A certain mass of nitrogen required 12 grams of oxygen to produce nitrogen monoxide, NO. If the same mass of this nitrogen was converted to nitrogen dioxide, NO₂, what would the mass of oxygen required be? A) Six grams, B) 12 grams, C) 24 grams, D) 36 grams, or E) 48 grams.
Our journey begins with an unknown mass of nitrogen gas. And it’s being reacted with 12 grams of oxygen gas and our product is nitrogen monoxide. We need two lots of nitrogen monoxide to balance our equation. In our second scenario, we’re taking exactly the same amount and exactly the same mass of nitrogen. And we’re producing nitrogen dioxide. And what we need to work out is what mass of oxygen is required to convert this mass of nitrogen into the nitrogen dioxide. We need two oxygen molecules per nitrogen molecule in order to balance the equation, producing two molecules of nitrogen dioxide.
To make this question easier, we’re assuming that we’re not generating biproducts. We’re assuming that all of the oxygen is being consumed and integrating into the nitrogen oxides. Now, a little word of warning this question is actually an awful lot simpler than you might think. Here’s what you might have thought. Let’s take the mass of oxygen in the first equation and work out the amount in moles of oxygen. From there, we can work out the amount of nitrogen we consumed in the first reaction. And then, the next step will be to work out the amount of oxygen we consume in the second reaction. And the last step of our process would be to work out the mass of the oxygen in the second reaction.
This would be a reliable, albeit long process. But if you think about it, there’s a much quicker way of doing it. Converting nitrogen to nitrogen dioxide requires twice as much oxygen as converting nitrogen to nitrogen monoxide. In nitrogen monoxide, we have one oxygen atom per nitrogen atom. And in nitrogen dioxide, we have two oxygen atoms per nitrogen atom. Therefore, in order to convert the same amount of nitrogen into nitrogen dioxide, we need double the amount of oxygen. So the mass of oxygen required is simply two times 12 grams, which is 24 grams.
You should have got exactly the same result if you took the long route. You can convert from the mass of oxygen to the amount of oxygen in moles by dividing by the molar mass of O₂, which is 32 grams per mole. Then, you can use the stoichiometric relationship in the first equation, converting from moles of oxygen to moles of nitrogen by multiplying by one mole of nitrogen per mole of oxygen. And then plug the same amount of nitrogen into the second equation and worked out the amount of oxygen by multiplying by two moles of oxygen per mole of nitrogen. And then, in the last step, finally converted back to mass of oxygen by multiplying by the molar mass of oxygen, 32 grams per mole.
However, the first route is much quicker and just as precise. We’re observing the relationship between the atoms in the product and using that to convert from grams in the first equation to grams in the second. And we don’t need to go through lots of individual calculations which might introduce some mistakes. However, whichever way you do it, you should have worked out that if we have a certain mass of nitrogen and 12 grams of oxygen are used to convert it to nitrogen monoxide, if we take the same mass of nitrogen, we’ll need 24 grams of oxygen to turn it into nitrogen dioxide.