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Gas Laws

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**What do we know about gases?**

Gases have unique properties because the distance between the particles is so great. Gases behave like liquids because they can “flow” but have their own unique properties. Gases have low densities and are highly compressible. Gases have weight (mass) and pressure.

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**Kinetic Molecular Theory of Gases**

Gases are made up of lots of tiny particles that are far apart relative to their size (1000 times greater than liquid or solid!). No kinetic energy (KE) is lost during collisions. These are called elastic collisions. Gases are in constant random motion. Gases particles do not attract or repel each other. All gases at the same temperature have the same KE.

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**Pressure If you pump air into a tire, the tire pressure will increase.**

This is caused by the increase in the number of collisions of molecules of air with the inside walls of the tire. Pressure: the force per unit area (force/area)

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**The SI unit of Force is called a Newton (N)**

Newton: the force that will increase the speed of a one-kilogram mass by one meter per second each second the force is applied. 1N=1kg X 1m/s2 This means that if the same force is applied to a smaller area, the pressure is greater! One unit of Pressure is Pascal (Pa) 1Pa=N/m2 There are several units of pressure (Pa, atm, mm Hg) and we can convert from one unit to another.

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Unit Coversion There are several units of pressure.

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**Measurable Properties of Gases**

P= pressure exerted by the gas T= temperature in kelvins of the gas V= total volume occupied by the gas n= number of moles of the gas

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Boyle’s Law Robert Boyle studied the relationship of between the volume and the pressure of a gas Boyle found that doubling the pressure on a sample of gas at constant temperature reduces its volume by one-half. Boyle’s Law: For a fixed amount of gas at a constant temperature, the volume of the gas increases as the pressure of the gas decreases and the volume of the gas decreases as the pressure of the gas increases.

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**Let’s look at Pressure and Volume**

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**Boyle’s Law Boyle’s Law can be stated as follows: P1V1=P2V2**

Boyle’s Law is used to solve problems involving pressure and volume where temperature is constant.

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Boyle’s Law Example A sample of oxygen gas has a volume of mL when its pressure is atm. What will the volume of the gas be at atm if temperature remains constant?

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Boyle’s Law A balloon filled with helium gas has a volume of 500 mL at a pressure of 1 atm. The balloon is released and reaches an altitude of 6.5 km, where the pressure is 0.5 atm. If the temperature has remained the same, what volume does the gas now occupy?

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Boyle’s Law Practice A sample gas has a volume of 9.66 mL at a pressure of 64.4 kPa. When the pressure is changed to 94.6 kPa, what is the new volume? A balloon has a volume of 456 mL at a pressure of 1.0 atm. It is taken under water in a sub to a depth where pressure is 3.3 atm. What is the new volume of the balloon assuming constant temperature? A sample of gas occupies 1.55L at 27oC and 1.00 atm. What will the pressure be if volume is decreased to 31 mL if temperature is constant?

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**Boyle’s Law Practice Cont…**

A sample of gas occupies 15.1 mL at 27 C. The pressure is increased to 50.0 atm along with a new volume of 8.31 mL. What was the initial pressure if the temperature remains constant? (27.5 atm) A small cylinder of oxygen contains 300 mL of gas at 15 atm. What will the volume be when released into an atmosphere at atm? (5000 mL)

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**Temperature Volume Relationship**

What happens as a gas is heated or cooled? Jacques Charles, a balloonist, determined that when temperature is increased, the volume must increase if the pressure is to remain constant. Think about your car tires. What happens to them when they get cold?

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Charles’s Law The direct relationship between temperature and volume is known as Charles’s Law We ALWAYS use Kelvin scale when working with gas laws. To go from Degrees C to Kelvin add 273 20 deg C = 293 Kelvin (K) V1/T1 = V2/T2 or V1T2=V2T1

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Charles’s Law A sample of neon gas occupies a volume of 752 mL at 25 C. What volume will the gas occupy at 50 C if the pressure remains constant? Remember you MUST use Kelvin scale!! What if temp changes to 100 C?

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**Charles’s Law Practice Problems**

The volume of a gas in a syringe is 15.0 mL at 23.5 C. What will the volume of the gas be at 72.5 C if the pressure is constant? A balloon with volume 15.5 L is inflated in a room at 20.0C then taken outside where it is 7.0C. What will the new volume be? A sample of neon gas has a volume of 752 mL at 25.0C. What is the temperature in celsius if the volume changes to 815 mL if pressure is constant?

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When 1.5x103L of air at 5.0C is injected into a household furnace, it comes out at 30.0C. Assuming pressure is constant, what is the volume of the heated air? (1.63x103 L) A sample of nitrogen has a volume of 275 mL at 273 K. The sample is heated and the volume becomes 325mL. What is the new temperature in K? (323 K)

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**Temperature Pressure Relationship**

Joseph Gay-Lussac determined the relationship between pressure and temperature. As the temperature of a gas increases, so does the average kinetic energy of the molecules. This means pressure increases with temperature. P1/T1=P2/T2 or P1T2=P2T1

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Example The gas in a container is at a pressure of 3.00 atm at 25 C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52 C. What would the gas pressure in the container by at 52 C?

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Example A sample of Helium gas is at 122 kPa and 22 deg C. Assuming constant volume, what will the temperature be when the pressure is 203 kPa?

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Practice The air in a steel-belted tire is at a pressure of 29.8 psi and a temp of 20 deg C. After the tire is driven fast of a hot road, the temp in the tire is 48 deg C. What is the new pressure? At 120 C the pressure of a sample of nitrogen gas is 1.07 atm. What will the pressure be at 205C? At 122 C the pressure of a sample of nitrogen gas is 1.07 atm. What will the temperature be (inC) at 1.29 atm?

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Combined Gas Law We can combine the previous 3 gas laws into one equation! P1V1/T1 = P2V2/T2 or P1V1T2 = P2V2T1 To solve problems using the combined gas law, simply ignore the variable being held constant.

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**So far, we have learned three different law which correspond to varying conditions**

No gas perfectly obeys all of the law we have discussed. However, they work for most all gases under most conditions As a result, one way to model a gas’s behavior is to assume that the gas is an ideal gas

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**Ideal Gas Law The Ideal Gas Law includes four variables: P,V,T and n.**

The relationship between the four variables is expresses mathematically as: PV=nRT R is a constant. The value for R depends on the units used for pressure and volume.

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**Ideal Gas Law If pressure is in kilopascals (kPa)**

R=8.314 LkPa/molK If the pressure is in atmospheres R= Latm/molK Remember: Convert any temperatures to Kelvin. Make sure you convert volume to liters to make your units cancel!!

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Examples How many moles of gas are contained in L at kPa and 0 deg C?

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Examples Calculate the pressure in kPa exerted by 43 moles of N2 in a 65 L cylinder at 5 deg C?

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Example A 5.21 L container holds 16.1 g of Fluorine at deg C. What is the pressure in atm?

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**Gas Laws & Stoichiometry**

How many liters of hydrogen gas will be produced at 280K and 96.0 kPa if 1.74 moles Na react with excess H2O? 2Na + 2H2O 2NaOH + H2

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