Which of the following is true regarding the following reaction? 2NO₂ gas plus 4H₂ gas react to form N₂ gas plus 4H₂O gas. And we’re given five options, where we’re consuming an amount of NO₂ and either producing or consuming an amount of another substance. A) If 0.5 moles of NO₂ is consumed, one mole of N₂ is produced. B) If one mole of NO₂ is consumed, two moles of H₂O is produced. C) If one mole of NO₂ is consumed, one mole of H₂O is produced. D) If one mole of NO₂ is consumed, 0.5 moles of H₂ is consumed. Or E) If two moles of NO₂ is consumed, one mole of H₂O is produced.
Our job is to find the true statement. And presumably, we’ll find four false ones as well. The first thing we can check is whether the thing that’s consumed or produced appears on the right side of the equation. NO₂ is a reactant. So it should be consumed. And it’s NO₂ being consumed in each statement. So there’s no problem there yet. In the first statement, N₂ is said to be produced. And it’s a product. So that makes sense. H₂O is also a product. And it’s said to be produced in statements B, C, and E. So as far as that’s concerned, that’s correct. And in statement D, H₂ is said to be consumed. H₂ is a reactant. So that’s correct as well.
Now we know that the language looks correct, let’s have a look at the amounts. Statement A says that if 0.5 moles of nitrogen dioxide, NO₂, is consumed, one mole of N₂, nitrogen gas, is produced. This would suggest a molar ratio of one nitrogen dioxide per two nitrogen molecules. But the equation actually tells us that the ratio between nitrogen dioxide and nitrogen in this reaction is two to one, not one to two. So if we did consume half a mole of nitrogen dioxide, we’d expect to produce 0.25 moles of nitrogen gas. So option A is false and an incorrect answer.
Statement B says that if one mole of nitrogen dioxide is consumed, we’ll generate two moles of water. That would suggest a ratio of one nitrogen dioxide molecule per two water molecules. The equation tells us that two molecules of nitrogen dioxide will react with hydrogen to produce four molecules of water, which simplifies to the same ratio. Therefore, the production of two moles of water when we consume one mole of nitrogen dioxide is consistent with the reaction equation. So we found our answer. But let’s have a look at the others, just in case.
Statement C says that if one mole of nitrogen dioxide is consumed, we produce one mole of water. This suggests the ratio in the equation of one molecule of nitrogen dioxide for every molecule of water we produce. We’ve already demonstrated that this is inconsistent with the equation. So we can move on. Statement D says that if we consume one mole of nitrogen dioxide, we’ll also consume 0.5 moles of H₂ or hydrogen gas. This corresponds with the relationship where we’d have two molecules of nitrogen dioxide per molecule of hydrogen. But the equation tells us that two molecules of nitrogen dioxide require four hydrogen molecules in order to react and produce the stated products. Even if we simplify it, the ratio is the wrong way around. So option D joins the pile of false statements.
Lastly, statement E suggests that if two moles of NO₂ is consumed, we’ll produce one mole of H₂O. This is consistent with the reaction where we have two molecules of NO₂ reacting to produce one molecule of water. However, this is not consistent with the equation we’ve been given. In our equation, one molecule of nitrogen dioxide would go into reaction. And two molecules of water would come out.
So all this boils down to the fact that, of the five statements, the only one that’s true regarding the given reaction is that if one mole of NO₂ is consumed, two moles of H₂O is produced.