What is the empirical formula of something that is made of 31g of phosphorous and 35g of Cl?

The empirical formula is the simplest whole-number ratio of atoms in a compound.

Your compound contains 31 g #"P"# and 35 g #"Cl"#.

#"Moles of P" = 31 color(red)(cancel(color(black)("g P"))) × "1 mol P"/(30.97color(red)(cancel(color(black)( "g P")))) = "1.00 mol P"#

#"Moles of Cl "= 35 color(red)(cancel(color(black)("g Cl"))) × "1 mol Cl"/(35.45 color(red)(cancel(color(black)("g Cl")))) = "0.987 mol Cl"#

From this point on, I like to summarize the calculations in a table.

#"Element"color(white)(Ag) "Mass/g"color(white)(X) "Moles"color(white)(Xll) "Ratio"color(white)(mll)"Integers"#
#stackrel(————————————————————)(color(white)(m)"P" color(white)(XXXmm)31 color(white)(Xml)1.00 color(white)(Xmll)1.01color(white)(mmmm)1)#
#color(white)(m)"Cl" color(white)(XXXXll)35 color(white)(mml)"0.987 color(white)(Xml)1 color(white)(mmmmml)1#

There is 1 mol of #"P"# for 1 mol of #"Cl"#.

The empirical formula is #"PCl"#.

Here is a video that illustrates how to determine an empirical formula.