|Recognize three common patterns in experimental data.||
standard temperature and pressure (STP)
- Avogadro's experiment
- objective: relate amount of gas to volume; hold everything else constant
- sample data at 1 atm, 298 K
- molar volume is almost independent of the type of gas
- volume is directly proportional to moles of gas when P, T are constant
- samples of two gases with the same V, P, T contain the same number of moles, and so, the same number of molecules!
- molecular view
- type of gas doesn't influence distance between molecules much
- example: Which is denser: dry air or moist air? Assume both air samples are at the same P, V, and T.
- Boyle's experiment
- objective: relate volume to pressure, when everything else is held constant
- sample data at 298 K for a trapped air bubble
||PV (mL Torr)
||7.60 x 103
||7.59 x 103
||7.60 x 103
||7.64 x 103
- volume is inversely proportional to pressure, when everything else is held constant
- molecular view
- confining molecules to a smaller space increases the number of collisions, and so increases the pressure
- Charles' experiment
- objective: relate volume to temperature, holding everything else constant
sample data for a trapped He bubble at 1 atm
- volume is proportional to kelvin temperature, when everything else is held constant
- molecular view
- raising temperature increases number of collisons with container wall.
If the walls are flexible, they'll be pushed back: and the gas expands.
|changing these variables in an experiment...
||while holding these variables constant...
||...reveals this relationship:
||P1 V1 = P2 V2
||V1 /T1 = V2 /T2
||P1 /T1 = P2 /T2
||V1 /n1 = V2 /n2
|P, V, T
||P1 V1/T1 = P2 V2/T2
||Combined Gas Law
|P, V, T, n
||P1 V1/n1T1 = P2V2/n2T2
||Ideal Gas Law|
applying the ideal gas law
- convenient for reporting gas volumes
- standard temperature is 0°C (273.15 K).
- standard pressure is 1 atm in America, 1 bar elsewhere
The gas in the headspace of a soda bottle has a volume of 9.0 mL at 298 K and 2 atm. What is the volume of gas at STP?
- estimating a property from constant values of the other 3 properties
- make a PVnT table
- convert to units consistent with R
- solve PV = nRT for the unknown property
- finding how one property changes when some of the other 3 properties change
- make a PVnT table with rows for initial and final conditions
- convert inconsistent units (always use K, not °C!!)
- Eliminate constant values from P1 V1/n1T1 = P2V2/n2T2
- solve the resulting equation for the unknown property
A steel-belted car tire is inflated to a gauge pressure of 32 psi at 27°C in a garage. What will the gauge pressure be after a drive on a hot road that brings the temperature to 45°C? Note that gauge pressure is pressure above atmospheric pressure (14.7 psi).
- finding gas density given pressure, temperature, and molar mass
- find moles per liter ( n/V = P/RT )
- convert moles/L to g/L
- finding molar mass
- find moles of gas ( n = PV/RT)
- molar mass = g/mol
Reactions involving gases
- predicting volume of gas produced or consumed in a reaction
- strategy: convert between gas volumes and moles using the ideal gas law
molar volume = V/n = RT/P
Sodium metal reacts violently with water to produce aqueous sodium hydroxide and hydrogen gas. How many liters of hydrogen gas are produced for every gram of sodium that reacts, at STP?
- Nitroglycerine explodes according to
3 CO(g) + 2 CO2(g) + 4 H2O(g) + 6 NO(g) + H2CO(g)
If the product gases are at a temperature of 4500°C and a pressure of 1 atm, what is the total volume of gas produced from detonation of 1 mole of nitroglycerine?
|A useful average speed is the root mean square velocity, vrms. Maxwell related vrms with temperature T and molecular weight M: ||
- average molecular speed
- higher temperature = higher average molecular speed
- higher molecular weight = lower average molecular speed
- many important properties are related to average molecular velocity
- diffusion rates: gas movement due to random molecular motion
- faster molecules = faster diffusion rate
- effusion rate: gas movement through a pinhole in a container
- faster molecules = faster effusion rate
- heat conduction
- faster molecules = faster transfer of heat energy
- speed of sound
- faster molecules = faster speed of sound
Molecules traveling faster than 1.1 km/s can escape earth's atmosphere. Which is escaping into space faster: water vapor, or oxygen gas?.
- Diving chambers often use helium/oxygen mixtures instead of air. Which would conduct heat better: helium/oxygen or nitrogen/oxygen atmospheres? In which atmosphere would sound move fastest?
- average molecular kinetic energy
- kinetic energy of one molecule:
average kinetic energy of one mole of molecules:
½ M(vrms)2 = (3/2) RT
- average molecular kinetic energy depends only on temperature for ideal gases
Mixtures of gases
- mole fraction = moles of component per mole of mixture
- by Avogadro's law, mole fraction = volume fraction for ideal gases
2 L of He gas is mixed with 3 L of Ne gas. What is the mole fraction of each component?
- Air is approximately 79% N2 and 21% O2 by mass. What is the mole fraction of O2 in air?
partial pressure: pressure exerted by one gaseous component in a mixture
- partial pressure = mole fraction times total pressure
One mole of air contains 0.79 mole of nitrogen, 0.21 mole of oxygen. Compute the partial pressure of these gases at a total pressure of 1 atm and at a total pressure of 3 atm (about the pressure experienced by a diver under 66 feet of seawater).
- vapor pressure of water: partial pressure of water vapor over water in a sealed container
What is the mole fraction of water in the headspace of a soda bottle, if the gas is at 2.0 atm and 25°C? The vapor pressure of water at 25°C is 23.756 torr.
- total pressure = sum of all partial pressures
- a. k. a. Dalton's Law
- useful in correcting calculations for the effect of moisture
1.0 L of oxygen gas is collected over water at STP. How many grams of oxygen are present? The vapor pressure of water at 0°C is