Measurement – An Interdimensional Journey

In the past I’ve gotten a little preachy about definitions. I’ve probably said some hurtful things in the name of getting my point across. Well today will be no different, and if you don’t like it, you can go to hell. I’m kidding, please keep reading.

Today we’re going to delve in to a topic that lays the groundwork for our foray in to any science. Measurement. Without a good understanding of this concept, you’re never going to be able to work out chemical problems or perform biology experiments. Oh and if you’re going in to medicine, guess what? Medications are given based on SI units (Standard International Unit) and unit conversion ratio’s. In short, if you don’t have a solid understanding of units of measurement, you won’t be able to science.

SI Units

An SI Unit is an internationally agreed upon unit that represents a specific measurement. SI Units are based on a base and factor of 10. For example a meter (the fundamental unit of length) is equal to 100 centimeters. That is, it takes 100 cm to equal 1 meter. 1,000 meters is likewise equal to 1 kilometer etc. As you can see, using SI units is much more intuitive than standard “Imperial” form of measurement.

The reason that increments of 10 are used is because, well, hold up your hands in front of you. Ten is our default setting, 10 fingers means that it’s easiest for us to keep track of 10 things at a time. If humans had evolved with 12 fingers, then that would most likely be the increment that we used.

SI Base Units

For every unit that you encounter in your science career, you’re going to need to know what the base unit is for that dimension (physical quantity). For example, for mass the base unit is actually the kilogram, not the gram. Below you will find a table listing 7 common base units that you will use. There are more out there but it’s easier to start with these and introduce new ones as they become relevant.

SI Base unit Table.jpg
If you’re having trouble with memorizing these units, try making some Quizlet cards and click on the “Learn” function after you’ve made your set.

Knowing base units is helpful, but you’re going to need a little bit more if you want to succeed in problem solving. Below you will find a table with different decimal prefixes. Basically the prefix shows you how much of something is in one of the base, or how many times the base goes into a higher unit. This can be confusing so just look below.

Common decimal prefixes table.jpg
The bolded prefixes are the ones most commonly used in these lower level science classes.

As you can see if I want to go from one to kilo I’m going to need 1,000 “one’s”. If I want to cut up that “one” by 1,000 I now have a “milli” of something.

Important!!! Save yourself some heartache. Don’t worry about memorizing all of the units on that table, and how they relate to each other. All you need to understand is the base unit and what a prefix means. Let’s say I want to convert a millimeter to kilometer. I don’t need to know how many times a “milli” goes into a “kilo”. All I need to know is how many times milli goes in to one of the base and how many times a base goes into kilo’s. This adds an extra step when converting units, but it will ultimately leave more brain space for problem solving, not just trying to memorize information.

SI Units conversion example.png

*Become comfortable with scientific notation. Rather than show you what I mean, here’s a Khan Academy video explaining scientific notation.

Important Units

Let’s dive straight in to some of the more important units in scientific study. Like I mentioned above, these are not the end all be all, however it is likely that you will encounter these more often.

As you read this think about dimensions. What do we mean when we say that something is a certain dimension? Well there’s the 0-dimension which consists of a point in a space, or a line which is representative of  a 1-dimensional space, so on and so forth. Dimensions are a way to describe something based on how many measurable coordinates there are. For example a rectangle has 4 sides but you only need two measurements to describe the shape, length and width. Humans are capable of understanding up to 4-dimensions, from the 0-D of a point to the 4-D known as time. Though in reality we don’t understand time all that well, but we do know that it’s there, and we can perceive it.

It is possible that there are more dimensions out there, but we are incapable of seeing them or knowing if there is a life form that inhabits those dimensions. At some point, billions of years from know, it is possible that we can find out, by evolving in to beings that occupy 4 dimensional space and then in to beings that occupy the 5th and so on.

Note: Anything after the 4th dimension is a theoretical construct. At this point in our knowledge there’s just simply no reliable way of knowing if or how these dimensions would manifest.

Length

A meter is defined as how far light travels in a vacuum in 1/299,792,458 second. Don’t ask me how and or why. As you start to delve farther in to your scientific study, you’ll begin to see that assignments are arbitrary. Just be grateful that you’re not the one that had to figure it out.

Volume

This unit of measurement reminds us that when it comes to agreeing on something, scientists can be notoriously sucky at it. The SI unit for volume is a cubic meter (m3) yet much of what we deal with in chemistry is the liter (L) and the milliliter (mL). Oh and do you want to hear something totally messed up? 1 mL is equal to 1 cm3 it’s almost as if they thought, “hey you know what will really eff with their heads?” Luckily for us , we now have the power of the internet and all of those nerdy scientists are about to get a knowledge swirly.

If you remember that 1 equals 1 then you’re golden for any calculation you need because it still works off of multiples of 10.

Mass

It is notoriously difficult to explain mass. In fact it’s a question that is still one of the big unanswered questions in physics. It basically all starts with the Higgs boson (we think), and ends with what we see in front of us. Mass is the amount of matter an object has, the tangible piece of stuff that gives us the feedback we need, to know that we’re not just floating through an abyss.

Luckily most of general chemistry is performed at Earth gravity so we don’t need to worry too much about the difference between mass and weight. Just keep in mind that if you take something like your cell phone to the moon, from earth, its mass is going to stay the same, but it’s weight is entirely different. Weight is our perception of the effects of gravity on an object’s mass!

