Chapter 13 Section 13.2 The Ideal Gas Law

Avogadro’s Principle Avogadro proposed the idea that equal volumes of all gases at the same conditions of temperature and pressure contain the same number of particles. An extension of Avogadro’s principle is that one mole (6.02 x 1023 particles) of any gas at standard temperature and pressure (0°C and 1.00 atm pressure, STP) occupies a volume of 22.4 L. needs a multiply sign instead of an “x”

Avogadro’s Principle Given that the mass of a mole of any gas is the molecular mass of the gas expressed in grams, Avogadro’s principle allows you to interrelate mass, moles, pressure, volume, and temperature for any sample of gas. needs a multiply sign instead of an “x”

Applying Avogadro’s Principle What is the volume of 7.17 g of neon gas at 24°C and 1.05 atm? Start by converting the mass of neon to moles. The periodic table tells you that the atomic mass of neon is 20.18 amu. Therefore, the molar mass of neon is 20.18 g. needs a multiply sign instead of an “x”

Applying Avogadro’s Principle Next, determine the volume at STP of 0.355 mol Ne. If you needed only the volume at STP, you could stop here. Finally, use the combined gas law equation to determine the volume of the neon at 24°C and 1.05 atm pressure. needs a multiply sign instead of an “x”

Applying Avogadro’s Principle needs a multiply sign instead of an “x”

The Ideal Gas Law The pressure, volume, temperature, and number of moles of gas can be related in a simpler, more convenient way by using the ideal gas law. The following is the law’s mathematical expression, where n represents the number of moles. PV = nRT

The Ideal Gas Law The ideal gas constant, R, already contains the molar volume of a gas at STP along with the standard temperature and pressure conditions.

The Ideal Gas Law The Value of R depends on the units in which the pressure of the gas is measured, as shown below. These values are all equivalent. Use the one that matches the pressure units you are using.

Applying the Ideal Gas Law What pressure in atmospheres will 18.6 mol of methane exert when it is compressed in a 12.00-L tank at a temperature of 45°C? As always, change the temperature to kelvins before doing anything else.

Applying the Ideal Gas Law Next solve the ideal gas law equation for P. Substitute the known quantities and calculate P.

Using Mass with the Ideal Gas Law Recall that it is possible to calculate the number of moles of a sample of a substance when you know the mass of the sample and the formula of the substance.

Using Mass with the Ideal Gas Law You can substitute this expression into the ideal gas law equation in place of n. Notice that this equation enables you to determine the molar mass of a substance if you know the values of the other four variables.

The Ideal Gas Law and density PV = nRT PV = mRT M P = mRT VM P = DRT D = PM RT

Determining Molar Mass and Density Determine the molar mass of an unknown gas if a sample has a mass of 0.290 g and occupies a volume of 148 mL at 13°C and a pressure of 107.0 kPa. First, convert the temperature to kelvins.

Determining Molar Mass and Density Next, solve the ideal gas law equation for M, the molar mass. Finally, substitute values and calculate the value of M. Notice that you must use the value of R that uses kilopascals as pressure units and express the volume in liters.

Determining Molar Mass and Density Notice that the units cancel to leave grams per mole, the appropriate units for molar mass.

Determining Molar Mass and Density Calculate the density of Oxygen gas at STP conditions. (Molar mass of O=16g/mol) D= PM = 1 x 32 RT 0.0821 x (0 + 273) = 1.43g/L

Real versus Ideal Gas Ideal Gas: is one whose particles take up no space, have no intermolecular attractive forces and it follows the gas laws under all conditions of temperature and pressure. Real Gas: is one whose particles have some volume and are subject to intermolecular attraction. This is why there is no true ideal gas in nature. Likely to behave nearly ideally Likely not to behave ideally Gases at high temperature and low pressure Gases at low temperature and high pressure Small non-polar gas molecules Large, polar gas molecules

End section 13.2