Combined Gas Laws and Dalton’s Law of Partial Pressures

Combined Gas Laws and Dalton’s Law of Partial Pressures

Today… • Collect all assignments • Qualitative testing of water (+ rubric for your group) • AQHI assignment (online) • Gizmo’s Quiz due!!!!? (did you submit yours???) • Addressing Some CURIOUS questions • Take-up Homework • Combined Gas law • Dalton’s Law of Partial Pressures

Celsius and Kelvin Scales If you double the degrees Celsius, what happens to the temperature in Kelvin?

Graph of four experiments in which the same amount of gas was used and data were collected at four different pressures (P1 to P4). The solid lines represent actual data, dashed lines represent extrapolated values. All of the plots intersect at −273.15°C.

Why Kelvin and Not Celsius for gas temperature? Identify the x and y-intercepts for each graph. (A) Using the Celsius temperature scale produces straight-line graphs that have three different y-intercepts. (not a direct proportion, doubling temp does not double volume) (B) Using the Kelvin temperature scale produces straight-line graphs with the same y-intercept (direct proportion, y-intercept 0, doubling temp doubles the volume)

The Combined and Ideal Gas Laws • All three variables can be changed at the same time: Temperature, Pressure, and Volume. • A combination of Boyle’s and Charles’s law. • When the mass (amount) of gas is constant you can use:

Different forms of Equations P1V1 = P2V2 T1 T2 • pressure and volume of a given amount of gas are inversely proportional to each other, and directly proportional to the Kelvin temperature of the gas. V1 = P2V2 T1 P1T2 T1 = P1V1 T2 V2 P2 P1 = P2V2 T1 T2 V1 T2 = P2V2 T1 V1 P1 P2 = P1V1 T2 T1 V2 V2 = P1V1 T2 T1 P2

The Combined Gas law Sample Problem: • A weather balloon with a volume of 55.0 L is filled with hydrogen gas at a pressure of 98.5 kPa and a temperature of 13ºC. When the balloon is released, it rises to the stratosphere, where the temperature is -48ºC and the pressure is 19.7 kPa. What is the volume of the balloon under these conditions?

Class work Worksheet: Combining Gas Laws

Dalton’s Law of Partial Pressures Gas Mixtures: • In a mixture of gases, each gas exerts a pressure. The pressure exerted by a single gas in a mixture is called the Partial pressure of the gas. In a mixture of gases, each gas exerts a pressure. • Air is made up of many gases, including water vapour. • Dalton performed experiments to measure water vapour content of air and found if water placed in sealed container, some evaporates to form vapour that exerts pressure on walls of the container. He observed… Pwater vapour

FOR ANY GAS…This means that if a mixture is made of two gases, A and B, then: Pt = PA + PB Pt = Total pressure PA = Partial pressure of gas A (if it was alone) PB = Partial pressure of gas B (if it was alone) Law of Partial Pressures: The total pressure of aMixture of gases is equal to the sum of the partialpressures of the component gases (if the gases do notreact chemically).

Example 1: 1 L of N2 at 50 kPa is mixed with 1 L of O2 at 60 kPa, to form a 1 L mixture of the gases. What is the resulting pressure? Ptot = 60 kPa + 50 kPa = 110 kPa Example 2: A balloon contains 75 kPa N2, 15 kPa O2, 5 kPa CO2, and water vapour. If atmospheric pressure is 100 kPa what is the partial pressure of water vapour? PH2O=PTOT-(PN2+PO+PH2O)=100 - (75 + 15 + 5) = 100 - 95 = 5 kPa

Why does the law work? • This works according to the KMT because at the same temperature molecules of different gases have the same Ek. It doesn’t matter if the molecules are O2 or H2. Both collide with the container or other molecules with the same force. • When two separate gases originally at the same temperature are mixed, the temperature—and thus the average speed of the gases—does not change. Only the total number of molecules in the container increases. • Therefore there are more molecules colliding with the walls of the container and, thus, the pressure is higher.

Pressure of a Gas • The pressure of a gas in a mixture is also related to the amount of molecules of that gas in the mixture. Mathematically this can be stated as: is called the mole fraction of gas A.

Mole Fraction of a Gas The number of moles of gas A divided by the total number of moles of ALL gases in the mixture.

Recap of Key Formulas PA = Pt x nA ntotal PA = partial pressure of A Pt = total pressure nA= moles of gas A ntotal = total moles of gas PT = PA + PB PT = Total pressure PA = Partial pressure of A PB = Partial pressure of B _nA_ = mole fraction A ntotal nA = moles of gas A ntotal = Total moles of gas

The Atmosphere • N2: 78.08%, O2: 20.95%, CO2: 0.04%. • These add up to 100% of dry air, so there are almost no other gases (really, 0.002%). • The amount of water vapour varies widely.

Partial Pressure Sample Problem A mixture of 6.0 g of argon gas and 8.0 g of oxygen gas has a total pressure of 66 kPa. Calculate the partial pressure exerted by each gas.

Assigned Work • p. 457 # 17-21 • p. 460 #22-25 • p. 461 #1-2,3-5

Combined Gas Laws and Dalton’s Law of Partial Pressures