Mass Relationships in Chemical Reactions Atomic Mass (0.9890) (12 amu) + (0.0110) (13.00335) = 12.01 amu Mole Avogadro’s number: 6.022x1023 (atoms, molecules, particles) Molar mass is numerically the same as atomic mass of an element Molar Mass Molecular mass of a molecule is the sum of all atomic masses x how many atoms Ex) Find the molar mass of H2O (1.01 x 2) + 16.00 = 18.02 amu 18.02 amu = 18.02g H2O Formula mass of a compound is the sum of all atomic masses x how many atoms Ex) Find the molar mass of NaCl 22.99 + 35.45 = 58.44 amu 58.44 amu = 58.44g NaCl Examples 1. Helium (He) is a valuable gas used in industry, low-temperature research, deep-sea diving tanks and balloons. How many moles of He atoms are in 6.46 g of He? 1. How many atoms are in 112g of Fe? 1. Methane (CH4) is the principal component of natural gas. How many moles of CH4 are present in 6.07g of CH4? 4. How many hydrogen atoms are present in 25.6 g of urea [(NH2)2CO], which is used as a fertilizer, in animal feed, and in the manufacture of polymers? Mass Spectrometry Hydrate Percent Composition % comp. = n × molar mass of element × 100 molar mass of compound Ex) Find percent H and percent O in hydrogen peroxide (H2O2) %H = 2 × 1.008g H × 100 = 5.926% 34.02g H2O2 %O = 2 × 16.00g O × 100 = 94.06% 34.02g H2O2 Empirical Formula Steps: 1. Percent to mass 2. Mass to moles 3. Divide by small 4. Multiply ‘til whole Example 1. Ascorbic acid (vitamin C) cures scurvy. It is composed of 40.92% C, 4.58% H, and 54.50% O by mass. Determine its empirical formula. Example 2. When ethanol is burned, carbon dioxide and water are given off. Suppose that in one experiment the combustion of 11.5 g of ethanol produced 22.0 g of CO2 and 13.5 g of H2O. Determine the empirical formula for ethanol. Molecular Formula Steps: 1. Find empirical formula 2. Determine the molar mass of the empirical formula 3. Find multiplier (molar mass given/empirical molar mass) 4. Multiply empirical formula subscripts by the multiplier Example A sample of a compound contains 30.46% N and 69.54% O by mass, as determined by a mass spectrometer. In a separate experiment, the molar mass of the compound is found to be between 90 g and 95 g. Determine the molecular formula and the accurate molar mass of the compound. Chemical Reactions and Equations “Reactants with” “to produce” or “yield” 2 H2 (g) + O2 (g) Reactants 2 H2O (l) Product(s) Balancing Chemical Reactions Steps: 1. List elements present on each side 2. Add coefficients to balance (“met a non hairy oxen”) KClO3 O2+ KCl Stoichiometry • Mole method: coefficient in a reaction can be interpreted as the number of moles • Allows us to write conversion factors from a chemical equation Example The food we eat is degraded, or broken down, in our bodies to provide energy for growth and function. A general overall equation for this very complex process represents the degradation of glucose (C6H12O6) to carbon dioxide (CO2) and water (H2O): C6H12O6 + 6 O2 6 CO2 + 6 H2O If 856 g of C6H12O6 is consumed by a person over a certain period, what is the mass of CO2 produced? Limiting Reagents CO(g) + 2 H2(g) CH3OH(g) Example Urea [(NH2)2CO] is prepared by reacting ammonia with carbon dioxide in the following process: 2 NH3(g) + CO2(g) (NH2)2CO(aq) + H2O(l) In one process, 637.2g of NH3 are treated with 1142g CO2. Which of the reactants is the limiting reagent? Calculate the mass of [(NH2)2CO] formed. How much excess reagent (in grams) is left at the end of the reaction? Reaction Yield Example Titanium is a strong, lightweight, corrosion-resistant metal that is used in rockets, aircraft, jet engines, and bicycle frames. It is prepared by the reaction of titanium(IV) chloride with molten magnesium between 950°C and 1150°C: TICl4(g) + 2 Mg(l) Ti(s) + 2 MgCl2(l) In a certain industrial operation 3.54 x 107 g of TiCl4 are reacted with 1.13 x 107 g of Mg. Calculate the theoretical yield of Ti in grams. Calculate the percent yield if 7.91 x 106 g of Ti are actually obtained.