Percent yield/excess reactant problem

[Lori]

Homework Statement

N2 reacts with H2 to form NH3

assume equal moles of N2 and H2 in container, and react to form NH3 with 100% yield. there are 2.0 moles of excess reactants left over. How many moles of each reactant was originally present?

Homework Equations

AY/TY = % yield

The Attempt at a Solution

I know that the answer is 3 moles after much trial and error. Cause if i had started with 3 moles of each reactant, then i used 1 mole of N2. Which means 2 moles in excess. How could i have shorten this problem without doing trial error?

 

[I like Serena]

Homework Statement

N2 reacts with H2 to form NH3

assume equal moles of N2 and H2 in container, and react to form NH3 with 100% yield. there are 2.0 moles of excess reactants left over. How many moles of each reactant was originally present?

Homework Equations

AY/TY = % yield

The Attempt at a Solution

I know that the answer is 3 moles after much trial and error. Cause if i had started with 3 moles of each reactant, then i used 1 mole of N2. Which means 2 moles in excess. How could i have shorten this problem without doing trial error?

Hi Lori!

We can set up equations, or we can do 'smart' trial and error.

With equations
We have 2 unknowns: the initial amount of reactants, and the amount of NH3 formed.
Let's call them x and y.
Then the equation becomes: x N₂ + x H₂ → y NH₃ + 2 N₂
Can we make a set of equations from that and solve it?

With 'smart' trial and error
Let's first balance the equation:
? N₂ + ? H₂ → ? NH₃ + ? N₂
Can we find the question marks such that the equation is balanced?
After that we need to figure out what to do to ensure we're left with 2 moles of initial reactant.