Avogadro’s Law: History and Work Problem

We’re back for another entry in the gas laws series! And today…. we’ve found a mole in our blog.

Not a spy. It’s just me writing these. And not an animal, however the starry-nosed mole deserves a better reputation.

Photo: Kenneth Catania – Ntl. Geographic. (x)

I mean, take a closer look at that snout.

I mean a mole (mol), a way we can quantify how much of a chemical substance we have in a reaction.

Moles are tricky, fun, and incredibly useful when communicating new discoveries, as we’ll see. For now, let’s review what our overall goal is here with the gas laws series.

The overall goal with this series is to familiarize yourself with the gas laws, as they play a very important part not only in your chemistry studies but also in everyday life.

We define a gas as, “one of the four states of matter, the other three being liquid, solid, and plasma”. And as always, here’s a link to all the weird and fun different phases of matter.

We also know that generally a gas is not defined by its volume or shape, and ideally all reactions are elastic; that is, all the energy in the reaction is conserved within the system. You can read more into these background details on the Boyle’s Law post where I went a little more into depth.

Today we’ll be looking at how the amount of gas interacts with the volume of the gas.

Lorenzo Romano Amedeo Carlo Avogadro

Lorenzo Romano Amedeo Carlo Avogadro, or more well known as Amedeo Avogadro, was a prominent Italian politician and scientist. He was born into an influential family, his father Filippo being both a senator and a Count, and his mother Anna, a noted noblewoman. He was born on what is now known as the Island of Sardinia.

Amedeo Avogadro.
From A History of Chemistry by F. J. Moore (McGraw-Hill Book Company, New York, 1918)
Amedeo Avogadro.
From A History of Chemistry by F. J. Moore (McGraw-Hill Book Company, New York, 1918). Britannica.com

From an early age, Avogadro was quick. He initially followed in his family’s footsteps, graduating with a doctorate in canon law at the age of 20. He practiced ecclesiastical law for a bit, but found his interest in physics and mathematics.

It’s important to note that during Avogadro’s youth, France was going through the later years of its revolution. Exactly 10 years later, Italy’s Holy Roman Empire would get canceled due to Napoleon giving a vibe check would dissemble after being defeated by Napoleon in Austerlitz, leaving a huge power vacuum. This comes into play later in Avogadro’s life, so put a pin in that.

Avogadro published his first scientific paper in 1803, with the support of his brother Felice. This paper focused on electrical potential of various salt solutions.

In 1806, Avogadro began his stint teaching physics and mathematics at a high school or liceo in Vercelli. 3 years later would present an opportunity as a senior instructor at the College of Vercelli.

Avogadro would marry Felicita Mazze, they would go on to have six kids. Reports vary of when they married, ranging from 1815-1818.

I’ve only seen in one place that Avogadro was inducted into the Academy of Royal Sciences of Turin in 1819. I’m not certain if this is actually true, as I’ve only seen one source cite this. It was also reported that he would be appointed the First Chair of Mathematical Physics for the University of Turin in 1820, and he would go on to help establish the metric system along with others. This of course, is research from a patchwork of sources, so details have been lost in between the gaps.

Again, at this time Italy was still unstable. The fallout from no more Holy Roman Empire allowed political superpowers like France, Spain, and Austria to scrabble for dibs on Italian land. Eventually after different groups conquered, ruled, and surrendered (or were defeated), the title of King of Italy emerged alongside the Holy Roman Emperor.

This is relevant, I swear. The contest for power in Italy manifested in many early revolutions, that often left revolutionaries exiled. Exile became a huge theme in Italian revolutionary literature at the time – along with the rejection of certain Italian stereotypes that had been established.

Portrait of Amedeo Carlo Avogadro (Turin, 1776-1856), Count of Quaregna and Cerreto, Italian chemist and physicist, Engraving. © De Agostini Editore/age fotostock. Britannica.com

Avogadro was a professor at Turin during this time. In March 1821, it is reported that he was a part of a revolutionary movement known as the Piedmont Movement, whose goal was to oust the Austrians in the area and set up the House of Savoy as the ruling body in Italy.

This didn’t work. And it cost Avogadro his chair at the University of Turin in 1823. Allegedly.

But no matter, as Avogadro would be reappointed to his chair in 1833, ten years later. It’s difficult to find what he did with this ten year gap. Not much is known about his later years. Most sources report his golden years teaching at Turin until his retirement.

When re-appointed in 1833, Avogadro would hold his teaching position until 1850 when he retired at the age of 74 .

Amedeo Avogadro died on July 9th, 1856 in Turin, Italy.

Avogadro’s Law: The Details

Avogadro’s publication Essai d’une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons (Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies and the Proportions by Which They Enter These Combinations) first introduced the world to his hypothesis. This law wasn’t fully recognized until 1858, and now is considered one of the main laws considering gaseous behavior.

Avogadro states that equal volumes of different gases contain the same number of particles when temperature and pressure are kept constant.

When we change the number of particles or volume, the corresponding variable will be affected.

Avogadro’s law looks like:

V1 / n1 = V2 / n2

Where V is the volume of the gas, and n refers to the number of particles present.

6.022 * 1023 is just the number needed of a certain element or compound to clock in at approximately 1 gram of the matter and 1 dalton (or unified atomic mass unit). It helps us standardize the actual amount of reactant used or product created in a reaction. It also helps scientists understand exactly what was in the reaction, boosting peer-review accuracy and subverting confusion if an unknown unit was used (this was more of a problem back in Avogadro’s time, but still relevant!).

Avogadro’s Law: Work Problem

Initial Question: A gas at 6.15 L contains .254 moles of a gas. Assume this gas has the same composition as Earth’s air. If the volume decreases to 2.55 L, how many moles are now present?

Given: V1= 6.15 L n1= .254 mol

V2= 2.55 L n2= wanted

Avogadro’s Law: V1 / n1 = V2 / n2

Step 1: Set up your equation with all your knowns and the variable you’re looking for – in this case it’s n2. We cannot do a simple cross-multiplication here because the units don’t work out. So we’ll take a long way around.

Step 2: Multiply everything out. This is going to be tricky. I first calculated my value for 6.15 L/ .254 mol to get 24.21 L/mol. I then set this where it was in the equation, and started on isolating the n2 variable. I can isolate by mulitplying by n2/n2 (my high school math teacher referred to this as a ‘big fat One’ so if you hear me say that, this is what I mean). By multiplying n2/n2 on both sides of the equation, we can get rid of that messy denominator variable. At the end of the equation, you should have (n2) 24.21 L/mol = 2.55 L. A much neater equation, and our units are aligned.

Step 3: Now that n2 is on the 24.21 L/mol side of the equation, we can divide by 24.21 L to isolate n2. Our liters will cancel out and we’ll be left with moles – the unit we’re looking for in this equation. It’s a nice fail-safe to check units – it you see you’re going to end up with the units you’d like, you’re probably on the right track.

Step 4: Finally, we can clean up the equation after dividing through. We end up with an answer of .1053 moles of gas – the amount of moles present after volume decreases.

This is a fun one, and takes some brain power to wrap your head around. Don’t be discouraged if you didn’t get it the first time, keep working at it.

Sources:

Amedeo Avogadro, Famous Scientists.

Amadeo Avogadro, Wikipedia.

Amedeo Avogadro, Britannica.

Biography of Amedeo Avogadro, Influential Italian Scientist, ThoughtCo.

Amedeo Avogadro, Tonouchi, K.

Mole (unit), Wikipedia.

Many thanks to the Oregon State Chemistry Department for their help teaching me, so I can hopefully teach you. Go Beavs!

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