Boyle’s Law 𝑉 1 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑃 1 𝑉 2 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑃 2 𝑉 1 𝑃 1 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑉 2 𝑃 2 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 Therefore 𝑉 1 𝑃 1 = 𝑉 2 𝑃 2

Ideal Gases Any gas that behaves according to the predicted linear relationships. Pressure/Volume Volume/Temperature

PROBLEM Given an ideal gas held at constant mass and temperature, what would be the volume of the gas if it was originally 125 ml, and its pressure is dropped from 1.40 atm to 0.500 atm?

Charles’s Law For a given mass of a gas at constant pressure, volume is directly proportional to temperature on an absolute (Kelvin) scale. 𝑉=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ×𝑇

Implications of Charles’s Law 𝑉 1 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑇 1 𝑉 2 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑇 2 𝑉 1 𝑇 1 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑉 2 𝑇 2 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 Therefore 𝑉 1 𝑇 1 = 𝑉 2 𝑇 2

Kelvin Scale So far we have measured temperature in degrees Celsius, a relative scale. Absolute temperature is measure in Kelvin (K, note no degree sign is used), this scale is related to the absolute motion of atoms. 0 K = -273.15 °C Therefore Temp °C +273.15 = Temp K

PROBLEM Calculate the following temperatures in Kelvin. Boiling Point of Water Freezing Point of Water

PROBLEM Given an ideal gas held at constant mass and pressure, what would be the temperature of the gas if it was originally at 125 °C, and its volume is dropped from 1.00 L to 0.500 L?

Combined Gas Law Combining Boyle’s and Charles’s Law results in the following equation. 𝑃 1 𝑉 1 𝑇 1 = 𝑃 2 𝑉 2 𝑇 2

PROBLEM A sample of Hydrogen gas occupies 1.25 L at 80.0 °C and 2.75 atm. What would its volume be at 185 °C and 5.00 atm?

Guy-Lussac and Avagadro Guy-Lussac’s Law stated that combined gases always reacted in small whole number ratios (sound familiar?) Avagadro hypothesized that the volume occupied by a gas is proportional to the number of gas particles and hence the moles of gas.

Avagadro’s Hypothesis At a given pressure and temperature, equal volumes of gas contain equal numbers of moles. Standard Temperature and Pressure (STP) are defined as 273.15 K and 1 atm, at which 1.00 mole of gas occupies 22.414 L, defined as molar volume

PROBLEM What volume would 1.00 mole of gas occupy at 37°C and 1.00 atm?

9.3 The Ideal Gas Law

Review of the Relationships Boyle’s Law: (C is a constant) 𝑉= 𝐶 𝑃 at constant n, T Charles’s Law: 𝑉=𝐶𝑇 at constant n, P Avagadro’s Hypothesis: 𝑉=𝐶𝑛 at constant P, T

Combine the Equations Assume the constants combined equal another constant we will call the Ideal Gas Constant, R 𝑉= 𝑅𝑛𝑇 𝑃 Rearrange this into the Ideal Gas Law 𝑷𝑽=𝒏𝑹𝑻

So What is the Value for R? Assuming a standard gas you can calculate the value of R 𝑃𝑉=𝑛𝑅𝑇 becomes 𝑅= 𝑃𝑉 𝑛𝑇 For a Standard gas 1.000 mole at 273.15 K and 1.000 atm has a volume of 22.414 L 𝑅= (1.00 𝑎𝑡𝑚)×(22.414 𝐿) (1.00 𝑚𝑜𝑙)×(273.15 𝐾) = 0.08206 𝐿∙𝑎𝑡𝑚 𝑚𝑜𝑙∙𝐾

PROBLEM Calculate the Ideal Gas Constant if pressure is measured in torr

PROBLEM The volume of an oxygen cylinder is 2.025 L. At a temperature of 32 °C the cylinder has a pressure of 945 torr. How many moles of Oxygen gas are in the cylinder?

PROBLEM Given the amount of oxygen in the previous question, what is its mass? What is its density?

Partial Pressures Dalton’s Law of Partial Pressure: Gases in a mixture behave independently and exert they same pressure as they would alone. 𝑃 𝑚𝑖𝑥𝑡𝑢𝑟𝑒 = 𝑃 𝐴 + 𝑃 𝐵 + 𝑃 𝐶 …

PROBLEM Given a 2.500 L container at 45.00°C, what would be the total pressure in the container from a mixture of 2.100 moles gaseous sulfur dioxide and 1.800 moles hydrogen sulfide?

9.5 Gases and Chemical Reactions

The return of Stoichiometry You can use the gas laws to solve stoichiometry problems by converting values between states of matter.

CuO(s) + H2(g)  Cu(s) + H2O(g) Example A sample of hydrogen gas has a volume of 8.00 L at a pressure of 5.00 atm and a temperature of 25 °C. What volume of gaseous water is produced in the following reaction at 150.0 °C and 0.947 atm, if all the hydrogen gas reacts with copper (II) oxide CuO(s) + H2(g)  Cu(s) + H2O(g) ALGORITHM mol of Hydrogen (PV=nRT) mol of Water (formula) V of Water (PV=nRT)

PROBLEM How many grams of calcium carbonate is formed if 3.45 L of carbon dioxide, measured at 45.0 C and 1.37 atm, react with excess CaO? CaO(s) + CO2(g)  CaCO3(S)