Luckily for you, back here on earth a gram of hydrochloric acid is a gram of hydrochloric acid. It’s weight and mass are essentially equal in earth’s gravitational field. Oh and don’t forget that it’s the kilogram, not the gram that is the SI unit for mass.

Density

Density

Density is pretty self explanatory based on the equation above. Where it becomes absolutely crucial, is in the ability to convert between units using that equation. Instead of ranting about the usefulness of density, why don’t we work out a problem.

Note: You’re going to be given 2 of the variables in the equation. Without at least two, you’re not going to be able to solve the problem.

Density Problem

You have a 1000 kilogram (kg)  sphere of pure iron that is being delivered to your company’s warehouse tomorrow. You are put in charge of finding a place for the iron. what volume is the iron going to occupy in liters? *the density of iron is 7.874 g/cm3

  1. You’re going to be tempted to just plug in you’re values in to the given equation, DON’T. First you need to ask yourself if all of the units jive together. Through our collective powers of observation we see that the units on mass are different. Kilograms won’t readily cancel out grams and vice-versa. We need to choose whether we’re going to convert grams to kilograms or kilograms to grams. Feel free to do either, but in all reality the easiest way to do it, is to convert everything over to grams.FullSizeRender.jpg
  2. Now that we’ve converted over to a common unit we can begin solving the problem. Plug in the given information and make some magic happen.Solving for Volume using density.jpg
  3. Whoa now, you’re not done yet. After you’ve isolated the unit for volume (cm3), you are going to need to convert over to liters (L). Remember that 1mL = 1cm3.FullSizeRender 2.jpgWe’ll get to significant figures later but did you notice how I didn’t use all of the numbers that were available to me. In the end I only used 4 numbers and rounded it to 127.0L

Intensive and Extensive Properties.

Have you ever tried to put a water bottle in the freezer only to find that it has exploded when you check on it the next day? Temperature greatly affects the volume of different substance, so if temperature changes so too can volume and in turn density. However, at a given temperature density is what’s known as an intensive property, meaning that it does not change no matter how much or how little of a substance you have. On the other hand, if you have a bigger iron sphere, you increase it’s mass and in turn it’s volume, these are known as extensive properties.

When we start to think about it, it all makes sense. Density is tied to the ratio (mass/volume). That means that if mass increases so does volume, but it does so in a consistent way so that density is always constant at a given temperature.

Temperature

I’m sure you’re all familiar with the concept of temperature, but there’s a few things we need to clear up when it comes to this unit. First, temperature is how cold or hot something is when you compare it to something else. There’s a distinct difference between temperature and heat. Heat is energy, as you work through more problems in chemistry you’ll start to become more familiar with this concept. For now think of this way.

Let’s say that you it’s a hot day out, oh let’s say it’s 100°F (37.8°C), that’s your temperature. You need to make a beer run so you decide to go for a drive. When you get in to your car and sit on the hot black leather seat you’re reaction is a series of expletives because you’re leg just got burned. The reason you were burned is because there was energy stored up in the leather seat in the form of heat. That heat flowed from the seat on to your skin because your skin had a lower temperature than the seat.

Heat is an extensive property. You’re all familiar with this concept. A cup of boiling water holds less energy than a big pot of boiling water. Think about it, would you rather get burned by more or less boiling water? Temperature, however, is an intensive property. A cup of water and a pot of water both boil at 100°C, it is independent of the amount of water, you will just need more or less energy (heat) to boil the water depending on the amount.

The SI unit for temperature is Kelvin (K), this is an absolute value scale that doesn’t use the term degree. However you’ll be using Celsius as well. The great thing about kelvin is that no matter what value you have in Celsius if you add 273.15 to that number, you end up with kelvin; 0°C is 273.15 kelvin, 20°C is 293.15 kelvin, and so on. I’m not going to talk about Fahrenheit because if you’re reading this, then you have access to a computer and you can look up that conversion.

Pro Tip #12: Use your resources.

You need to become comfortable with researching information. Google is your best friend, but be warned, make sure that wherever you’re getting your information, that it’s a reliable source. Look at multiple sites and make sure that the information being presented is consistent. Having said that, working in the medical field you learn that doctors and nurses don’t know everything, this applies to student’s as well. You will need enough information to allow you to solve problems. Anything outside of that you can look up.

Time

I’m sure we all have a basic understanding of what time is. It’s a concept that is difficult to explain, but you know when it’s happening. Think about your childhood, that was the past. Now think about you’re current age. No matter what age that might be, you have a pretty solid understanding of what time is.

Time, however isn’t just what you experience in day to day life. As with all things, time is deeper, and more precise than you can imagine. The SI unit for time is the second (s), and again the definition is arbitrary. Unless you become a chemist and work directly with definitions of SI units chances are that you’ll never need to know that there are 9,192,631,770 oscillations of a microwave absorption in cooled cesium atoms in one second. Seriously at this stage in your learning just get a Timex.

Time is important because of how we study chemical reactions. Many times it’s not only important what the end product is, but also how long it takes to get there. It can mean the difference between losing or keeping your arm during a volatile reactions.

[Chemistry 211 Chapter 1 Section 4]

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