Video: Formula Mass and Mole Concept: Calculation of Molar Mass

Which of these substances has the highest molar mass? [A] The anaesthetic halothane, C₂HBrClF₃ [B] The herbicide paraquat, C₁₂H₁₄N₂Cl₂ [C] Caffeine, C₈H₁₀N₄O₂ [D] Urea, CO(NH₂)₂ [E] A typical soap, C₁₇H₃₅CO₂Na.

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Video Transcript

Which of these substances has the highest molar mass? A) The anaesthetic halothane, C₂HBrClF₃. B) The herbicide paraquat, C₁₂H₁₄N₂Cl₂. C) Caffeine, C₈H₁₀N₄O₂. D) Urea, CONH₂₂. Or E) A typical soap, C₁₇H₃₅CO₂Na.

The first thing we should remind ourselves of is what a molar mass is. Molar masses are measured in grams per mole. A molar mass is the mass in grams per mole, that’s per 6.022 times 10 to 23 of something. 6.022 times 10 to 23 is Avogadro’s number. Avogadro’s number is equal to the number of carbon-12 atoms. That’s atoms with six protons and six neutrons in 12 grams of carbon-12. Our job is to look at each substance, workout its mass per mole, and then find the one with the greatest mass per mole. We’ve been given the molecular formula for each substance.

The molecular formula of a substance tells us how many atoms of each element are present in a single molecule of that substance. To work out the molar mass of each molecular, we take the atomic masses of each element in that molecule in unified atomic mass units. One unified atomic mass unit is equal to one twelfth of the mass of a carbon-12 atom. The atomic masses of the elements can be found on your periodic table. We can then take these atomic masses and combine them together to form the molecular mass in unified atomic mass units and then take the molar mass in unified atomic mass units and convert it to the molar mass in grams per mole.

We’ll be using the relationship that a mole’s worth of unified atomic mass units is equivalent to one gram. You may have seen the unit amu instead of u. u is the symbol for a unified atomic mass unit which is defined as one twelfth of a mass of a carbon-12 atom. Well, amu stands for atomic mass unit which is defined as one sixteenth the mass of an oxygen-16 atom. However, amu is sometimes incorrectly used in place of u because even though they are defined differently, their values are very very similar.

So for this question, I will be using the unit u. The next step is to use our periodic tables to look up the values for the atomic masses of all the elements in the molecules in the question. We could do this molecule by molecule separately. But it would be much easier if we built a table and repurposed it for each option. Here are the atomic masses of all the elements included in the question. I got each of these numbers by going to my periodic table, looking at the element, and taking the number at the bottom. This number represents the atomic mass of the element in unified atomic mass units. Take a few moments to check that all the elements in the question are included in the table.

The next thing we’re going to do is look at the number of atoms of each element present in our first candidate, the anaesthetic halothane. We can now start populating this row of the table. In one molecule of halothane, there are two carbon atoms, one hydrogen atom, one bromine atom, one chlorine atom, and three fluorine atoms. In the next row, I’m going to take the atomic mass of each element and multiply it by the number of atoms of that element in the molecule.

We have one atom of hydrogen in a molecule of halothane. So it contributes 1.008 unified atomic mass units to the mass of the molecule. Two carbon atoms contribute 24.022 u. Three fluorine atoms have a combined mass of 56.994 u. One chlorine atom has a mass of 35.45 u. And, finally, one bromine atom has a mass of 79.904 u. The molecular mass of halothane is equal to the sum of the atomic masses of the atoms in halothane. 1.008 plus 24.022 plus 56.994 plus 35.45 plus 79.904 is equal to 197.378 u.

The next step is to convert the molecular mass in unified atomic mass units into a molar mass in grams per mole. As I mentioned before, one mole is worth 6.022 times 10 to the 23 unified atomic mass units is equal to one gram. Therefore, one unified atomic mass unit is equal to one gram per mole. This is because 6.022 times 10 to the 23 is a mole. Therefore, the molar mass of halothane is 197.378 grams per mole. Let’s record that value next to halothane. Now, we can clean out the table and reuse it for the other four options. Here it is repurposed for a molecule of paraquat, 12 carbon atoms, 14 hydrogen atoms, two nitrogen atoms, and three chlorine atoms.

This is what we get for each element when we multiply the number of atoms of each element by the element’s atomic mass. Summing these together gives us a molecular mass for paraquat of 257.158 unified atomic mass units and a molar mass of 257.158 grams per mole. Once again, we can store away that value and refresh the table. A molecule of that all-important caffeine has eight carbon atoms, 10 hydrogen atoms, four nitrogen atoms, and two oxygen atoms. Multiplying this through gives us the masses due to each element, giving us a molar mass of 194.194 grams per mole.

Meanwhile, one molecule of urea has one carbon atom, one oxygen atom, two nitrogen atoms, being careful here to multiply through by two because we have two NH₂ groups and four hydrogen atoms. This is what we get when we multiply through. And we end up with a molar mass of 60.056 grams per mole.

Lastly, we come to a typical soap. A molecule of this particular soap contains 18 rather than 17 carbon atoms. Remember to count that extra loan carbon as well as 35 hydrogen atoms, two oxygen atoms, and one sodium atom. Following through gives us combined molar mass of 306.466 grams per mole. So the substance out of the five with the highest molar mass is a typical soap, C₁₇H₃₅CO₂Na. Halothane, caffeine, and urea, all have significantly fewer atoms than paraquat or the typical soap and, therefore, could have been eliminated as candidates early on. However, it never hurts to practice a technique.

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