TBR Gen Chem Chapter 1 Passage V, Q.33

[Lunasly]

I was under the impression that mass percent was an intensive property. Meaning that regardless of the sample size, the mass percent of an element of a compound would not change. If the mass percent of an element is 40% for a given compound, then it doesn't matter if you have 10g, 100g, or a 1000g of that compound. Therefore, for any given hydrocarbon, how do you go about increasing the mass percent?

The question asks: Which of the following is not associated with an increasing mass percent of carbon in a hydrocarbon?

I. An increase in the mass of carbon per gram of the compound.
- Ok, I understand that the more moles of carbon atoms you have in your compound, the higher the mass percent of carbon.

II. An increase in the mass of water formed upon oxidation of one gram of the compound.
- I understand that if you increase the amount of water formed, that must mean you have increased amounts of hydrogen present in your compound.

III. An increase in the mass of hydrogen per gram of the compound.

The answer says that if you increase the mass of water produced through the combustion process, then there is an increase in the mass of hydrogen atoms per gram of compound, increasing its mass percent. If hydrogen has a larger mass percent this would decrease the mass percent of carbon. Similar idea for the third response.

My question: If I have a simple hydrocarbon chain and I increase the mass of carbon per gram of hydrocarbon, then how does this increase the mass percent of carbon? The formula for mass percent of carbon is [(molar mass of carbon)(# moles of carbon)]/[molecular mass of the hydrocarbon]. The only two variables in this formula that can change are the # moles of carbon and the molecular mass of the hydrocarbon. If the number of moles increases (e.g., we extend our hydrocarbon chain from 6 carbons to 12 carbons), then won't that be reflected by the increase in molecular mass of the hydrocarbon? How do you increase the mass percent of carbon for the SAME hydrocarbon chain?

Furthermore, if you have a higher mass of hydrogen per gram of compound, don't you also need to increase the amount of carbons? How can you increase the number of hydrogens without increasing carbon for a hydrocarbon chain?

I am under the impression that for any given compound, the mass percent is always the same. That is, the mass percent of oxygen in C6H12O2 is some given constant percent.

Thanks for the help!

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[Czarcasm]

I was under the impression that mass percent was an intensive property. Meaning that regardless of the sample size, the mass percent of an element of a compound would not change. If the mass percent of an element is 40% for a given compound, then it doesn't matter if you have 10g, 100g, or a 1000g of that compound. Therefore, for any given hydrocarbon, how do you go about increasing the mass percent?

The question asks: Which of the following is not associated with an increasing mass percent of carbon in a hydrocarbon?

I. An increase in the mass of carbon per gram of the compound.
- Ok, I understand that the more moles of carbon atoms you have in your compound, the higher the mass percent of carbon.

II. An increase in the mass of water formed upon oxidation of one gram of the compound.
- I understand that if you increase the amount of water formed, that must mean you have increased amounts of hydrogen present in your compound.

III. An increase in the mass of hydrogen per gram of the compound.

The answer says that if you increase the mass of water produced through the combustion process, then there is an increase in the mass of hydrogen atoms per gram of compound, increasing its mass percent. If hydrogen has a larger mass percent this would decrease the mass percent of carbon. Similar idea for the third response.

My question: If I have a simple hydrocarbon chain and I increase the mass of carbon per gram of hydrocarbon, then how does this increase the mass percent of carbon? The formula for mass percent of carbon is [(molar mass of carbon)(# moles of carbon)]/[molecular mass of the hydrocarbon]. The only two variables in this formula that can change are the # moles of carbon and the molecular mass of the hydrocarbon. If the number of moles increases (e.g., we extend our hydrocarbon chain from 6 carbons to 12 carbons), then won't that be reflected by the increase in molecular mass of the hydrocarbon? How do you increase the mass percent of carbon for the SAME hydrocarbon chain?

Furthermore, if you have a higher mass of hydrogen per gram of compound, don't you also need to increase the amount of carbons? How can you increase the number of hydrogens without increasing carbon for a hydrocarbon chain?

I am under the impression that for any given compound, the mass percent is always the same. That is, the mass percent of oxygen in C6H12O2 is some given constant percent.

