Molar Volume of Gas

Molar Volume of Gas Avogadro's hypothesis states that at the same temperature and pressure, all gases with the same volume will contain the same number of particles as well. Because 1 mole of each gas has the same number of molecules, then at the same temperature and pressure, 1 mole of each gas has the same volume. The volume per mole of gas is called the molar volume and is denoted Vm. with: V = volume of gas (liters) n = number of moles (mol) Vm = molar volume (liters/mol) The molar volume of a gas depends on temperature and pressure. Some conditions of temperature and pressure that are usually used as a reference for determining the volume of gas are as follows. 1. Standard State Conditions with a temperature of 0 °C and a pressure of 1 atm are called standard conditions and expressed by STP (Standard Temperature and Pressure). with: P = pressure (atm) V = volume of gas (liters) n = number of moles (mol) R = gas constant = 0.082 L atm/mol K T = 0 °C = 273 K V= So, at standard state (STP), the molar volume (volume of 1 mole of gas) is 22.4 liters/mol. 2. Room Conditions The gas measurement condition at a temperature of 25 °C and a pressure of 1 atm is called the room state and is expressed by RTP (Room Temperature and Pressure). with: P = pressure (atm) V = volume of gas (liters) n = number of moles (mol) R = gas constant = 0.082 L atm/mol K T = 0 °C = 298 K V= So, at room state (RTP), the molar volume (volume of 1 mole of gas) is 24.4 liters/mol. 3. Certain Conditions with Known Temperature and Pressure The volume of a gas at a known temperature and pressure can be calculated using the gas equation called the ideal gas equation. The ideal gas equation, namely PV = nRT, to determine the gas volume becomes: with: P = gas pressure (atm) V = volume of gas (liters) n = number of moles of gas (mol) R = gas constant = 0.082 L atm/mol K T = absolute temperature of gas (K = 273 + temperature Celsius) 4. Conditions Referring to Other Gas States At the same temperature and pressure, the volume of a gas depends only on the number of moles. Suppose the first gas with the number of moles n1 and volume V1 and the second gas with the number of moles n2 and volume V2 , then at the same temperature and pressure apply: = or = Example 1. Determine the volume of 2 moles of nitrogen gas if measured at: a. standard state (STP) b. room condition (RTP) \c. temperature 30 °C and pressure 1 atm d. the same temperature and pressure at which 0.5 moles of oxygen gas has a volume of 15 liter Answer: a. At standard conditions (STP), Vm = 22.4 liters/mol V = n × Vm = 2 mol × 22.4 liters/mol = 44.8 liters b. At room state (RTP), Vm = 24.4 liter/mol V = n × Vm = 2 mol × 24.4 liter/mol = 48.8 liter c. At 30 °C and 1 atm pressure, calculated as PV = nRT T = 273 + 30 = 303 K d. At the same temperature and pressure, when 0.5 moles of oxygen gas has a volume of 15 liters. Exercise 1. 1. Determine the volume of 0.25 moles of oxygen gas at 27 °C and 1 atm pressure! 2. Determine the volume of 5 moles of carbon dioxide gas at standard state (STP)! 3. What is the volume of 0.75 mol of sulfur gas measured at temperature and pressure the same as when 3 moles of nitrogen gas volume 12 liters? 4. What is the volume of 2.5 moles of nitrogen dioxide gas at room state (RTP)? 5. Determine the volume of 0.6 moles of hydrogen gas measured at: a. standard state (STP) b. room condition (RTP) c. temperature 28 °C and pressure 1 atm d. the same temperature and pressure when 2 moles of carbon monoxide gas has a volume of 25 liter