Combined and ideal gas laws

Combined and ideal gas laws

Combined gas law • If we combine all of the relationships from the 3 laws covered thus far (Boyle’s, Charles’s, and Gay-Lussac’s) we can develop a mathematical equation that can solve for a situation where 3 variables change :

Combined gas law • Amount is held constant • Is used when you have a change in volume, pressure, or temperature

- P1 • - P2  • - V1  • - V2  • - T1  • - T2  Example problem A gas with a volume of 4.0L at STP. What is its volume at 2.0atm and at 30°C?

P1V1 P2V2 = T1 T2 Example problem =

Avogadro’s Law • So far we’ve compared all the variables except the amount of a gas (n). • There is a lesser known law called Avogadro’s Law which relates ____. • It turns out that they are _________ related to each other. • As ____________ increases then V increases. V/n = k

Ideal Gas Law • Which leads us to the ideal gas law – • The fourth and final variable is amount • ___________________________. • We can set up a much more powerful eqn, which can be derived by combining the proportions expressed by the previous laws.

Ideal Gas Law • If we combine all of the laws together including Avogadro’s Law mentioned earlier we get: Where R is the universal gas constant Normally written as

Ideal Gas Constant (R) • R is a constant that connects the 4 variables • R is dependent on the units of the variables for P, V, & T • Temp is always in ________ • Volume is in ________ • Pressure is in either ____________ ____________

Ideal Gas Constant • Because of the different pressure units there are 3 possibilities for our ideal gas constant • If pressure is given in atm • If pressure is given in mmHg • If pressure is given in kPa

Using the Ideal Gas Law What volume does 9.45g of C2H2 occupy at STP? • P • R • V • T • n

L•atm mol•K (____ ) (___atm) (V) (_________) = PV =nRT (______) (V) = (___K) (_______) V = ______L

A camping stove propane tank holds 3000g of C3H8. How large a container would be needed to hold the same amount of propane as a gas at 25°C and a pressure of 303 kpa? • P • R • V • T • n

L•kPa mol•K (____ ) (___kPa) (V) (_________ L•kPa) = PV = nRT (______) (V) = (___K) (____ mol)

Classroom Practice Use the Ideal Gas Law to complete the following table for ammonia gas (NH3).

PV = nRT Ideal Gas Law & Stoichiometry What volume of hydrogen gas must be burned to form 1.00 L of water vapor at 1.00 atm pressure and 300°C? (____ atm) (___ L) nH2O= (___K) (____L atm/mol K) nH2O= _______ mols

_ mol H2 ____ L H2 = _ mol H2O 1mol H2 Ideal Gas Law & Stoichiometry 2H2 + O2 2H2O .021257 mol _____ L H2

Classroom Practice To find the formula of a transition metal carbonyl, one of a family of compounds having the general formula Mx(CO)y, you can heat the solid compound in a vacuum to produce solid metal and CO gas. You heat 0.112 g of Crx(CO)y Crx(CO)y(s)  x Cr(s) + y CO(g) and find that the CO evolved has a pressure of 369 mmHg in a 155 ml flask at 27C. What is the empirical formula of Crx(CO)y?

Variations of the Ideal Gas Law • We can use the ideal gas law to derive a version to solve for MM. • We need to know that the unit mole is equal to m ÷ MM, where m is the mass of the gas sample PV = nRT

Variations of the Ideal Gas Law • We can then use the MM equation to derive a version that solves for the density of a gas. • Remember that D = m/V

Classroom Practice 1 A gas consisting of only carbon and hydrogen has an empirical formula of CH2. The gas has a density of 1.65 g/L at 27C and 734 mmHg. Determine the molar mass and the molecular formula of the gas. Silicon tetrachloride (SiCl4) and trichlorosilane (SiHCl3) are both starting materials for the production of electro-nics-grade silicon. Calculate the densities of pure SiCl4 and pure SiHCl3 vapor at 85C and 758 mmHg.

Real Vs. Ideal • All of our calculations with gases have been assuming ideal conditions and behaviors. • We assumed that there was ____ __________ established between particles. • We assumed that each particle has _____________ of its own. • Under normal atmospheric conditions gases tend to behave as we expect and as predicted by the KMT.

Real Vs. Ideal • However, under ______________ and _______________, gases tend to deviate from ideal behaviors. • Under extreme conditions we tend to see a tendency of gases to not behave as independently as the ideal gas law predicts. • Attractive forces between gas particles under high pressures or low temperature cause the gas not to behave predictably.

