Video: Estimating the Heat Absorbed When 1 Mol of Nitrogen Dioxide If Formed from Its Elements in Their Standard States, Given the Heat Absorbed per Gram

When nitrogen and oxygen react to form nitrogen dioxide, the heat absorbed is approximately 0.72 KJ per gram of nitrogen dioxide formed. The amount of heat absorbed when 1 mol of nitrogen dioxide is formed is approximately _. [A] 0.7 KJ [B] 21 KJ [C] 32 KJ [D] 46 KJ [E] 64 KJ

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Video Transcript

When nitrogen and oxygen react to form nitrogen dioxide, the heat absorbed is approximately 0.72 kilojoules per gram of nitrogen dioxide formed. The amount of heat absorbed when one mole of nitrogen dioxide is formed is approximately blank. (A) 0.7 kilojoules, (B) 21 kilojoules, (C) 32 kilojoules, (D) 46 kilojoules, or (E) 64 kilojoules.

The chemical reaction that describes the process in the question is N2 gas plus 2O2 gas reacting to form 2NO2 gas. The reaction in this problem absorbs heat, which means that it’s endothermic. If the reaction released heat instead, it would be an exothermic reaction. We’re told that this reaction absorbs 0.2 kilojoules per gram of nitrogen dioxide formed. But we want to know how much heat is absorbed when one mole of nitrogen dioxide is formed.

So, to answer this question, we’ll need to convert our kilojoules per gram of NO2 into kilojoules per one mole of NO2. So, to answer this question, we need to convert the given kilojoules per gram of NO2 into kilojoules per one mole of NO2. The first thing that we’ll need to do is calculate the molar mass of nitrogen dioxide, which we can do using the periodic table.

Nitrogen’s molar mass is about 14 grams per mole. And oxygen has a molar mass of about 16. And there’s two oxygen atoms in one molecule of nitrogen dioxide. So nitrogen dioxide has a molar mass of 46 grams per mole. Now, we can convert from grams of NO2 to moles of NO2 by multiplying by the molar mass. This puts us in units of kilojoules per mole.

And we’re interested in the amount of heat that’s absorbed when we have one mole of NO2 that’s formed, which we can find by multiplying this expression by one mole of NO2. Which gives us the correct units of kilojoules that we’re looking for. Now, we just have to multiply through to solve this problem.

Unfortunately, 0.72 times 46 might not be so easy to do in our heads. So let’s do a little bit of rounding. 0.72 is really close to 0.7. And 0.7 is equal to seven-tenths. And let’s round 46 up to 50 to give us a nice even number to work with. Now, we have a much simpler expression to evaluate. If we divide the 50 by 10, we’d get seven times five. And seven times five is 35. This is closest to answer choice (C), 32 kilojoules. So, the amount of heat that’s absorbed when one mole of nitrogen dioxide is formed is approximately 32 kilojoules.

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