A67.2 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

The density of water is 1 g/cm cubed and in order for the pebble to sink its density has to be greater than the density of water and in order for the twig to float its density has to be less than the density of water

You would do 1500/4 and the answer is 375