Video Transcript
Which of the following alkanes diffuses the quickest?
An alkane is a type of molecule with a central chain of singly bonded carbon atoms surrounded by single bonds to hydrogen atoms. Thankfully, we don’t have to be an expert on alkanes to answer this question. The question is asking about diffusion, defined as the process through which a gas or liquid spreads out into another gas or liquid. Specifically, the question is asking about the different speeds of diffusion. And a key relationship to know when discussing speeds of diffusion is that lighter particles leads to faster diffusion.
Another characteristic that could contribute to different diffusion speeds is the kinetic energy of the molecules involved. However, for this problem, we will assume that all the molecules have the same kinetic energy.
So if we wanna figure out which alkane diffuses the quickest, we need to figure out which one is the lightest. By calculating each choice’s molecular mass and comparing them, we can select the one with the lowest value. For example, we can calculate the molecular mass of choice (A), which includes one carbon atom and four hydrogen atoms. We can take the atomic mass of carbon, 12.011, and add it to four times the atomic mass of hydrogen, 1.008. We multiply the atomic mass of hydrogen by four because there are four hydrogen atoms in the molecule. If we carry out the arithmetic, we will arrive at a final answer of 16.043 unified atomic mass units.
We can set up a similar equation for choice (B): two carbon atoms, two times 12.011, the atomic mass of carbon, plus six hydrogen atoms, six times 1.008, the atomic mass of hydrogen. The molecular mass for choice (B) is 30.070 unified atomic mass units.
After determining the number of carbon and hydrogen atoms in each choice, we can calculate the molecular mass for each choice in the same way. Choice (C) has a molecular mass of 44.097 unified atomic mass units. Choice (D) has a molecular mass of 58.124 unified atomic mass units. And choice (E) has a molecular mass of 72.151 unified atomic mass units. So which choice is the lightest? Well, that’s choice (A) CH4. 16.043 unified atomic mass units is the lowest molecular mass for any of the choices available.
Earlier on in the problem, you may have been able to deduce without calculating the molecular masses that choice (A) was the lightest of the five options. This is a good observation to make. Since all five options are made up of just carbon and hydrogen atoms and choice (A) has the fewest carbon atoms and the fewest hydrogen atoms, it must necessarily have a lower molecular mass than the other choices. So it’s not fully necessary to calculate the molecular mass for all five options. However, we can do it just to be thorough or in case we want to confirm our initial suspicions.
It’s worth noting that we’re making some simplifications or assumptions while working with this problem. For example, we’re assuming that all of these different alkanes are at the same temperature with the same kinetic energy. It’s also worth noting that choice (E) pentane is a liquid at room temperature. So in order to compare all of these alkanes as gases, we might need to heat them up a bit, beyond pentane’s boiling point of 36 degrees Celsius.
Alkanes involve carbons singly bonded to each other and surrounded by more hydrogen atoms singly bonded to the carbon atoms. Alkanes are frequently used as sources of fuel. You may be familiar with the propane, found in the tank of a gas grill, or the butane, found in a lighter. Alkanes or a mix of alkanes are used in other sources of fuel, like torches or camping stoves. Choice (A) is known as methane. And it is the correct answer, as the lightweight CH4 is the alkane that diffuses the quickest.
