This relationship is known as the ideal gas law and is mathematically described with the formula below:

Transcription

1 Chemistry 20 Ideal as law If we combine all the information contained in Boyle s, Charles and Avoadro s laws, we can derive an expression that describes the temperature, pressure and volume of a as. This relationship is known as the ideal as law and is mathematically described with the formula below: PV=nRT where: P = pressure (kpa) V = volume (L) amount of moles (mol) T = temperature in Kelvin (K) R = universal as constant kpa L mol K The universal as constant is a value relatin the molar volume of a as to temperature and pressure. It is a mathematical correction factor to account for non-ideal behaviour of real ases. An ideal as behaves perfectly and predictably under all conditions of pressure, temperature and volume. That is: Ideal ases do not condense into liquids. Ideal ases have particles (molecules/atoms) of zero size (point masses) that have no forces of attraction (such as London Force, dipole-dipole). The name ideal as law implies that there must be some ases whose behaviour is non-ideal. In fact there is no such thin as an ideal as that obeys the PV=nRT equation perfectly under all conditions; all real ases deviate slihtly from the behaviour predicted by the law for the followin reasons: The kinetic-molecular theory assumes that the volume of the as particles themselves is neliible compared with the total as volume. This does not hold true at either hih pressures or very low temperatures. The smaller the volume of as, the more important the size of the as molecule becomes. A second problem with real ases is the assumption that there are no attractive forces between molecules. At lower pressures, this assumption is a ood one because the as particles are far apart and the attractive forces between them are neliible. At hiher pressures, however, the particles are much closer toether and the attractive forces between them become more important. Chemistry 20 Lesson 2-06 Pae 1

2 Consider the followin raph of pressure vs. volume for an ideal and real as: If we subject an ideal as to increasin pressure, it always remains a as. If we subject a real as such as SO 2 to increasin pressure, we find that at a certain point (different for each real as) intermolecular forces of attraction (London, dipole-dipole, hydroen bondin) are stron enouh to cause the as molecules to attract each other and turn into a liquid (and then a solid if the pressure is hih enouh). This is because the pressure forces the as molecules closer and closer toether, allowin intermolecular forces to attract as molecules toether. Real ases deviate most from ideal ases at low temperatures and/or hih pressure. This is because these conditions brin the as molecules so close toether, they start interactin with each other (attractin, repellin and collidin). As you increase the temperature and/or decrease the pressure of a real as, the particles (molecules or atoms) separate far apart enouh from each other so that intermolecular interactions become neliible. Thus a real as starts to behave more ideally. Small as molecules behave more ideally than larer as molecules. Gas olar ass /mol Boilin Point C l à phase chane* He most ideal H N CO C 3 H 8 (propane) least ideal * ideal ases never turn into liquids (or solids). Of all real ases helium (He) most closely resembles an ideal as as it is monoatomic with a completely filled valence enery level (even chare distribution of electrons around the nucleus). Since hydroen is diatomic, it is subject to stoner London force that helium, thus chanin into a liquid easier than helium. Chemistry 20 Lesson 2-06 Pae 2

3 Technolooical Applications of Real Gase Behaviour Butane Lihters A butane lihter is a reat example of real as behaviour and its technoloical application. Butane (C4H10) is forced into the reservoir under pressure. The pressure causes London Force (butane is nonpolar) to chane the butane as into a liquid as the as molecules are attracted to each other under pressure. By pressin the trier, the internal pressure is reduced, allowin some of the butane to chane back into a as. A flint or electric spark mechanism then inites the aseous butane. The approximately 10 ml of (pressurized) liquid butane in the lihter will turn into approximately ml of aseous butane! Liquified Natural Gas (LNG) Transportation Natural as (methane, CH4) is a very common fuel used world-wide. Transportin as-phase chemicals is very inefficient because ases occupy a lare volume of space. By pressurizin and coolin natural as to its condensation point (that point at which it turns into a liquid), you can transport enormously larer amounts of natural as than if it was in its as phase Specialized transport ships are used for this, actin as iant pressurized thermos bottles to keep the methane in the liquid phase. Chemistry 20 Lesson 2-06 Pae 3

4 Lesson summary Any sample of as can be described by four variables: pressure, volume, temperature and moles. The ideal as law relates these four variables to each mathematically: PV=nRT. Example Problem Determine the volume occupied by 15.5 of propane (C 3 H 8 ) at 23.3 C and kpa. Solution: m = 15.5 = /mol T = K P = kpa V =? Since PV=nRT requires moles (n) which we are not iven, we will first have to calculate it usin: n m 15.5 = = = mol mol Now we can use the ideal as law to solve for V: kpa L mol K nrt V = = mol K P 99.75kPa V = 8.69 L Chemistry 20 Lesson 2-06 Pae 4

5 Chemistry 20 Ideal Gas Problems 1. A sample of 4.25 moles of hydroen at 20.0 C occupies a volume of 25.0 L. What is the pressure of this sample? 2. What volume will 30.0 of NO () occupy at 3.26 atm and 19.0 C? 3. What is the temperature of 45.3 of ammonia as if it occupies 64.2 L at 150 kpa? 4. What mass of sulfur trioxide is present in a 4.8 L container at 55 C and 150 kpa? Chemistry 20 Lesson 2-06 Pae 5

