Gases Alan, Mila, Chloe

Kinetic molecular theory While the chemical properties of gases vary widely, the physical behavior of all gases is extraordinarily similar. Ideal gas law Kinetic molecular theory While the chemical properties of gases vary widely, the physical behavior of all gases is similar, to the extent that one equation, the ideal gas law, defines the relationships among the volume, pressure, temperature, and moles of gas in any sample. Similarly, only one theory, the kinetic molecular theory, is commonly used to describe the behavior of all gases. A thorough understanding of the ideal gas law is necessary for numerical calculations based on gases, and a similar understanding of the kinetic molecular theory provides the basis for explaining why gases behave as they do.

Gases have four properties: Temperature ; T (K) The relationship between each properties can be described by three different gas laws and a principle. Pressure；P (atm) Volume ; V (L) Moles of gas ; n (mol) Each of the gas laws holds two of these constant while measuring the change of one property as another is varied. Boyle’s law describes the inverse pressure-volume relationship Charles’s law describes the direct temperature-volume relationship Gay-lussac’s law describes the direct pressure-temperature relationship Units: K is kelvins, a temperature measurement used in more advanced science that can be found by adding 273.15 to the temperature in Celsius atm is the amount of pressure from the earth’s atmosphere at sea level (called standard atmosphere) Although we will use the ideal gas law for almost all calculations, It is necessary to be familiar with the individual gas laws. Gases have four properties: temperature, T; pressure, P; volume ,V ; and the moles of gas, n. Each of the gas laws holds two of these constant while measuring the change of one property as another is varied.

Boyle’s Law(1660) Boyle’s law describes pressure-volume relationship as shown below in three ways. P*V=constant When pressure is low in a close system, the volume of the gas is high(Total mole of gas and temperature retain the same) When pressure is high in a close system, the volume of the gas is low(Total mole of gas and temperature retain the same)

Charles’s Law(1787) Charles’s law describes the direct temperature-volume relationship as illustrated below in three ways. V/T=constant When volume is low in a close system, the temperature of the gas is low(Total mole of gas and pressure retain the same) When volume is high in a close system, the temperature of the gas is low(Total mole of gas and pressure retain the same)

Gay-Lussac’s Law(1787) Gay-Lussac’s law describes the direct pressure-temperature relationship. It is shown in the representation below. P/T=constant When pressure is low in a close system, the temperature of the gas is low(Total mole of gas and volume retain the same) When pressure is high in a close system, the volume of the gas is high(Total mole of gas and pressure retain the same)

Avogadro’s Principle Avogadro’s principle describes the direct relationship between the volume and the moles of gas. V/n = constant When there are fewer moles of gas in a closed system (with the same temperature and pressure), the volume is smaller. When there are more moles of gas in a closed system (with the same temperature and pressure), the volume is greater. Finally, in 1811, Avogadro suggested the principle that equal volumes of gases contain equal numbers of molecules or atoms. under identical conditions of temperature and pressure. This direct relationship between the number of moles and volume is written in equation form and shown graphically as this.

Ideal Gas Law The ideal gas law combines the previous gas laws to describe how gases would theoretically behave in most situations. It also introduces a new constant, the universal gas constant (R). PV = nRT R = 0.08206 atm L / mol K The ideal gas law works for most situations with low concentrations of gas, but it doesn’t work for every situation, which is why it’s called ideal. Ideally, it would be able to describe the behavior of all gases in all situations, but in reality, things don’t work out perfectly like that. The four laws of Boyle, Charles, Gay-Lussac, and Avogadro are combined into the ideal gas law PVE=nRT where P is the pressure, V is the volume, n is the number of moles of gas, and T is the temperature in kelvins The constant, R, called the universal gas constant, is needed to make all of the relationships fit together. The numerical value of R depends upon the units used. For example R=0.08206 L atm

Ideal gas law practice question # 1 A gas occupies 250. mL,and its pressure is 550. mmHg at 25 C If the gas is expanded to 450.mL, what is the pressure of the gas now? How many moles of gas are in this sample? (1 atm = 760.0mmHg) P1V1 = P2V2 250mL(550mmHg) = 450mL(P2) P2 = 250(550)/450 P2 = 306mmHg 550mmHg = 0.724atm 25oC = 298K 250mL = 0.250L PV = nRT n = PV/RT n = 0.250L(0.724atm)/(0.08206atm L / mol K)(298K) n = 0.00740mol

