What volume of methanol (ρ=0.8g/cm^3) needs to be oxidized to produce 500mL 40% formaldehyde (ρ=1.11g/cm^3)?

Step 1. Calculate the mass of formaldehyde

#"Mass of formalin" = 5000 color(red)(cancel(color(black)("mL formalin"))) × ("1.11 g formalin")/(1 color(red)(cancel(color(black)("mL formalin")))) = "555 g formalin"#

#"Mass of formaldehyde" =555 color(red)(cancel(color(black)("g formalin"))) × "40 g formaldehyde"/(100 color(red)(cancel(color(black)("g formalin")))) = "222 g formaldehyde"#

#"Moles of CH"_2"O" = 222 color(red)(cancel(color(black)("g CH"_2"O"))) × ("1 mol CH"_2"O")/( 30.03 color(red)(cancel(color(black)("g CH"_2"O")))) = "7.393 mol CH"_2"O"#

Step 2. Calculate the moles of methanol

#"2CH"_3"OH" + "2O"_2 → "2CH"_2"O" + "2H"_2"O"#

#"Moles of CH"_4 = 7.393 color(red)(cancel(color(black)("mol CH"_2"O"))) × ("2 mol CH"_3"OH")/(2 color(red)(cancel(color(black)("mol CH"_2"O")))) = "7.393 mol CH"_3"OH"#

Step 3. Calculate the mass of methanol

#"Mas of methanol" = 7.393 color(red)(cancel(color(black)("mol CH"_3"OH"))) × ("32.04 g CH"_3"OH")/(1 color(red)(cancel(color(black)("mol CH"_3"OH")))) = "236.9 g CH"_3"OH"#

Step 4. Calculate the volume of methanol

#"Volume of CH"_3"OH" = 236.9 color(red)(cancel(color(black)("g CH"_3"OH"))) × ("1 cm"^3color(white)(l) "CH"_3"OH")/(0.8 color(red)(cancel(color(black)("g CH"_3"OH")))) = "300 cm"^3color(white)(l) "CH"_3"OH"#