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?

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