Answer:
The density is 3g/L
Explanation:
The reaction that occurs in the vessel is:
4 NH₃ + 5 O₂ → 4 NO + 6 H₂O
10,0g of NH₃ are:

6,50 g of O₂ are:

For a complete reaction of O₂ there are necessaries:

O₂ is limiting reactant. The excess moles of NH₃ are:
0,587 - 0,163 = <em>0,424 moles of NH₃</em>
These moles are:
<em>7,22g of NH₃</em>
Knowing O₂ is limiting reactant, mass of NO and H₂O are:
<em>4,87g of NO</em>
<em>4,39g of H₂O</em>
The total mass is: 7,22g + 4,87g + 4,39g = 16,48g ≡ <em>16,5g </em>
<em>-</em><em>The same mass add in the first. By matter conservation law-</em>
As vessel volume is 5,50L, density is:
16,5g/5,50L = <em>3g/L</em>
I hope it helps!