Gas Stoichiometry

Gas Stoichiometry Moles  Liters of a Gas: STP - use 22.4 L/mol Non-STP - use ideal gas law

Gas Stoichiometry Problem What volume of CO2 forms from 5.25 g of CaCO3 at 103 kPa & 25ºC? CaCO3  CaO + CO2 5.25 g ? L non-STP Looking for liters: Start with stoich and calculate moles of CO2. 5.25 g CaCO3 1 mol CaCO3 100.09g 1 mol CO2 CaCO3 0.052 mols CO2 Plug this into the Ideal Gas Law to find liters.

n R T (0.052mol)(8.314kPa L/mol K)(298K) P V = n R T = V = P 103kPa = 1.25 LCO2

Gas Stoichiometry Problem How many grams of Al2O3 are formed from 15.0 L of O2 at 97.3 kPa & 21°C? 4 Al + 3 O2  2 Al2O3 15.0 L non-STP ? g GIVEN: P = 97.3 kPa V = 15.0 L n = ? T = 21°C = 294 K R = 8.315 LkPa/molK WORK: PV = nRT (97.3 kPa) (15.0 L) = n (8.315LkPa/molK) (294K) n = 0.597 mol O2 Given liters: Start with Ideal Gas Law and calculate moles of O2. NEXT 

Gas Stoichiometry Problem How many grams of Al2O3 are formed from 15.0 L of O2 at 97.3 kPa & 21°C? 4 Al + 3 O2  2 Al2O3 15.0L non-STP ? g Use stoich to convert moles of O2 to grams Al2O3. 0.597 mol O2 2 mol Al2O3 3 mol O2 101.96 g Al2O3 1 mol Al2O3 = 40.6 g Al2O3

Zn (s) + 2 HCl (aq) ZnCl2(aq) + H2(g) Gas Stoichiometry Find vol. hydrogen gas made when 38.2 g zinc react w/excess hydrochloric acid. @ STP. Zn (s) + 2 HCl (aq) ZnCl2(aq) + H2(g) 38.2 g excess X L The relationship between the amounts of gases (in moles) and their volumes (in liters) in the ideal gas law is used to calculate the stoichiometry of reactions involving gases, if the pressure and temperature are known. • Relationship between the amounts of products and reactants in a chemical reaction can be expressed in units of moles or masses of pure substances, of volumes of solutions, or of volumes of gaseous substances. • The ideal gas law can be used to calculate the volume of gaseous products or reactants as needed. • In the lab, gases produced in a reaction are collected by the displacement of water from filled vessels — the amount of gas can be calculated from the volume of water displaced and the atmospheric pressure.

2 Mg (s) + CO2 (g) 2 MgO (s) + C (s) What mass solid magnesium is required to react w/250 mL carbon dioxide at 1.5 atm and 77oC to produce solid magnesium oxide and solid carbon? 2 Mg (s) + CO2 (g) 2 MgO (s) + C (s) X g Mg 250 mL 0.25 L V = 250 mL 0.25 L oC + 273 = K T = 77oC 350 K P = 1.5 atm 151.95 kPa n = R T P V 151.95 kPa 1.5 atm (0.250 L) P V = n R T n = = 0.013 mol CO2 0.0821 L.atm / mol.K 8.314 L.kPa / mol.K (350 K) 2 mol Mg 24.3 g Mg x g Mg = 0.013 mol CO2 = 0.63 g Mg 1 mol CO2 1 mol Mg CO2 Mg

Gas Stoichiometry 2 Na + Cl2 NaCl 2 How many liters of chlorine gas are needed to react with excess sodium metal to yield 5.0 g of sodium chloride @ STP? 2 Na + Cl2 NaCl 2 excess X L 5 g

Sample problem 2 Ammonia (NH3) gas can be synthesized from nitrogen gas + hydrogen gas. What volume of ammonia at 450 kPa and 80°C can be obtained from the complete reaction of 7.5 kg hydrogen? First we need a balanced equation: N2(g) + 3H2(g)  2NH3(g) 1 mol H2 2.02 g H2 x 2 mol NH3 3 mol H2 x # mol NH3= 7500 g H2 = 2475 mol PV = nRT P = 450 kPa, n = 2475 mol, T = 353 K (450 KPa) (2475 mol)(8.31)(353 K) = V = 16 135 L NH3

Sample problem 3 Hydrogen gas (and NaOH) is produced when sodium metal is added to water. What mass of Na is needed to produce 20.0 L of H2 at STP? First we need a balanced equation: 2Na(s) + 2H2O(l)  H2(g) + 2NaOH(aq) PV = nRT P= 1atm, V= 20.0 L, T= 273 K (0.0821atm•L/K•mol)(273 K) (1 atm)(20.0 L) = n = 0.893 mol H2 or # mol = 20.0 L x 1 mol / 22.4 L = 0.893 mol 2 mol Na 1 mol H2 x 22.99 g Na 1 mol Na x # g Na= 0.893 mol H2 = 41.1 g Na