Molecular formula of a hydrocarbon

Question

A is a non cyclic hydrocarbon chain with $\ce{C_{3x-1}H_{6x}}$ as a molecular formula which is mainly used in cars as fuel, its cracking leads to hydrocarbon (B) which belongs to the same family of hydrocarbon A, also two molecules of ethene form the second product in the above reaction.

My effort: To determine if it is an alkane, we compare the given subscripts on $\ce{C}$ and $\ce{H}$ ($3x-1$ and $6x$, respectively) to those in the general formula for an alkane, $\ce{C_{n}H_{2n+2}}$. Let $n=3x-1$ where $n$ is the number of carbon atoms.

$$6x\buildrel{?}\over{=}2(3x-1)+2=6x$$

and therefore A is an alkane, with the molecular formula satisfying the form $\ce{C_{n}H_{2n+2}}$.

Answer 1

You're right in thinking that it's an alkane. Now I think I shouldn't blame you for getting confused by

$\ldots$ as a molecular formula which is mainly used in cars as fuel $\ldots$

Because

• First off, we don't know if $x$ in the molecular formula is an integer or a decimal number.

• Second, we don't know what fuel is meant. It's just supposed to be a fuel used in cars. And what are the fuels used in motor vehicles again?

  Currently, the majority of motor vehicles worldwide are powered by gasoline or diesel. Other energy sources include ethanol, biodiesel, propane, compressed natural gas (CNG), electric batteries charged from an external source, and hydrogen.

  What are these?

  1. The bulk of a typical gasoline consists of $\mathrm{\color{red}{hydrocarbons~with~between~4~and~12~carbon~atoms~per~molecule}}$ (commonly referred to as C4-C12).

  2. Petroleum-derived diesel is composed of about 75% saturated hydrocarbons (primarily paraffins including n, iso, and cycloparaffins), and 25% aromatic hydrocarbons (including naphthalenes and alkylbenzenes). The average chemical formula for common diesel fuel is $\color{red}{\ce{C12H23}}$, ranging approximately from $\ce{C10H20}$ to $\ce{C15H28}$.

  3. Ethanol is an $\color{red}{alcohol}$.

  4. Biodiesel refers to a vegetable oil - or animal fat-based diesel fuel $\mathrm{\color{red}{consisting~of~long-chain~alkyl~(methyl,~ethyl,~ or~ propyl)~ esters}}$.

  5. Propane is an $\color{navy}{alkane}$.

  6. CNG is made by compressing natural gas (which is mainly composed of $\color{red}{methane}$, $\ce{CH4}$), to less than 1 percent of the volume it occupies at standard atmospheric pressure.

  7. Electric batteries and hydrogen are $\ldots$ a bit irrelevant. Let's not make this answer longer.

  Thus, the answer would be propane, since it's the only alkane among the common car fuels. But is it? Of course not; since propane cracking isn't in high school syllabuses anywhere in the world. There is a very very good chance the querent had gasoline mind.

• Now that we trust our natural instincts (!) that they meant gasoline when they were referring to the fuel, we should remain perplexed and run in circles. Because gasoline isn't consisted of one or two distinctive and well-known substances, and it's a mixture of It is a mixture of paraffins (alkanes), cycloalkanes (naphthenes), and olefins (alkenes), where the usage of the terms paraffin and olefin is particular to the oil industry. To make matters worse, gasoline composition is obviously not the same around the world.

$\hspace{25ex}$ $\hspace{25ex}~\small{\mathrm{Some~of~the~compounds~commonly~found~in~gasoline}}$ $$\small{source}$$

So, let me rephrase your question into something actually meaningful:

$\ldots$ as a molecular formula which is mainly known to be a really smooth-burning species in gasoline $\ldots$

Now we're talking. The best known gasoline would be one that consists of 100% isooctane, and that's why we have octane rating. It's not a real fuel, just the material in an imaginarily ideal mixture that would burn "real smooth". That's why your question is problematic and scientifically incorrectly asked.

Back to the question, 2,2,4-Trimethylpentane must have been the compound the querent had in mind. Now we have the answer for A.

$\hspace{25ex}$
$\hspace{28ex}$ Isooctane (PIN: 2,2,4-Trimethylpentane) $\hspace{43ex}$ $\small{source}$

But what would the products of the cracking be?

According to the Wikipedia article on cracking the cracking process in entropy-driven and the radicals formed in certain conditions usually move the reaction forward. But the final products (and even which radicals form) highly depend on the methods of cracking (thermal, steam etc.) and/or the catalysts. There are numerous catalysts which demonstrate the diversity in the mechanism of cracking.

For example, take a look at this paper (It's just an abstract, but it gives you an idea)

$\ldots$ The main reaction route on FAU is hydride transfer followed by β-scission leading to mainly C4 species, while on MFI protolytic scission is responsible for the formation of high amounts of C1−C3 species. $\ldots$

So, we're left with speculations. This isn't a real question. The only answer the examiners want is B's most probably butane, as it must be an alkane.

As this also demonstrates, a very simplistic view is that an octane can break into two ethene molecules and one butane molecule. So, the reaction they must have had in mind is $$\ce{C8H18 -> C4H10 + 2C2H4}$$ Pfft.

TL;DR:

This isn't a good or correct question to ask at all; at the very least, it's very poorly worded. The answers are supposedly isooctane for A and butane for B, but the OP's confusion was innocent.

Answer 2

You have done the first step in the solution.

So we know now that A is an alkane and after cracking it leads to a molecule B and $\ce{2C2H4}$. But $\ce{2C2H4}$ contains $4$ carbon atoms so the number of carbon atoms in A must be $5$ or more (i.e. $3x-1\geq5 \Longrightarrow x\geq3$)

let us start trying:

• $x=3$ will lead to $\ce{C8H18}$
• $x=4$ will lead to $\ce{C11H24}$
  .
  .
  .
  .

And I suppose that you as a student only studied alkanes till octane ($\ce{C10H22}$) so the answer will be $\ce{C8H18}$.

I know that is not a good reasoning but I am sure that it is the true answer.