The Ideal Gas Law Section 11.3

Standard Molar Volume of a Gas Assume the gas is an ideal gas Standard molar volume of a gas: the volume occupied by one mole of a gas at STP, the value is 22.4 L Knowing the volume of gas at STP, you can find the number of mol by dividing by 22.4 L

Continued Knowing the mol of the gas, you can multiply by 22.4 L to find the volume of the gas (at STP) At STP, what is the volume of 7.08 mol of nitrogen gas? 159 L N 2

Another Problem A sample of hydrogen gas occupies 14.1 L at STP. How many moles of the gas are present? mol H 2

The Ideal Gas Law Ideal gas law: the mathematical relationship among pressure, volume, temperature, and the number of moles of a gas If “R” is a constant and “n” is the number of moles: PV = nRT

The Ideal Gas Constant The constant “R” is the ideal gas constant The value and units of “R” vary according to the units used for P and V If P is in kPa, and V is in L, then R = Temperature has to be K

Problem A tank of hydrogen gas has a volume of 22.9 L and holds 14.0 mol of the gas at 12°C. What is the pressure of the gas in kPa? Given: V = 22.9 L n = 14.0 mol T = = 285 K R = P = ?

Solution PV = nRT P = P = 1450 kPa

Another Formula You can use the ideal gas law to find the molar mass of a substance M = molar mass m = mass of the substance R, T, P, and V represent the regular stuff

Problem What is the molar mass of a gas which has a mass of g and a volume of 8.13 L at 20.0 °C and 99.2 kPa? = 61.1 g/mol

Problems Calculate the volume that a mol sample of a gas will occupy at 265 K and a pressure of 91.2 kPa L What is the pressure in kPa of a mol sample of helium gas at a temperature of 20.0°C if its volume is L? 521 kPa

Another Problem Determine the kelvin temperature required for mol of gas to fill a balloon to 1.20 L under kPa 307 K