MOLAR MASS - knockhardy.org.uk

1 MOLESThe mole the standard unit of amount of a substance (mol) the number of particles in a mole is known as avogadro s constant (NA) avogadro s constant has a value of x 1023 mass of one mole of substance. It has units of g mol-1 or kg the MOLAR mass of water is 18 g mol-1molar mass = mass of one particle x avogadro 's constant ( x 1023 mol-1) ExampleIf 1 atom has a mass of x 10-23g1 mole of atoms will have a mass x 10-23g x x 1023= CALCULATIONSS ubstancesmass g or kgmolar massg mol-1 orkg mol-1 ExampleCalculate the number of moles of oxygen molecules in 4goxygen molecules have the formula O2the relative mass will be 2 x 16 = 32 so the MOLAR mass will be 32g mol-1moles = mass = 4gANS. molmolar mass32g mol -1 Moles 1 F321 KNOCKHARDY PUBLISHING 2008 moles = mass MOLAR the mass of one mole of carbon-12 atoms. [ mass of proton x 10-24g, mass of neutron x 10-24g, mass of electron x 10-28g ] the number of moles in10g of Ca atoms10g of CaCO34g of hydrogen atoms4g of hydrogen moleculesCalculate the mass mol of mol of NaNO36 mol of nitrogen atoms6 mol of nitrogen moleculesSolutionsmolarityconcentration / mol dm-3volumedm3 or cm3 Example 1 Calculate the number of moles of sodium hydroxide in 25cm3 of 2M NaOHmoles =molarity x volume in cm3 1000=2 mol dm-3 x 25cm3 ANS.

2 Mol 1000 Example 2 What volume of H2SO4 contains moles ?volume = 1000 x moles (re-arrangement of above)in cm3 molarity = 1000 x 20 cm3 mol dm-3 Example of Na2CO3 is dissolved in water and the solution made up to 250 is the concentration of the solution in mol dm-3 ? MOLAR mass of Na2CO3= 106g mol -1no. of moles in 250cm3= / 106g mol -1= molesno. of moles in 1000cm3 (1dm3)= moles ANS. mol dm-3. 2 MolesF321 KNOCKHARDY PUBLISHING 2008 moles = concentration x volume=molarity x volume in dm3=molarity x volume in cm3 1000 The 1000 takes intoaccount that there are1000 cm3 in the number of moles in1dm3 of 2M NaOH250cm3 of 2M NaOH5dm3 of HCl25cm3 of H2SO4 Calculate the concentration (in moles dm-3) of solutions moles of HCl in moles of NaOH in 25cm3 EMPIRICAL FORMULAE AND MOLECULAR FORMULAEE mpirical FormulaDescriptionExpresses the elements in a simple ratio ( CH2).

3 It can sometimes be the same as the molecular formula ( H2O and CH4)CalculationsYou need mass , or percentage mass , of each element present relative atomic masses of the elements presentExample 1 Calculate the empirical formula of a compound containing C (48%), H (4%) and O(48%) C H O1) Write out percentages (by mass )48%4%48%2) Divide by the relative atomic mass48/124/148/16 .. this gives a MOLAR ratio 4 4 3 3) If not whole numbers then scale up4) Express as a formulaC4H4O3 Example 2 Calculate the empirical formula of a compound with C ( ), O ( ), H ( ) C H O1) Write out ratios by mass ) Divide by relative atomic / / 1 / 16 (this gives the MOLAR ratio) ) If not whole numbers then scale up - try dividing by smallest value ( ) 5 10 14) Express as a formulaC5H10 OMolecular FormulaDescriptionExact number of atoms of each element in the formula ( C4H8)CalculationsCompare empirical formula relative molecular mass .

4 The relative molecular massof a compound will be an exact multiple (x1, x2 etc.) of its relative empirical mass . ExampleCalculate the molecular formula of a compound of empiricalformula CH2 and relative molecular mass of CH2 unit = 14divide molecular mass (84) by 14 = 6molecular formula = empirical formula x 6 = C6H12 Moles 3 F321 KNOCKHARDY PUBLISHING 2008 MOLAR mass CALCULATIONSRELATIVEMASSR elative Atomic mass (Ar)The mass of an atom relative to that of thecarbon 12 isotope having a value of mass per atom of an element x 12 mass of an atom of 12C*Relative Molecular mass (Mr)The sum of all the relative atomicmasses present in a moleculeoraverage mass of a molecule x 12 mass of an atom of 12 CMOLAR VOLUMEAt rtpThe MOLAR volume of any gas at rtp is 24 dm3 mol-1 ( m3 mol-1)rtp Room Temperature and PressureAt stpThe MOLAR volume of any gas at stp is dm3 mol-1 ( m3 mol-1) stp Standard Temperature and Pressure ( 273K and x 105 Pa ) of a gas occupies 250cm3 at rtp.

