Chapter 14 – Gas Laws

Gases and Pressure A. Pressure: the force per unit area on a surface B. The SI unit for force is a Newton. It is the force that will increase the speed of a 1 kg mass by one m/s each second the force is applied. C. Barometer: a device used to measure atmospheric pressure

Gases and Pressure D. Units of pressure: 1. Millimeters of mercury (mmHg): 1 mmHg is also called one torr 2. atmospheres (atms): 1 atm = 760 mmHg 3. kilopascal (kPa): 1 atm = 101.325 kPa

Gases and Pressure E. Standard Temperature & Pressure (STP): The agreed upon standard conditions of exactly 1 atm pressure and 0 °C

Gases and Pressure convert 4.60 atm to kPa convert 793.8 kPa to atm F. Conversion Practice: convert 4.60 atm to kPa convert 793.8 kPa to atm convert 580 mmHg to atm 964.54 mmHg to kPa

Gases and Pressure convert 4.60 atm to kPa F. Conversion Practice: convert 4.60 atm to kPa 4.60 atm 1 × 101.325 kPa 1 atm =466 kPa convert 793.8 kPa to atm 793.8 kPa 1 × 1 atm 101.325 kPa =7.834 atm

Gases and Pressure convert 580 mmHg to atm F. Conversion Practice: convert 580 mmHg to atm 580 mmHg 1 × 1 atm 760 mmHg =0.76 atm convert 964.54 mmHg to kPa 964.54 mmHg 1 × 101.325 kPa 760 mmHg =128.59 kPa

Gases and Pressure H. Conversion Practice 1. convert 24.8 ˚C to K G. Absolute zero: – 273.15 °C or 0 K K = ˚C + 273.15 ˚C = K – 273.15 H. Conversion Practice 1. convert 24.8 ˚C to K 2. convert 376 K to ˚C

Gases and Pressure H. Conversion Practice 1. convert 24.8 ˚C to K G. Absolute zero: – 273.15 °C or 0 K K = ˚C + 273.15 ˚C = K – 273.15 H. Conversion Practice 1. convert 24.8 ˚C to K K = 24.8 + 273.15 = 298.0 K 2. convert 376 K to ˚C ˚C = 376 – 273.15 = 103 ˚C

𝐓𝐡𝐞 𝐆𝐚𝐬 𝐋𝐚𝐰𝐬 A. Dalton’s Law of Partial Pressures: states that the total pressure of a gas mixture is the sum of the partial pressures of the component gases

𝐓𝐡𝐞 𝐆𝐚𝐬 𝐋𝐚𝐰𝐬 1. Partial pressure: the pressure of each gas in a mixture 2. PT = P1 + P2 + P3

𝐓𝐡𝐞 𝐆𝐚𝐬 𝐋𝐚𝐰𝐬 𝐏 𝐚𝐭𝐦 = 𝐏 𝐠𝐚𝐬 + 𝐏 𝐇 𝟐 𝐎 3. Gas collected by water displacement 𝐏 𝐚𝐭𝐦 = 𝐏 𝐠𝐚𝐬 + 𝐏 𝐇 𝟐 𝐎

PT = P1 + P2 + P3 B. Partial Pressure Practice The total pressure of a mixture of gaseous nitrogen, oxygen, and argon is 762.4 mmHg. If the pressure of the nitrogen is 286.3 mmHg and the pressure of the oxygen is 312.8, what is the pressure of the argon gas?

PT = P1 + P2 + P3 𝐏 𝐀𝐫 = 163.3 mmHg B. Partial Pressure Practice The total pressure of a mixture of gaseous nitrogen, oxygen, and argon is 762.4 mmHg. If the pressure of the nitrogen is 286.3 mmHg and the pressure of the oxygen is 312.8, what is the pressure of the argon gas? 𝐏 𝐚𝐭𝐦 = 𝐏 𝐍 𝟐 + 𝐏 𝐎 𝟐 + 𝐏 𝐀𝐫 762.4 = 286.3 + 312.8 + PAr 𝐏 𝐀𝐫 = 163.3 mmHg

𝐏 𝐚𝐭𝐦 = 𝐏 𝐠𝐚𝐬 + 𝐏 𝐇 𝟐 𝐎 B. Partial Pressure Practice 𝐏 𝐚𝐭𝐦 = 𝐏 𝐠𝐚𝐬 + 𝐏 𝐇 𝟐 𝐎 B. Partial Pressure Practice Gas was collected over water using a eudiometer. A barometer shows the atmospheric pressure is 748.2 mmHg. If the pressure of the gas is the eudiometer is 721.7 mmHg, what is the pressure of the water vapor?

𝐏 𝐚𝐭𝐦 = 𝐏 𝐠𝐚𝐬 + 𝐏 𝐇 𝟐 𝐎 𝐏 𝐚𝐭𝐦 = 𝐏 𝐠𝐚𝐬 + 𝐏 𝐇 𝟐 𝐎 𝐏 𝐚𝐭𝐦 = 𝐏 𝐠𝐚𝐬 + 𝐏 𝐇 𝟐 𝐎 B. Partial Pressure Practice Gas was collected over water using a eudiometer. A barometer shows the atmospheric pressure is 748.2 mmHg. If the pressure of the gas is the eudiometer is 721.7 mmHg, what is the pressure of the water vapor? 𝐏 𝐚𝐭𝐦 = 𝐏 𝐠𝐚𝐬 + 𝐏 𝐇 𝟐 𝐎 748.2 = 721.7 + P H 2 O 𝐏 𝐇 𝟐 𝐎 = 26.5 mmHg

