"molality"="mol solute"/"kg solvent"#
Molality = mol/kg and is abbreviated #"m"#.
We need to determine the moles #"C"_12"H"_22"O"_11"#, then convert moles to grams.
The solute is #"C"_12"H"_22"O"_11"#, and the solvent is water.
Since the mass of the solvent needs to be in kilograms, we first need to convert #2.50xx"10"^2"# g water to kg.
#"1 kg"##=##"1000 g"#
#2.50xx"10"^2"g H"_2"O"xx((1"kg")/(1000"g"))="0.250 kg H"_2"O"#
Plug the known values into the molality formula.
#"2.00 m"=("? mol C"_12"H"_22"O"_11)/(0.250"kg")#
To determine mol #"C"_12"H"_22"O"_11"#, multiply #"0.250 kg"# by #"2.00 mol/kg"#.
#0.250color(red)cancel(color(black)("kg"))xx2.00"mol"/color(red)cancel(color(black)("kg"))="0.500 mol C"_12"H"_22"O"_11"#
To convert #"0.500 mol C"_12"H"_22"O"_11"# to grams, multiply moles #"C"_12"H"_22"O"_11"# by its molar mass #("342.297 g/mol")#.
#0.500color(red)cancel(color(black)("mol C"_12"H"_22"O"_11))xx(342.297"g C"_12"H"_22"O"_11)/(1color(red)cancel(color(black)("mol C"_12"H"_22"O"_11)))="171 g C"_12"H"_22"O"_11"# (rounded to three significant figures)
