Chapter 10 – Gases
Luckily, we do things easier these days: Combined Gas Law Luckily, we do things easier these days: P1V1 = P2V2 n1T1 n2T2 By combining the three equations and Avogadro’s Law, we get the combined gas law.
Given pressure and volume: Just cross out the unit that’s not involved: P1V1 = P2V2 P1V1 = P2V2 T1 T2 Look! It gives you Boyle’s Law!
Given volume and temperature: Luckily, we do things easier these days: V1 = V2 P1V1 = P2V2 T1 T2 T1 T2 This way we get Charles’ Law!
Temperature (T) Pressure (P) Volume (V) Moles (n) Kelvin (K) Degrees Celsius (°C) Pressure (P) Atmospheres (atm) Kilopascals (kPa) Torr mmHg Volume (V) Liters (L) Milliliters (mL) Cubic centimeters (cm3) Moles (n) Mole (mol)
To solve any gas law problem: Practice Problem 3: A hot air balloonist heats the air in his 1,500 L balloon from 374 K to 400 K. What is the volume of the air in his balloon after it is heated? 1.) Underline your given, box your unknown. 2.) Label the givens, and make your equation. 3.) Plug in given numbers and solve for unknown. 4.) Check that the answer makes sense!
More Practice! Mr. George likes to bike around Hermann Park on the weekends, but his tires lose air during the week. If the tire’s pressure at 295K is 200. kPa, what would the temperature be if the pressure decreases by 35.0 kPa?
More Practice! A balloon filled with air has a volume of 5.56 mL at a pressure of 1.56 atm and a temperature of 53oC. How much volume would the balloon occupy at STP?
Kinetic Molecular Theory The kinetic molecular theory is a set of assumptions that allow us to predict the behavior of matter in the gas phase: 1.) Matter is composed of tiny particles. 2.) The particles of matter are in continual motion. 3.) The total kinetic energy of colliding particles remains constant.
The Relationships….. P V Inverse T V Direct P T Direct
Dalton’s Law of Partial Pressure Ptotal = P1 + P2 + P3…. Pi = XiPT where mole fraction Xi = ni/nT Ex: Natural gas contains 8.24 moles of CH4, 0.421 moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37, what is the partial pressure of CH4?
Dalton’s Law of Partial Pressure Ex: Determine the total pressure of a gas mixture that contains O2, N2, and He. If the partial pressures of the gasses are PO2 = 20 kPa, PN2=45 kPa, and PHe=36.5 kPa
Dalton’s Law Ex: A container contains water and oxygen. What is the partial pressure of oxygen at 28°C if the total pressure is 98.74 kPa and the vapor pressure of water at 28°C is 3.8 kPa.
Gas Particles & Diffusion The Kinetic Molecular Theory reminds us that gas is composed of small particles. NH3 + HCl NH4Cl Small particles will undergo diffusion, or spread from areas of high concentration to low concentration. This happens faster if temperature is high, or if the particles are very small.
Effusion Gas effusion is the process by which a gas under pressure escapes from one compartment of a container to another by passing through a small opening. r1/r2 = √(M2/M1) Ex: An unknown gas ‘X’ effuses two times faster than a sample of SO3 (g) through a porous container. Which of the following is the unknown gas? (H2, CH4, Ne, Ar)
Gas Stoichiometry Be sure all reactions are balanced! Ex: When AgNO3 is treated with 2.34 L of HI gas to give AgI, and HNO3, how many g of AgI are produced? AgNO3 + HI HNO3 + AgI
Gas Stoichiometry Ex: If you have 2.3 L of nitrogen gas that reacts with oxygen gas to make nitrogen monoxide gas, how many Liters of nitrogen monoxide were made? N2 + O2 NO
Ideal Gas Law Ideal gas law equation: PV = nRT. P = pressure (kPa, atm, mmHg) V= volume (L) n = number of moles R = constant (8.31 L kPa/K mol, 0.0821 L atm/K mol, or 62.36 L mmHg/K mol) T = temperature (K)
Ideal Gas Law Ex: What is the volume occupied by 36.0 g of water vapor at 125C and 102 kPa?
Ideal Gas Law Ex: At what temperature will 0.0100 mole of argon gas have a volume of 275 mL at 100.0 kPa?
Ideal Gas Law Ex: What volume is occupied by 5.34 moles of HCl gas at 35.0°C and 115.23 atm?
Density (d) Calculations d = m/V = PM/RT where m = mass of the gas (grams) M = molar mass of the gas M = dRT/P where d = density of the gas (g/L)
Density Calculations Ex: Calculate the density of methane (CH4) gas at STP. Ex: A 2.10 liter container has 4.65 g of a gas at 1.00 atm and 27.0 oC. What is the molar mass of the gas?