Thanks for the help!

You have the right understanding, but your line of thought for the question is wrong. You are exactly right in stating that increasing the mole sample of a given compound will not change the mass percent (it's an intrinsic property). But what the question is basically comparing is different compounds and the effect they would have on the mass percent. So in this case, we're not increasing the number of moles for the same given compound. We are actually changing the compound itself to something entirely different. Here, mass percent would indeed change.

They give you 3 scenarios. Before considering any, realize that if you decided to increase the mole concentration for the initial compound, the ratio of moles CO2 and H2O produced would increase proportionally. However, consider what they are telling us:

I. An increase in the mass of carbon per gram of the compound.

Relative to the original compound, if we were to increase the mass of carbon per gram of the compound (by chemically altering it somehow), then ofcourse the mass percent would increase: (grams carbon/molecular weight of compound). We are not referring to the same compound if we are changing the mass of carbon per gram of the compound.

II. An increase in the mass of water formed upon oxidation of one gram of the compound.
Instead, if we somehow increase the mass of water, this would indicate the mass percent of hydrogen is increasing within the compound. For the same given starting mass of the compound, carbon would have to decrease proportionally and therefore for this new theoretical compound we are considering, the mass percent carbon would beless.

III. An increase in the mass of hydrogen per gram of the compound.

Same logic as the explanation I gave for scenario II.

 

[BerkReviewTeach]

What should help on this passage and the MCAT in general, is to consider the question within the context of the passage. This passage describes an experiment where an unknown undergoes combustion and the products are collected an analyzed to determine the mass percentages of various elements. They do not give a specific compound, but they do mention carbohydrates and hydrocarbons, which will have different mass percentages of C, H, and O.

What you say about mass percent is true for any specific given molecule. The mass percent of an element is the same regardless of the sample size (as long as it's the same compound). So knowing that, you have to think that this question must not be asking about that concept, but instead must be comparing different compounds, such as a hydrocarbon to a carbohydrate.

Let's consider your example of a six-carbon hydrocarbon versus a twelve-carbon chain. Assuming the simplest alkane, that would be C6H14 and C12H26. 72/86 does not equal 144/170; if we double the numerator and denominator of the first fraction we get 144/172, which is slightly less than 144/170, so the mass percent of carbon actually goes up slightly when comparing aliphatic alkanes of increasing carbon chain length.

Your second question was "if you have a higher mass of hydrogen per gram of compound, don't you also need to increase the amount of carbons? How can you increase the number of hydrogens without increasing carbon for a hydrocarbon chain?" Think about the simple case of ethane, ethene, and ethyne. Each has exactly two carbons, but the number of hydrogens drops from six, to four, to two. A different number of degrees of unsaturation will result in a different mass percent of hydrogen and of carbon.

Some MCAT questions are designed to make you think from a "what if" perspective. In such instances, breaking away from a basic mantra of the topic and considering the context of the passage becomes paramount to your success. That's the case here. Hopefully the examples help.

 

[Lunasly]

Thank you both for the replies. I appreciate your thorough answers. I understand where I went wrong.

That tip about a hydrocarbon chain containing double bonds and triple bonds makes sense. It doesn't have to be saturated.

Also, I am assuming that the reason behind a decrease in the mass percent of carbon when the mass if hydrogen increases is because the the total mass percent of each individual component of a compound has to add up to 100% and cannot exceed it.

Thank you!

 

[Czarcasm]

Thank you both for the replies. I appreciate your thorough answers. I understand where I went wrong.

That tip about a hydrocarbon chain containing double bonds and triple bonds makes sense. It doesn't have to be saturated.

Also, I am assuming that the reason behind a decrease in the mass percent of carbon when the mass if hydrogen increases is because the the total mass percent of each individual component of a compound has to add up to 100% and cannot exceed it.

Thank you!

Exactly, mass percent is just a fancy way of asking what percentage is the total grams of "so and so atom" to the total molecular weight for the compound (a ratio x 100%). Provided the total weight of each constituent atom adds up to the molecular weight of the compound, you would never exceed 100%. If you did, then you calculated something wrong.