A gas occupies 250. mL,and its pressure is 550. mmHg at 25 C If the gas is expanded to 450.mL A.what is the pressure of the gas now? B.How many moles of gas are in this sample? (1 atm = 760.0mmHg) A. P1V1 = P2V2 250mL(550mmHg) = 450mL(P2) P2 = 250(550)/450 P2 = 306mmHg B. 550mmHg = 0.724atm 25oC = 298K 250mL = 0.250L PV = nRT n = PV/RT n = 0.250L(0.724atm)/(0.08206atm L / mol K)(298K) n = 0.00740mol

Ideal gas law practice question # 2 Calculate the mass of 15.0 L of NH3 at 27 C and 900.0 Mm Hg. P = 900. mmHg T = 27° C + 273 = 300 K V = 15.0 L R = 0.0821 L·atm/mol·K PV = nRT n = PV/RT n = {【（900. mmHg x 1 atm）/ 760 mm】 x 15.0 L}/(0.0821 L·atm/mol·K x 300 K) n = 0.721 moles NH3 x 17.04 g NH3/1 mol NH3 = 12.3 g NH3 P = 900. mm Hg T = 27° C + 273 = 300 K V = 15.0 L R = 0.0821 L·atm/mol·K PV = nRT n = PV/RT n = 900. mm x 1 atm/760 mm x 15.0 L/(0.0821 L·atm/mol·K x 300 K) = n = 0.721 moles NH3 x 17.04 g NH3/1 mol NH3 = 12.3 g NH3

Ideal gas law practice question # 3 6.3 mg of a boron hydride is contained in a flask of 385 mL at 25 c and a pressure of 11 torr. Determine the molar mass of the hydride. Which of the following hydrides is contained in the flask, BH3, B2H6, or B4H10? P = 11 torr T = 25.0° C + 273 = 298 K V = 385 mL R = 0.0821 L·atm/mol·K m = 6.3 mg PV = nRT n = m/MM PV = mRT/MM MM = 6.3 mg x 1 g/103 mg x 0.0821 L·atm/mol·K x 298 K)/ (11 torr x 1 mm/1 torr x 1 atm/760 mm x 385 mL x 1 L/103 mL) = 27.7 g/mol B2H6 because its molar mass is 27.7 g. P = 11 torr T = 25.0° C + 273 = 298 K V = 385 mL R = 0.0821 L·atm/mol·K m = 6.3 mg PV = nRT n = m/MM PV = mRT/MM MM = 6.3 mg x 1 g/103 mg x 0.0821 L·atm/mol·K x 298 K)/ (11 torr x 1 mm/1 torr x 1 atm/760 mm x 385 mL x 1 L/103 mL) = 27.7 g/mol B2H6 because its molar mass is 27.7 g.

Standard temperature and pressure The ideal gas law has four variables, P, V, n, and T, along with the constant R. By defining the standard pressure as exactly 1 atm, and the standard temperature as exactly 0 degree Celsius, two variables can be started quickly and easily. Therefore any gas at STP is understood to have P=1.00 atm and T=273K :The ideal gas law has four variables, P, V, n, and T, along with the constant R. By defining the standard pressure as exactly 1 atmosphere and the standard temperature as exactly 0 degrees Celsius, two of the variables can be stated quickly and easily. Therefore, any gas at STP is understood to have P= 1.00 atm and T= 273 K, and only n and V need be stated in a problem.

Molar mass,density,and molar volume The molar mass of different gases has to be calculated individually, since it depends on the atoms that make up each molecule. Molar volume, on the other hand, is constant for all gases at standard temperature and pressure (STP). 1mol = 22.4L Since gases have both a molar mass and molar volume, the molar density of a gas can be calculated using those the same way normal densities can be calculated. D = m / v

Sources http://chemistry.bd.psu.edu/jircitano/gases.html (general information on the gas laws) https://chem.libretexts.org/Textbook_Maps/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Physical_Chemistry_(Fleming)/2%3A_Gases/2.2%3A_The_Ideal_Gas_Law (the ideal gas law) https://chem.libretexts.org/Textbook_Maps/Introductory_Chemistry/Book%3A_Introductory_Chemistry_Online!_(Young)/09%3A_The_Gaseous_State/9.S%3A_The_Gaseous_State_(Summary) https://www.chemteam.info/GasLaw/PressureConversions.html (pressure unit conversions) , The eye thing on the side just means this slide won’t be shown while presenting, you can change that if you want by going to the slide tab and clicking “skip slide” again