How many moles of silver are in #8.907xx10^27# #"atoms Ag"#?

Question

Ellie Andrews · Accepted Answer

The mass of #8.907xx10^27# atoms of Ag is #color(blue)(1.595xx10^6 "g"#.

#6.022xx10^23 "atoms Ag"=1"mol Ag"# #"Molar mass Ag"##=##107.87 "g/mol"# First calculate moles #"Ag"#, then calculate mass #"Ag"#. Determine how many moles of Ag there are. Divide the number of moles #"Ag"# by #(6.022xx"10"^23"atoms")/("mol")#. Since this is a fraction, divide by inverting and multiplying. #8.907xx10^27 color(red)cancel(color(black)("atoms Ag"))xx(1"mol Ag")/(6.022xx10^23 color(red)cancel(color(black)("atoms Ag")))=1.47908xx10^4 "mol Ag"# To minimize rounding errors, I'm holding onto a few guard digits. The final answer will be rounded to four significant figures. Determine the mass. Multiply #"mol Ag"# by its molar mass. #1.47908xx10^4 color(red)cancel(color(black)("mol Ag"))xx(107.87"g Ag")/(1color(red)cancel(color(black)("mol Ag")))=1.595xx10^6 "g Ag"# (rounded to four significant figures)

Cooper Anderson · Answer

undefined To determine the number of moles of silver atoms, you can use Avogadro's number, which states that one mole of any substance contains approximately $6.022 \times 10^{23}$ atoms.

$8.907 \times 10^{27}$ atoms Ag can be converted to moles using the following calculation:

$$\text{Number of moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}}$$

$$= \frac{8.907 \times 10^{27}\text{ atoms}}{6.022 \times 10^{23}\text{ atoms/mol}}$$

$$≈ \frac{8.907}{6.022} \times 10^{27-23}$$

$$≈ 1.48 \times 10^4 \text{ moles}$$

So, there are approximately $1.48 \times 10^4$ moles of silver atoms.