Question

A 67.2 g sample of a gold and palladium alloy contains 2.49 * 1023 atoms. what is the composition (by mass) of the alloy?

Answer 1

One mole of any substance contains 6.022 x 10^23 atoms
Therefore, number of moles containing 2.49×10^23 atoms can be calculated as follows:
number of moles = (2.49 x 10^23) / (6.022 x 10^23) = 0.4135 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 = 0.4135 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 = 0.4135 - moles of palladium
Substitute with this in equation 2:
(0.4135 - moles of palladium) x 197 + moles of palladium x 106.4 = 67.2
 81.4595 - 197 moles of palladium + 106.4 moles of palladium = 67.2
81.4595 - 67.2 = 197 moles of palladium - 106.4 moles of palladium
14.2595 = 90.6 moles of palladium
moles of palladium = 0.1574 moles
Substitute in equation 1 to get moles of gold:
moles of gold = 0.4135 - 0.1574 = 0.2561 moles

Now, the last step is to convert the number of moles to mass:
mass = number of moles x molar mass
mass of gold = 0.2561 x 197 = 50.4517 grams
mass of palladium = 0.1574 x 106.4 = 16.74736 grams