6 5. A 70.0 L tank on a car is drained of liquid asoline. How many moles of octane vapour are present in this tank at SATP? 6. A balloon is filled with 0.61 mol of air at kpa. At what temperature will the volume of the balloon be 15 L? 7. What is the volume of a hot air balloon if it contains mol at 102 kpa and 100 C? Chemistry 20 Lesson 2-06 Pae 6

7 Numerical Response Problems Record all answers to three diits in the spaces provided below and record in the boxes as shown below. Numerical Response directions. If an answer is a value between 0 and 1 (e ), then be sure to record the 0 before the decimal place. Boxes 2 or 3 could be a decimal point. Enter the first diit of your answer in the left-hand box and leave any unused boxes blank. Example calculation question and solution. The averae of the values 21.0, 25.5 and 24.5 is. (Record your three diit answer in the numerical-response section on your answer sheet) Averae = ( )/3 = =23.7 (round to three diits) Problems 1. Automotive tires are now bein filled with pure nitroen as to increase tire performance. Determine the mass of nitroen present in a tire containin 20.3 L of air at 20.0 o C and 327 kpa. 2. Calculate the mass of neon as in a neon sin with a volume of 50.0 L at 10.0 C and 3.10 kpa. 3. Calculate the volume of 8.40 of nitroen at 200 C and 130 kpa. 4. Hydroen as is enerated by the decomposition of water to fill a 1.10 kl weather balloon at 20.0 C and 100 kpa. What is the mass of hydroen required? 5. Calculate the volume of 16.0 of oxyen at 22.0 C and 97.5 kpa.

8 Chemistry 20 Ideal Gas Problems Answer Key nrt P = V æ kpal ö ( 4.25mol) ç ( K) molk P è = ø 25.0L P = 414kPa NO NO = mol mol = mol m mol 1.00mol nrt V = P æ kpal ö ç molk V è = ø æ kpa ö ( 3.26 atm) ç è atm ø V = 7.35 L ( 1.00 mol) ( K) 3. æ ö 4. NH = ç mol è mol ø NH = mol PV RT PV m T = ( 150 kpa)( 4.8 L) nr æ kpal ö ( 150kPa)( 64.2L) ç ( K) 45.3 T = molk è ø æ kpal ö ( 2.66mol) ç mol mol è molk ø 2.66 mol T = 435K SO3 SO3 æ ö = ç mol è mol ø = mol m m = n æ ö m = ( mol) ç è mol ø m = PV PV T = RT nr ( 100 kpa )( 70.0L) ( 101.5kPa)( 15L) T = æ kpal ö æ kpal ö ç ( K) ( 0.61mol) ç è molk ø è molk ø mol T = K or 27 º C nrt V = P kpal ç molk V è = ø 102kPa 5 æ ö ( mol) ( K) V = L Numerical Response Problems

9 Chemistry 20 formative problem set - Ideal Gas Law Formula: PV=nRT You may also need m n= The pressure must be in kpa and the temperature must be in Kelvin. Check your data book for the conversion factors. 1. A cylinder of neon as has a volume of 9.76 L. If the cylinder contains 61.2 of neon at 23.0 C, what is the pressure in the cylinder? 2. An experiment calls for of carbon monoxide at 55.0 C and kpa. Determine the volume occupied by the carbon monoxide. 3. The maximum safe pressure that a certain 4.00 L vessel can hold is kpa. If the vessel contains moles of a as, determine is the maximum temperature (in derees Celsius) to which this vessel can be subject. 4. We wish to compress 3.15 of methane as (CH 4 ) into a heavy-walled 2.00 L flask at 19.0 C. Calculate the pressure of the as. 5. Calculations show that a chemical reaction should yield 5.67 of carbon dioxide as. Determine the volume expected at SATP? 9. ethane as (CH 4 ) is sold in a 43.8 L cylinder containin 5.54 k of the as. Calculate the pressure inside the cylinder at 20.0 ºC. 10. any laboratory ases are sold in steel cylinders with a volume of 43.8 L. Determine the mass of aron inside a cylinder whose pressure is kpa at 20.0 ºC? Critical thinkin 11. A sample of methane as (CH 4 ) is at 50.0 ºC and 2.03 Pa. Would you expect it to behave more or less ideally if (include your reasonin): a) The pressure was reduced to 100 kpa? b) The temperature was reduced to -50 ºC? 12. In the diaram below, show usin a line, the approximate level of the movable piston in drawins (a), (b), and (c) after the indicated chanes have been made to the as. 6. A 2.50 L flask was used to collect a 5.65 sample of propane as, C 3 H 8. After the sample was collected, the as pressure was found to be kpa. Calculate the temperature of the propane in the flask. 7. If 458 ml of as measured at 30.5 C and kpa has a mass of 0.384, what is its molecular mass? 8. A volume of L of a as measured at 50.0 C and kpa has a mass of Calculate its molecular mass. Diaram for problem 12.