Chapter 7 Gases

A gas consists of small particles that move rapidly in straight lines until they collide; they have enough kinetic energy to overcome any attractive forces; gas molecules are very far apart; gas molecules have very small volumes compared to the volumes of the containers they occupy; have kinetic energies that increase with an increase in temperature; collisions of the gas cause pressure (force /unit area)

Atmospheric pressure is the pressure exerted by a column of air from the top of the atmosphere to the surface of the Earth; is about 1 atmosphere at sea level; depends on the altitude and the weather; is lower at high altitudes where the density of air is less;

What causes atmospheric pressure? Gravity A barometer measures the pressure exerted by the gases in the atmosphere indicates atmospheric pressure as the height in mm of the mercury column A water barometer would be 13.6 times taller than a mercury barometer because the density of Hg is 13.6 times as dense as water

The relationship between pressure and volume for a fixed amount of gas Note that the initial product between pressure and volume is 4L*1atm = 4 L atm In the final diagram: 2L*2atm = 4 Latm Decreasing the volume to ½ results in a doubling of the pressure We find that the product of volume and pressure is equal to a constant PV = a constant Initial Final

During inhalation, the diaphram moves down causing the the lungs to expand the pressure in the lungs decreases air flows towards the lower pressure in the lungs During exhalation, the diaphram moves up, the lung volume decreases, and the pressure within the lungs increases. In this case however air flows from the higher pressure in the lungs to the outside to relieve the increase in pressure

If the sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm, what is the new volume when the pressure is increased to 1.40 atm (T constant)?. 6.4 L *0.7 atm = 4.48 Latm = V x 1.4 atm V = 3.2 L 6.4 L; 0.7 atm3.2 L; 1.4 atm pressure x volume = constant Final volume

Temperature and Volume What happens to the number of collisions a molecule makes against the wall if we heat a gas? the number of collisions increase causing an increase in the pressure inside What will happen to the volume of the gas if the pressure outside the piston does not change and the pressure inside increases? Suppose we had a frictionless piston and a gas enclosed within the piston. What could we say about the pressure inside and outside of the piston if the piston was notionless? pressure P (inside) = P (outside) temperature (inside) = temperature (outside) Supppose we now heat the gas inside the piston V/T(K) = constant

Notice that temperature must be in K Suppose we now heat the gas enclosed in the cylinder keeping the volume constant Temperature and Pressure P/T = constant

Suppose now that we double the number of molecules in the same volume and at the same temperature. What will that do to the number of collisions with the walls? the pressure? If we allow the pressure to return to it original value, what will happen to the volume? n is directly proportional to pressure Pressure and the amount of gas, n

A Summary of The relationship between T, P, V, and n P x V = constant P/T = constant P/n = constant V/T = constant

The volume, temperature, pressure and amount of gas pressent can be summarized into one simple equation: PV = nRT When the temperature and amount of gas (n) are kept constant, nRT are equal to a constant When the volume and amount of gas is kept constant, P/T = nR/V, nR/V is a constant At constant pressure and amount of gas (n), V/T = nR/P; nR/P is a constant

A. Pressure _______, when V decreases at constant n, T. B. When T decreases, V _______ at constant n, P. C. Pressure _______ when V changes from 12 L to 4 L at constant n, T D. Volume _______ when T changes from 15 °C to 45 °C at constant n, P. triples

Vapor pressure: the pressure vapor exerts against the atmosphere; Boiling occurs when the vapor pressure of water equals the atmospheric pressure above it

Denver CO STL MO New Orleans LA pressure cooker One last thing: Notice in our discussion of gases, we never mentioned any particular gas; that is because the ideal gas law (PV=nRT) applies equally to all gases

Partial pressures The total pressure exerted by a mixture of gases is the sum of the individual partial pressures; remember the volume occupied by the gas is the same for all gases because their molecular volume is small in comparison. Gases in a mixture are always at the same temperature. Gases diffuse from higher pressure to lower pressure

Solving Some Problems Using the Gas Laws When sensors in a car detect a collision, they cause the decomposition of sodium azide, NaN 3 NaN 3 Na (s) + N 2 (g) This generates the gas nitrogen within 0.03 seconds which fills the air bags. How many liters of nitrogen are filled at 1 atm pressure (760 mm Hg) and 0 °C (STP) if the air bag contains 132 g of sodium azide? 2NaN 3 2Na (s) + 3N 2 (g) NaN 3 MW = *14 = 65 g/molHow many mols of NaN 3 are present? 132g/65g/mol = 2.03 mol 2 mol of NaN 3 produces 3 mol of N 2 PV = nRT 1atmV =3*0.0821(273); V = 67.2 L

A partially filled weather balloon has a volume of 750 L when filled with He at 8 °C and 760 mm Hg. What is the new volume of the balloon when it rises to an altitude where the temperature is -45 °C and the pressure is 100 Hg? How much He is there in the balloon originally?PV = nRT 760 mm Hg/760 mm Hg/atm =1.0 atm; K = (8 °C +273) = 281 K; V = 750 L; R = Latm/(Kmol) n = PV/RT; n = 750 L*1.0 atm/[ Latm/(K mol)*281 K] n = 32.5 mol He V = nRT/P; P = 100mm/760mm/atm = 0.13 atm ; T (273-45)= 228 K; n = 32.5 mol V = 32.5 mol* (Latm/Kmol)*228 K/0.13 atm V = 4680 L