Question #f8f5c

Start by writing the balanced chemical equation that describes this neutralization reaction.

#"Ca"("OH")_ (2(aq)) + 2"HNO"_ (3(aq)) -> "Ca"("NO"_ 3)_ (2(aq)) + 2"H"_ 2"O"_ ((l))#

Now, the trick here is to realize that in any chemical reaction, the total mass of the products must be equal to the total mass of the reactants #-># think the Law of Mass Conservation here.

So if you assume that #"126 g"# of nitric acid took part in the reaction, then you can say that if the reaction produced

#overbrace(" 36 g ")^(color(blue)("mass of water")) + overbrace(" 164 g ")^(color(blue)("mass of calcium nitrate")) = overbrace(" 200 g ")^(color(blue)("total mass of products"))#

it must have consumed

#overbrace(" 126 g ")^(color(blue)("mass of nitric acid")) + overbrace(" ? g ")^(color(blue)("mass of calcium hydroxide")) = overbrace(" 200 g ")^(color(blue)("total mass of reactants"))#

This implies that the mass of calcium hydroxide that reacted is equal to

#"mass Ca"("OH")_2 = "200 g " - " 126 g" = color(darkgreen)(ul(color(black)("74 g")))#

To double-check the answer, use the molar masses of calcium nitrate, water, and nitric acid to convert all the masses to moles--I'll round all the values to the nearest whole number to make the calculations easier.

#36 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18color(red)(cancel(color(black)("g")))) = "2 moles H"_2"O"#

#164 color(red)(cancel(color(black)("g"))) * ("1 mole Ca"("NO"_3)_2)/(164 color(red)(cancel(color(black)("g")))) = "1 mole Ca"("NO"_3)_2#

#126 color(red)(cancel(color(black)("g"))) * "1 mole HNO"_3/(126color(red)(cancel(color(black)("g")))) = "1 mole HNO"_3#

According to the balanced chemical equation, when #1# mole of calcium hydroxide reacts with #2# moles of nitric acid, the reaction produces #1# mole of aqueous calcium nitrate and #2# moles of water.

As you can see, the values that you have here are consistent with what you would need, i.e. #2# moles of nitric acid, and what you would get, i.e. #1# mole of calcium nitrate and #2# moles of water, when #1# mole of calcium hydroxide reacts.

Use the molar mass of calcium hydroxide to convert this to grams to get

#1 color(red)(cancel(color(black)("mole Ca"("OH")_2))) * "74 g"/(1color(red)(cancel(color(black)("mole Ca"("OH")_2)))) = color(darkgreen)(ul(color(black)("74 g")))#