Ammonia reacts with O2 problem

[skepticwulf]

Homework Statement

Ammonia reacts with O2 to form either NO(g) or NO2(g) according to these unbalanced equations:
NH3 + O2 ----> NO + H2O
NH3 + O2 ----> NO2 + H2O
In a certain experiment 2.00 moles of NH3 and 10.00 moles
of O2 are contained in a closed flask. After the reaction is
complete, 6.75 moles of O2 remains. Calculate the number
of moles of NO in the product mixture: (Hint: You cannot
do this problem by adding the balanced equations because you
cannot assume that the two reactions will occur with equal
probability.)

Homework Equations

The Attempt at a Solution

After the balance of equations,
x=mol of NH3 in the first equations(=mol of NO as well)

1st reaction:
2 mol NH3 gives 5/2 mole O2
x mol gives ... 5x/4 mole O2

2nd reaction:
2 mol NH3 gives 7/2 mole O2
(2-x) mol gives ... 7(2-x)/4 mole O2

5x/4 + 7(2-x)/4 + 6.75=10
I find: x=0.5 mole of NH3 as well as 0.5 mole of NO
But solution manual has 0.48 as answer, is my calculation wrong in any way??

 

[Borek]

Any particular reason to not write balanced reaction equations and to make us guess whether you had them right or wrong?

Ammonia doesn't "give" oxygen, it reacts with oxygen consuming it.

But in general 0.5 moles of NO look correct.

 

[skepticwulf]

No, no particular reason :)

2 NH3 + 5/2 O2 ----> 2NO + 3H2O
2 NH3 + 7/2 O2 ----> 2NO2 + 3H2O

 

[skepticwulf]

Thank you both! :)