𝐓𝐡𝐞 𝐆𝐚𝐬 𝐋𝐚𝐰𝐬 C. Boyle’s Law: states that the volume of a fixed mass of gas varies inversely with the pressure at constant temperature P1V1 = P2V2

𝐓𝐡𝐞 𝐆𝐚𝐬 𝐋𝐚𝐰𝐬 Charles’ Law: states that the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature V 1 T 1 = V 2 T 2

𝐓𝐡𝐞 𝐆𝐚𝐬 𝐋𝐚𝐰𝐬 E. Gay-Lussac’s Law: the pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature P 1 T 1 = P 2 T 2

P 1 V 1 T 1 = P 2 V 2 T 2 𝐓𝐡𝐞 𝐆𝐚𝐬 𝐋𝐚𝐰𝐬 F. Combined Gas Law: expresses relationships between pressure, volume, and temperature of a fixed amount of gas. P 1 V 1 T 1 = P 2 V 2 T 2

𝐓𝐡𝐞 𝐆𝐚𝐬 𝐋𝐚𝐰𝐬 G. Gas Law Practice A sample of neon gas has a volume of 4.38 L at a temperature of 254 K. If the volume increases to 13.48 L, what is the new temperature of the gas?

𝐓𝐡𝐞 𝐆𝐚𝐬 𝐋𝐚𝐰𝐬 G. Gas Law Practice A sample of xenon gas has a pressure of 864 mmHg at a temperature of 314 K. If the pressure decreases to 372 mmHg, what is the new temperature of the gas?

𝐆𝐚𝐬 𝐕𝐨𝐥𝐮𝐦𝐞𝐬 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐈𝐝𝐞𝐚𝐥 𝐆𝐚𝐬 𝐋𝐚𝐰 A. Gay-Lussac’s law of combining volumes of gases: states that at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers. hydrogen gas + chlorine gas → hydrogen chloride gas _____________________________________________ H2 + Cl2 → 2HCl 1 volume 1 volume 2 volumes

𝐆𝐚𝐬 𝐕𝐨𝐥𝐮𝐦𝐞𝐬 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐈𝐝𝐞𝐚𝐥 𝐆𝐚𝐬 𝐋𝐚𝐰 B. Avogadro’s Law: states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules

𝐆𝐚𝐬 𝐕𝐨𝐥𝐮𝐦𝐞𝐬 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐈𝐝𝐞𝐚𝐥 𝐆𝐚𝐬 𝐋𝐚𝐰 C. Standard molar volume of gas: the volume occupied by one mole of a gas at STP (22.4 L)

𝐆𝐚𝐬 𝐕𝐨𝐥𝐮𝐦𝐞𝐬 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐈𝐝𝐞𝐚𝐥 𝐆𝐚𝐬 𝐋𝐚𝐰 D. Ideal Gas Law: the mathematical relationship among pressure, volume, temperature, and the number of moles of a gas

𝐆𝐚𝐬 𝐕𝐨𝐥𝐮𝐦𝐞𝐬 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐈𝐝𝐞𝐚𝐥 𝐆𝐚𝐬 𝐋𝐚𝐰 D. Ideal Gas Constant: the constant R= 62.4 L∙mmHg mol∙K or R= 0.0821 L∙atm mol∙K F. Gas Law Practice 1. A 2.5 L cylinder is filled with helium gas to a pressure of 12.8 atm at 14.57 °C. How many moles of helium gas are in the cylinder?

𝐆𝐚𝐬 𝐕𝐨𝐥𝐮𝐦𝐞𝐬 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐈𝐝𝐞𝐚𝐥 𝐆𝐚𝐬 𝐋𝐚𝐰 F. Gas Law Practice 1. A 2.5 L cylinder is filled with helium gas to a pressure of 12.8 atm at 14.57 °C. How many moles of helium gas are in the cylinder? (12.8)(2.5) = (n)(.0821)(287.72) n = 1.4 mol He

𝐆𝐚𝐬 𝐒𝐭𝐨𝐢𝐜𝐡𝐢𝐨𝐦𝐞𝐭𝐫𝐲 A. Mass to Gas Problems: converting from mass of a gas to volume of the gas at STP What volume in mL will be occupied by 3.5 grams of methane (CH4) at STP?

𝐆𝐚𝐬 𝐒𝐭𝐨𝐢𝐜𝐡𝐢𝐨𝐦𝐞𝐭𝐫𝐲 B. Gas to Mass Problems: converting from the volume of a gas to the grams at STP A sample of hydrogen gas (H2) occupies 14.1 L at STP. How many grams of the gas are present?

𝐆𝐚𝐬 𝐒𝐭𝐨𝐢𝐜𝐡𝐢𝐨𝐦𝐞𝐭𝐫𝐲 C. Gas Stoichiometry: use the coefficients from the balanced equation to compare volumes of substances (mole ratio is now the volume ratio) a.) Hydrogen gas reacts with oxygen gas to produce water vapor. Write the balanced equation.

𝐆𝐚𝐬 𝐒𝐭𝐨𝐢𝐜𝐡𝐢𝐨𝐦𝐞𝐭𝐫𝐲 b.) Assuming all volume measurements are made at the same temperature and pressure, what volume of hydrogen gas is needed to react completely with 4.55 L of oxygen gas to produce water vapor?

𝐆𝐚𝐬 𝐒𝐭𝐨𝐢𝐜𝐡𝐢𝐨𝐦𝐞𝐭𝐫𝐲 c.) Using the volume of H2 from part b.) at STP, calculate the number of grams of H2O produced.