What weight of `AgCl` will be precipitated when a solution containing `4.77`g of `NaCl` is added to a solution of `5.77g` of `AgNO_3` ?

The first thing to do is to write down the reaction that is described in the question. Since the reactant and one of the product are given, we can write the balanced reaction:

`NaCl+AgNO_3->AgCl +NaNO_3`

In this type of questions, it is nice to write down a kind of 'scheme' in which we place all the information provided so we can have a clear look what to do. But first, it is important to calculate the masses into moles, before we on accident calculate with the wrong numbers. To do this, we need to molar masses of the compounds. This can be calculated by adding up the masses of the atoms in the compounds. We obtain:

`AgCl`=`1xxAg +1xxCl =107.9u+35.45u=143.35u`
`NaCl`=`1xxNa+1xxCl=22.99u+34.45u=57.44u`
`AgNO_3`=`1xxAg+1xxN+3xxO=107.9u+14.01u+3xx16.00u=169.91u`

Now we calculate a number of moles with the formula below.

`mol=(mass)/(molar mass)`

I only display the calculation for `NaCl` here.
`mol=(4.77 (color(red)(cancel(color(blue)(gram)))))/(57.44(color(red)(cancel(color(blue)(gram)))/color(blue)(mol)))=0.083 color(white)(a)color(blue)(mol)` `NaCl`
`AgNO_3=0.034 color(white)(a)color(blue)(mol)`

Now we have the moles, we write the molar ratio below the reaction and the moles at the correct places. We obtain something like this:

`color(white)(aa)``NaCl+AgNO_3->AgCl +NaNO_3``color(white)(aaa)color(blue)("reaction")`
`color(white)(aaaa)1 color(white)(aab):color(white)(aaa)1color(white)(aaab):color(white)(aaa)1color(white)(aa):color(white)(aaab)1color(white)(aa.aa)color(blue)("molar ratio")`
`color(white)(aa)0.083 color(white)(aaa)0.034color(white)(aaaaaaa)?color(white)(aaaaaaaaaaaaa)color(blue)("moles")`

We don't need to do anything with the `NaNO_3` in this question.

We calculate the question mark `?` by applying the law of conservation of mass. This can be done by:
mol `AgCl` =`(mol color(red)(AgNO_3)xxcolor(blue)(cancel(color(black)(molar ratio))) color(red)(AgCl))/(color(blue)(cancel(color(black)(molar ratio)) color(red)(AgNO_3))`
mol `AgCl` =`(0.034 xx1)/1=0.034`

Now we calculate the mass of `AgCl` that is created. The molar mass was `143.35 u`

mass `AgCl`=`mol xx molar mass`
mass `AgCl` =`0.034 color(red)(cancel(color(blue)(mol)))xx143.35 (color(blue)(gram))/(color(red)(cancel(color(blue)(mol))))=4.87 color(white)(a)color(blue)(gram)`

For this particular question, it seems useless to calculate the molar mass of the other reactant, but for future questions, they may ask something more about the reaction and then you already have made a nice scheme.