(a) Mass of "A"_2"B"
Step 1. Start with the balanced equation.
Your equation is not in its lowest terms. It should be
M_text(r):color(white)(m) 40.0color(white)(ml)30.0color(white)(mml)50.0
color(white)(mmmll)"A"_2 + "2AB" → "2A"_2"B"
Step 2. Calculate the moles of "A"_2"B".
"Moles of A"_2"B" = 2.50 color(red)(cancel(color(black)("mol A"_2))) × ("2 mol A"_2"B")/(1 color(red)(cancel(color(black)("mol A"_2)))) = "5.00 mol A"_2"B"
(b) Molecular mass of "A"_2"B"
If "Molec. mass of A"_2 = "40.0 u", then "at. mass of A" = "20.0 u"
"Molec. mass of AB" = "30.0 u" = "20.0 u + at. mass of B"
"At. mass of B" = "30.0 u - 20.0 u" = "10.0 u"
"Molec. mass of A"_2"B" = "2 × 20.0 u + 10.0 u" = "40.0 u + 10.0 u" = "50.0 u"
(c) Mass of "A"_2 required
Step 1. Calculate the moles of "AB"
"Moles of AB" = 15.0 color(red)(cancel(color(black)("g AB"))) × (1 "mol AB")/(30.0color(red)(cancel(color(black)("g AB")))) = "0.500 mol AB"
Step 2. Calculate the moles of of "A"_2
"Moles of A"_2 = 0.500 color(red)(cancel(color(black)("mol AB"))) × "1 mol A"_2/(2 color(red)(cancel(color(black)("mol AB")))) = "0.250 mol A"_2
Step 3. Calculate the mass of "A"_2
"Mass of A"_2 = 0.250 color(red)(cancel(color(black)("mol A"_2))) × "40.0 g A"_2/(1 color(red)(cancel(color(black)("mol A"_2)))) = "10.0 g A"_2
(d) Mass of "A"_2"B" formed
Step 1. Calculate the moles of "A"_2"B" formed
"Moles of A"_2"B" = 0.500 color(red)(cancel(color(black)("mol AB"))) × ("2 mol A"_2"B")/(2 color(red)(cancel(color(black)("mol AB")))) = "0.500 mol A"_2"B"
Step 2. Calculate the mass of "A"_2"B"
"Mass of A"_2"B" = 0.500 color(red)(cancel(color(black)("mol A"_2"B"))) × ("50.0 g A"_2"B")/(1 color(red)(cancel(color(black)("mol A"_2"B")))) = "25.0 g A"_2"B"
