The Ideal Gas Law and Dalton’s Law of Partial Pressures Gases Lecture III The Ideal Gas Law and Dalton’s Law of Partial Pressures

The Ideal Gas Law Is there a relationship between the following variables? pressure volume YES number of moles temperature they all have an affect on one another the ideal gas law allows us to quantify this relationship by providing us an equation to evaluate the effects of one variable on another

PV=nRT In equation form, the ideal gas law looks like this P is pressure in atmospheres V is volume in liters n is the number of moles of all gases present T is the temperature in Kelvin R is the ideal gas constant R= 0.0821 atm x L/mol x K

Here’s a problem using this equation What pressure, in atmospheres, is exerted by 0.450 mol of nitrogen gas in a 6.10 L container at standard temperature? 1. Identify the variables n=0.450 mol V=6.10 L T=273 K R= 0.0821 atm x L/mol x K 2. Rearrange the equation PV=nRT P=nRT/V

3. Solve the problem P=(0.450 mol)(0.0821)(273 K)/(6.10 L) P=1.65 atm

My lungs hold 6.30 L of air at normal body temperature (37 oC) and standard pressure. Assuming that air is made up of 20.9% oxygen, how many oxygen molecules are in my lungs after I take a breath? 1. Identify the variables V=6.30 L T=310 K P=1.00 atm R=0.0821 atm x L/mol x K 2. Solve the equation PV=nRT n=PV/RT

3. Solve the equation n=(1.00 atm)(6.30 L)/(0.0821 atm x L/mol x K)(310 K) n=0.2475 mol 4. Apply the percentage n is the number of molecules of any gas, so each gas contributes the same to the total volume and pressure, regardless of molar mass moles of oxygen=0.2475 mol x 20.9% moles of oxygen=0.05173 mol

5. Convert to molecules 0.05173 mol X 6.022 x 1023 molecules = 1 mol 3.12 x 1022 molecules

Dalton’s Law of Partial Pressures partial pressure is defined as the pressure of each individual gas in a mixture remember ideal gases all behave the same way Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the gases in the mixture In an equation, it looks like this. . . Ptotal=P1+P2+P3. . .

+ = barometer Poxygen=0.12 atm bulb with gas Pnitrogen=0.12 atm Ptotal=0.24 atm

What does the pressure of a gas depend on? Primarily the number of moles of gas present The greater the number of moles of a particular gas present in a sample, the greater that gas contributes to the total pressure of the sample if a gas makes up 3/5 of a sample, it accounts for 3/5 of the total pressure if a gas makes up 64% of a sample, it accounts for 64% of the total pressure the percentages and fractions refer to the number of moles, not the mass IMPORTANT

let’s try an example A 4.8 g sample of gas containing only nitrogen and oxygen contains 3.1 g of O2. The gas is sealed in a container and exerts a pressure of 940 mm Hg. What is the partial pressure of each gas in the container? 1. Find the number of moles of each gas #mol=mass(g)/molar mass #mol O2=(3.1 g)/(32.00g/mol) = 0.09688 mol O2 #mol N2=(1.7 g)/(28.02g/mol) = 0.06067 mol N2

2. Determine the mole fraction of each gas mole fraction=moles of individual gas total moles of gas total moles of gas= 0.09688 mol O2+ 0.06067 mol N2 = 0.15755 mol mole fraction O2=0.09688 mol/0.15755 mol = 0.6149 mole fraction N2=0.06067 mol/0.15755 mol = 0.3851

3. Multiply total pressure by the mole fraction to determine partial pressure of each gas Poxygen=940 mm Hg x 0.6149 = 578 mm Hg Pnitrogen=940 mm Hg x 0.3851 = 362 mm Hg check: 578 mm Hg + 362 mm Hg = 940 mm Hg

When chemists want to collect a gas, they often do it with a technique known as water displacement the reaction you are about to see makes hydrogen gas H2O is present due to slight evaporation reaction vessel What factor could increase the amount of evaporated H2O? temperature

the greater the temperature, the greater the number of water molecules present above the water What will this do to the partial pressure of H2O? Increased temperature will increase the partial pressure of H2O this can be observed in chart 8 in the appendix of your book

The gas inside the water displacement chamber is at equilibrium with the gas outside the chamber in other words, the gas inside is at the same pressure as the gas outside (Patm) the atmospheric pressure is the same as the total pressure inside the chamber Patm=Pgas+Pwater

Helium gas is collected over water at 25 oC Helium gas is collected over water at 25 oC. What is the partial pressure of the helium if the atmospheric pressure outside the water collection bottle is 765 mm Hg? 1. Find the pressure of water at that temperature

2. Rearrange the equation Patm=Pgas+Pwater Pgas=Patm-Pwater 3. Solve the equation Pgas=765 mm Hg – 23.8 mm Hg = 741.2 mm Hg