Loose Ends of Gases • There are a couple more laws that we need to address dealing with gases. • Dalton’s Law of Partial Pressures • Graham’s Law of Diffusion and Effusion.

Dalton’s Law of Partial Pressure • States that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases. • What that means is that each gas involved in a mixture exerts an independent pressure on its container’s walls

Dalton’s Law of Partial Pressure • Therefore, to find the pressure in the system you must have the ____ ______________of all of the gases involved. • This becomes very important for people who work at _____ altitudes like mountain climbers and pilots. • For example, at an altitude of about 10,000m air pressure is about ____ of an atmosphere.

Dalton’s Law of Partial Pressure • The partial pressure of oxygen at this altitude is less than ___ mmHg. • By comparison, the partial pressure of oxygen in human alveolar blood needs to be about _____ mmHg. • Thus, respiration cannot occur normally at this altitude, and an outside source of oxygen is needed in order to survive.

Simple Dalton’s Law Calculation • Three of the primary components of air are CO2, N2, and O2. In a sample containing a mixture of these gases at exactly 760 mmHg, the partial pressures of CO2 and N2 are given as PCO2= 0.285mmHg and PN2 = 593.525mmHg. What is the partial pressure of O2?

Simple Dalton’s Law Calculation PT = PCO2 + PN2 + PO2 760mmHg = ______ mmHg + _________ mmHg + P__ PO2= _____mmHg

Dalton’s Law of Partial Pressure • Partial pressures are also important when a gas is collected through water. • Any time a gas is collected through water the gas is “____________” with water vapor. • You can determine the pressure of the dry gas by __________ out the water vapor

Atmospheric Pressure Ptot = Patmospheric pressure = Pgas + PH2O • The water’s vapor pressure can be determined from ___ and subtract-ed from the atmospheric pressure

Simple Dalton’s Law Calculation • Determine the partial pressure of oxygen collected by water displace-ment if the water temperature is 20.0°C and the total pressure of the gases in the collection bottle is 730 mmHg.

Simple Dalton’s Law Calculation PT = PH2O + PO2 PH2O = ____ mmHg PT = ___ mmHg ___mmHg = _______ + PO2 PO2= _____ mmHg

Graham’s Law • Thomas Graham studied the _______ and ________ of gases. • __________ is the mixing of gases through each other. • _______ is the process whereby the molecules of a gas escape from its container through a tiny hole

Graham’s Law • Graham’s Law states that the rates of effusion and diffusion of gases at the same temperature and pressure is dependent on the size of the molecule. • The _________ the molecule the slower it moves the __________ it mixes and escapes.

Graham’s Law • Kinetic energy can be calculated with the equation ___________ • __ is the mass of the object • __ is the velocity. • If we work with two different gases at the same ______________ their energies would be equal and the equation can be rewritten as:

“M” represents molar mass • “v” represents molecular velocity • “A” is one gas • “B” is another gas • If we want to compare both gases velocities, to determine which gas moves faster, we could write a ____ of their velocities. • Rearranging things and taking the ____________ would give the eqn:

Rate of effusion of A MB = Rate of effusion of B MA • This shows that the velocities of two different gases are inversely propor-tional to the square roots of their molar masses. • This can be expanded to deal with rates of diffusion or effusion

Graham’s Law • The way you can interpret the equation is that the number of times faster A moves than B, is the square root of the ratio of the molar mass of B divided by the Molar mass of A • So if A is half the size of B than it effuses or diffuses ____ times faster.

Rate of effusion of A MB = Rate of effusion of B MA Graham’s Law Example Calc. If equal amounts of helium and argon are placed in a porous container and allowed to escape, which gas will escape faster and how much faster?

__ g _ g Graham’s Law Example Calc. Rate of effusion of He = Rate of effusion of Ar Helium is ____ times faster than Argon.

Classroom Practice 2 A mixture of 1.00 g H2 and 1.00 g He is placed in a 1.00 L container at 27C. Calculate the partial pressure of each gas and the total pressure. Helium is collected over water @ 25C and 1.00 atm total pressure. What total volume of gas must be collected to obtain 0.586 g of He? The rate of effusion of a gas was meas-ured to be 24.0 ml/min. Under the same conditions, the rate of effusion of pure CH4 gas is 47.8 ml/min. What is the molar mass of the unknown gas?

Combined and ideal gas laws