[liffey07]

--Statement--
Hydrogen cyanide is produced industrially from the reaction of gaseous ammonia, oxygen, and methane:
2NH₃(g) + 3O₂(g) + 2CH₄(g) --> 2HCN(g) + 6H₂O(g)

--Question--
If 5.00 x 103 kg each of NH₃, O₂, and CH₄ are reacted, what mass of HCN and of H₂O will be produced, assuming 100% yield?

--My process--
I assumed that one of the three reactants had to be limiting.  I first found the number of moles of each, which came out to be 293530.586 mol NH₃, 156250 mol O₂, and 311681.835 mol CH₄.  Then I set up two ratios of available moles:

293530.586 mol NH₃  = 1.8785957 mol NH₃
      156250 mol O2             1 mol O2

311681.835 mol CH₄  =  1.9947637 mol CH₄
      156250 mol O2              1 mol O2

I compared these ratios to the ratios of required moles (derived from the balanced equation):

.6666667 mol NH₃   .6666667 mol CH₄
      1 mol O2                 1 mol O2

Because the available moles of NH₃ and of CH₄ were both in excess, I assumed that the O₂ would be consumed first, and would therefore be the limiting reactant.  Next, I used the moles of the limiting reactant (O₂) to find the masses of the products:

156250 mol O2x 2 mol HCN   x 27.028 g HCN = 2.82 x 103 kg HCN
                       3 mol O2        1 mol HCN

156250 mol O2  x 6 mol H2O  x 18.015 g H2O  = 5.63 x 103 kg H2O
                           3 mol O2          1 mol H2O

I thought I solved the problem correctly, but my solution cannot be valid because it does not follow the Law of Conservation of Mass; the mass of the reactants (5.00 x 103 kg * 3 = 1.5 x 104 kg) does not equal the mass of the products (8.45 x 103 kg).  I don’t know whether my approach to the problem is completely off.  For example, maybe I should have set up a third mol ratio comparing NH3 and CH4.  Also, I don’t know how the 100% yield will influence the problem.  It means that the theoretical yield and actual yield are equal, but does that mean all the reactants will be consumed (i.e., there will be no limiting reactant?).  I am just very confused and need some help. Thanks for your patience!  

[xiankai]

is that 5 x 10³ or just 5 x 103?

[Yggdrasil]

Your answer is correct.  The reason the reaction seems to violate the conservation of mass is because the excess methane and ammonia cannot react to form hydrogen cyanide.  The missing 6.45x10³ kg on the products is in the form of unreacted methane and ammonia.

[Donaldson Tan]

... but my solution cannot be valid because it does not follow the Law of Conservation of Mass; the mass of the reactants (5.00 x 103 kg * 3 = 1.5 x 104 kg) does not equal the mass of the products (8.45 x 103 kg).  I don’t know whether my approach to the problem is completely off.  

the law of conservation of mass states that the mass of product formed equals the masss of reactants consumed.