Of course, I can help you with that! To find the mass in grams of 1.06 x 10^25 silicon atoms, we will use the given information that 28.09 g of silicon contains 6.02 x 10^23 silicon atoms.
First, let's calculate the molar mass of silicon. The molar mass is the mass of one mole of a substance and is equal to the atomic mass of the element in grams. For silicon, the atomic mass is approximately 28.09 g/mol.
Next, we can calculate the number of moles in 28.09 g of silicon. We divide the given mass by the molar mass:
Number of moles = mass / molar mass
Number of moles = 28.09 g / 28.09 g/mol = 1 mol
Now, let's find the number of moles in 1.06 x 10^25 silicon atoms. We can use Avogadro's number (6.02 x 10^23 atoms/mol) to convert the given number of atoms to moles:
Number of moles = number of atoms / Avogadro's number
Number of moles = (1.06 x 10^25 atoms) / (6.02 x 10^23 atoms/mol)
Now we have the number of moles of silicon atoms. To find the mass in grams, we can multiply the number of moles by the molar mass:
Mass = number of moles x molar mass
Let's plug in the values:
Mass = (1.06 x 10^25 atoms) / (6.02 x 10^23 atoms/mol) x (28.09 g/mol)
Simplifying the expression:
Mass ≈ 186.048 g
Therefore, the mass in grams of 1.06 x 10^25 silicon atoms is approximately 186.048 grams.