Boyle’s Law: History and Work Problem

Gases! The very thing us humans live on, and pretty much everything else on this planet.

The purpose of this series is to address what a gas is, and how different situational variables affect its state. We’ll dive into the scientists that coined these laws, and how they got to their conclusions. It is my belief that having a full rounded knowledge of a certain topic helps nurture curiosity and a willingness to approach secondary topics. We’ll begin with some background knowledge on what a gas exactly is. This will be a four-part series of posts, each one focused on the history and basic mechanics of a gas law.

A gas is one of the four traditional states of matter, the others being liquid, solid, and plasma. You can read more about the different states of matter here on Wikipedia. Imagine that all the particles in the gas are bouncing around the chamber they’re enclosed in – or spread freely in an open scenario.

How much gas there is, how fast it travels, and the temperature of the gas all impact each other, and the overall state of the gas.

A gas is a state of matter in which particles are not defined by volume or shape. Particles can be a homogenous or heterogenous mixture, examples include CH, CO, and He.

There’s a concept of what an “ideal” gas is. An ideal gas is defined as one whose particles are under the influence of two forces: One generated by the walls of the container and collision forces. It is accepted that the particles in an ideal gas bounce off each other with “elasticity” – or no energy is lost in the collision and the individual particles keep traveling with consistent energy. In this state, the variables of the equations are more straightforward and easy to work with, This website covers gas problems in a more in depth manner in this post here.

In these problems, we will assume that all gases are in an ideal state. Realistically, all gases have more than these two forces at play, and often collisions are not elastic.

The two variables we’re looking at today are pressure and volume, whose gas relationship was discovered during the Renaissance.

Boyle’s Law – Pressure & Volume

Robert Boyle (1627 – 1691) was well and truly a Renaissance alchemist. He was interested in the transmutations of metals, portions of physics such as crystallization, refraction, thermodynamics, and specific gravity. Boyle favored chemistry over all these. Boyle viewed chemistry as a study itself, instead of a bridge to alchemy or medicine, which was a common view at the time. He contributed to so many studies in so many different ways – and one he perhaps is most known for is his law concerning pressure and volume.

If the omniscient author of nature knew that the study of his works tends to make men disbelieve his Being or Attributes, he would not have given them so many invitations to study and contemplate Nature.

– Considerations of Touching the Usefulness of Experimental Philosophy, 1663.

In 1657, Boyle was 30 years old, residing in Oxford, and studying chemistry. In 1657, Otto von Guericke was well into publishing his work with Robert Hooke on vacuum pump systems and air pressures. Boyle read on Guericke and Hooke’s work, and wanted to pursue this himself.

Boyle and Hooke’s Pump, 1660.

In 1660, Boyle was able to create the first air pump for scientific reasons with the help of Robert Hooke. I wanted to be able to understand just how this precursor to modern air pumps worked, but I can’t find anything and that will honestly make this post longer than it already is.

This device allowed Boyle to be able to define one of his most influential pieces of work: Boyle’s Law.

(It should be noted that Edme Maiotte independently in 1679, about 19 years later. This is why Boyle’s law can sometimes be referenced as Boyle-Mariotte’s law or Mariotte’s Law)

Pressure and Volume

By adjusting the amount of volume in a container as it relates to pressure, Boyle found that volume and pressure are inversely related. That is, the smaller the volume of the container, the greater pressure the contents are under. This makes sense, if we compress an aerosol can it e entually explodes. The pressure is so great that the container cannot stand up to the pressure. This is represented as:

P1V1= P2V2

This means that i the overall ideal situation, the pressure and volume will correspond with each other. Let’s explore this in a work problem:

Initial Question: An initial volume of a gas is 2.75 L, its pressure is at 1.02 atm. If the volume increases to 3.25 L, what is the final pressure?

Given: Start with our known quanitites and what needs to be found.

Step 1: Set up Boyle’s equation with the known quanitites. P2 will be the place holder for our desired variable.

Step 2: Always go with PEMDAS, so multiply the initial pressure and volume together, and remember that your units are L*atm. I had a fun time with variables here, so sorry if it gets confusing. Let me know.

Step 3: Now you have a neater equation, divide through the final volume. This will isolate our P2 variable and cancel out the liters on the other side (a good sign, since our final units will be in atm and that’s our goal).

Step 4: Plug and Chug. Divide through your values and you should end up with P2 = .8630 atm. The original question has 3 sig figs, so we can answer it finally as P2= .863 atm.

The next installment in this series will be Charle’s Law, which relates volume and temperature.

Questions? Corrections? Drop us a comment here or email us at heychemistryblog@gmail.com.

Sources:

  1. States of Matter – Wikipedia
  2. Robert Boyle – Wikipedia
  3. Boyle’s Law – Wikipedia
  4. Drawing of Robert Boyle’s Air Pump – Columbia College
  5. The Enlightenment an Interpretation: The Science of Freedom – Peter Gay
  6. Otto von Guericke – Wikipedia
  7. Scientists and Inventors of the Renaissance – Britannica Educational Publishing
  8. Edme Mariotte – Wikipedia

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