To determine the mass of 2.86 moles of silver (Ag), we need to use the relationship between moles, molar mass, and mass. The molar mass is the mass of one mole of a substance.
The molar mass of silver (Ag) is 107.87 grams per mole (g/mol). This value means that one mole of silver weighs 107.87 grams.
To find the mass of 2.86 moles of silver, we'll multiply the number of moles by the molar mass of silver:
[tex]\[
\text{Mass of Ag} = \text{Number of moles} \times \text{Molar mass of Ag}
\][/tex]
[tex]\[
\text{Mass of Ag} = 2.86 \, \text{moles} \times 107.87 \, \text{g/mol}
\][/tex]
After performing this multiplication, we get:
[tex]\[
\text{Mass of Ag} = 308.5082 \, \text{grams}
\][/tex]
Looking at the options provided:
1. [tex]$37.7\, g\, Ag$[/tex]
2. [tex]$0.265\, g\, Ag$[/tex]
3. [tex]$227\, g\, Ag$[/tex]
4. [tex]$309\, g\, Ag$[/tex]
The closest value to our calculated mass of 308.5082 grams is option 4: [tex]$309\, g\, Ag$[/tex].
Therefore, the mass of 2.86 moles of silver (Ag) is approximately [tex]\(\boxed{309\, g\, Ag}\)[/tex].