5 Calculate its MOLAR mass . 250 cm3 has a mass of 1000 cm3 (1dm3)has a mass of to convert to dm3 24 dm3has a mass of to convert to 24dm3 ANSWER: The MOLAR mass is mol-1 4 MolesF321 KNOCKHARDY PUBLISHING 2008NB * Relative Formula mass is used if the species is the mass ) dm3 of carbon dioxide, CO2 at rtpb) 120 cm3 of sulphur dioxide, SO2 at rtpc) of a gaseous hydrocarbon occupies 120cm3 at rtp. Identify the include using the ideal gas equation PV = nRT the MOLAR Volume at stpFor 1 mole of gas PV = R Tfor n moles of gasPV = n R TalsoPV = m R T MwherePpressurePascals (Pa) or N m-2 Vvolumem3(there are 106 cm3 in a m3)nnumber of moles of gasRgas J K-1 mol-1 TtemperatureKelvin(K = C + 273)mmassg or KgMmolar massg mol-1 or Kg mol-1 Old units1 atmosphere is equivalent to 760 mm/Hg or x 105 Pa (Nm-2)1 litre (1 dm3) is equivalent to 1 x 10-3 m3 Example 1 Calculate the number of moles of gas present in 500cm3 at 100 KPa pressure andat a temperature of 27 100 KPa= 100000 PaV= 500 cm3 x 10-6 = m3T= 27 + 273= 300 KR= J K-1 mol-1= = nRT n = PV=100000 x moles RT 300 x 2 Calculate the relative molecular mass of a vapour if g of gas occupy 400 cm3 ata temperature of 223 C and a pressure of 100 100 KPa= 100000 PaV= 400 cm3 x 10-6 = m3T= 227 + 273= 500 Km= J K-1 mol-1= = mRT M = mRT = x 500 x PV 100000 x 5 F321 KNOCKHARDY PUBLISHING 2008 PV = n R T PV = m R T M CalculationThe volume of a gas varies with temperature and pressure.

6 To convert a volumeto that which it will occupy at stp (or any other temperature and pressure) one usethe relationship which is derived from Boyle s Law and Charles initial pressureV1 initial volumeT1 initial temperature (in Kelvin)P2 final (in this case, standard) pressureV2 final volume (in this case, at stp)T2 final (in this case, standard) temperature (in Kelvin)CalculationsConvert the volume of gas to that at stp then scale it up to the MOLAR mass of gas occupying dm3 ( litres , 22400cm3 ) is the MOLAR is possible to calculate the MOLAR mass of a gas by measuring the volume of agiven mass of gas and applying the above Gas syringe method Victor Meyer method Dumas bulb methodExampleA sample of gas occupies dm3 at 100 C and 5000 Pa pressure. Calculate itsvolume at stp [273K and 100 kPa].P1 initial pressure= 5000 PaP2 final pressure = 100000 PaV1 initial volume= dm3V2 final volume= ?T1 initial temperature= 373K T2 temperature= 273 Kthus5000 x x V2 373 273thereforeV2=273 X 5000 x dm3 ( dm3) 373 x 100000 6 MolesF321 KNOCKHARDY PUBLISHING 2008 P1V1 = P2V2 T1T2 Gay-Lussac s Law of Combining VolumesStatement When gases combine they do so in volumes that are in a simple ratio to each other and to that of any gaseous product(s) all volumes must be measured at the same temperature and s TheoryStatement Equal volumes of all gases, at the same temperature and pressure, contain equal numbers of molecules CalculationsGay-Lussac s Law and avogadro s Theory are used for reacting gas 1 What volume of oxygen will be needed to ensure that 250cm3 methane undergoescomplete combustion at 120 C ?

7 How much carbon dioxide will be formed ? CH4(g) + 2O2(g) > CO2(g) + 2H2O(g)1 molecule 2 molecules1 molecule 2 molecules 1 volume 2 volumes 1 volume 2 volumes (a gas at 120 C) 250cm3 500cm3 250cm3 of oxygen and 250cm3 of carbon tipsAn excess of one reagent is often included; excess O2 ensures completecombustionCheck the temperature, and state symbols, to check which compounds are notgases. This is especially important when water is present in the 220cm3 of propane vapour is reacted with 120cm3 of oxygen at 50 C. Calculatethe composition of the final mixture at the same temperature and pressure? C3H8(g) + 5O2(g) > 3CO2(g) + 4H2O(l)1 molecule 5 molecules 3 molecules 4 molecules 1 volume 5 volumes 3 volumes negligible (it is a liquid at 50 C) 20cm3 100cm3 60cm3 20cm3 will be unusedANSWER20cm3 of unused oxygen and 60cm3 of carbon 7 F321 KNOCKHARDY PUBLISHING 2008example 31g of gas occupies 278cm3 at 25 C and 2 atm pressure.

8 Calculate its MOLAR ) convert to stp2 x 278 = 1 x V V = 278 x 2 x 273 = 509 cm3 298 273 1 x 298ii) convert to MOLAR volume1goccupies509cm3 at stp1/509goccupies 1cm3 22400 x 1/509goccupies22400cm3 therefore44goccupies dm3at stp ANSWER: The MOLAR mass is 44g mol-1 8 MolesF321 KNOCKHARDY PUBLISHING Convert the following volumes into m3 a) 1dm3b) 250cm3c) Convert the following temperatures into Kelvin a) 100 Cb) 137 Cc) -23 C Calculate the volume of mol of propane gas at 298K and 105 Pa pressure Calculate the mass of propane (C3H8) contained in a m3 flask maintained at a temperature of 273K and a pressure of 9 F321 KNOCKHARDY PUBLISHING 2008 ANSWERS TO x 10-23g, = mol10/100 = mol4/1= 4 mol4/2 = 2 mol2 x 16g = 32gmol of x 85g = x 14g = 84g6 x 28g = the number of moles in2 mol5 mol (5 x 10-3) mol dm-34 mol the mass ) ) 5 x 10-3 ) Mr = 16 Formula = Convert the following volumes into m3 a) or 1x 10-3 m3b) or 10-4 m3 c) 1 x 10-7 m3 Convert the following temperatures into Kelvin a) 373Kb) 400Kc) 250K