One mole of any substance contains 6.022 x 10^23 atoms Therefore, number of moles containing <span>3.28×10^23 atoms can be calculated as follows: number of moles = (3.28 x 10^23) / (6.022 x 10^23) = 0.544 moles
From the periodic table: molecular mass of gold = 197 grams molecular mass of palladium = 106.4 grams Therefore: molar mass of gold = 197 grams molar mass of palladium = 106.7 grams
First equation: moles of gold + moles of palladium = 0.544 moles
Second equation: mass of gold + mass of palladium = 67.2 grams mass can be written as: mass = number of moles x molar mass therefore: (mass of gold + mass of palladium) can be rewritten as: moles of gold x 197 + moles of palladium x 106.4 = 67.2 grams
Now, we have two equations (highlighted in bold) in two unknowns, we can solve them simultaneously to get the number of moles of each element as follows: From equation one: moles of gold = 0.544 - moles of palladium Substitute with this in equation 2: </span>(0.544 - moles of palladium) x 197 + moles of palladium x 106.4 = 67.2 107.168 - 197 moles of palladium + 106.4 moles of palladium = 67.2 107.168 - 67.2 = 197 moles of palladium - 106.4 moles of palladium 39.968 = 90.6 moles of palladium moles of palladium = 0.4411 moles Substitute in equation 1 to get moles of gold: moles of gold = 0.544 - 0.4411 = 0.1029 moles Now, the last step is to convert the number of moles to mass: mass = number of moles x molar mass mass of gold = 0.1029 x 197 = 20.2713 grams mass of palladium = 0.4411 x 106.4 = 46.93304 grams
