Lesson Video: Units and Equations Chemistry

In this video, we will learn how to define SI and derived units and write and manipulate algebraic equations.

17:52

Video Transcript

In this video, we will learn about units, especially those used in chemistry, how to convert between different sized units, and how to rearrange and solve algebraic equations. In 1999, communication with a 125-million-dollar space probe sent into space to Mars was lost. The reason, different unit systems were used by the different teams which made the probe. Let’s start by having a look at the different unit systems used for measurement.

The commonly used unit and measuring systems are the metric system, the imperial system, and the international system of units or SI units, which are related to the metric system. The unfortunate incident with the space probe was because one team used the metric system and another the imperial system. The metric system has different variance and uses units such as meters, centimeters, and kilograms, while the imperial system uses units such as feet, inches, and pounds.

Scientists, doctors, pharmacists, engineers, and many the professionals worldwide need to understand each other when talking about the size or unit of a measurement. We also need to understand each other when using units in everyday life. And so the international system of units or SI units from the French “Système International d’unités” was developed. The international system of units or SI units is a standard system of units used worldwide in almost every country. A standard system is a way of doing things that is the norm or the usual model, usually with a reference to compare to. When we all use the same system for units and measuring, it removes confusion. For example, one meter and one yard are not equal to each other. If we measure length, are we gonna use meters or are we gonna use yards? The SI system uses meter as the standard unit for length or distance. This prevents any confusion.

There are seven SI base units which are the building blocks for all other SI units. These units are the unit for time, whose symbol is a lowercase s, and this is the second; length or distance measured in meters with a lowercase m; mass whose unit is the kilogram and whose symbol is kg; electrical current whose unit symbol is capital or uppercase A for ampere; temperature measured in the unit of kelvin with an uppercase K; amount of substance with unit mole and symbol mol; and luminous intensity symbol cd for the unit candela. Seconds, meters, kilograms, kelvin, and moles are used in chemistry. The units ampere and candela are not often used in chemistry.

Chemistry doesn’t often need to measure length, but more commonly volume or capacity. These are often measured in meters cubed, decimeters cubed, centimeters cubed, liters, or milliliters. We will look at what the prefixes deci- and centi- mean just now. And we will learn what liters and milliliters refer to and how they are all related but later on. The unit kilogram is not commonly used in chemistry. We most often use grams for measuring mass. We said that these seven units are the base or building block units from which all other SI units are derived. There are many derived units, but two common examples of derived units used in chemistry are the unit for pressure whose symbol is P. And this unit is called the pascal. And written in base SI units, a pascal is a kilogram per meter per second squared.

The derived unit for energy or heat is the joule, with symbol capital or uppercase J. And written in base SI units, it is the same as a kilogram meter squared per second squared. We won’t be investigating derived units any further in this video. Now it’s not always practical or convenient to measure everything in the base units as they stand. For example, if we were to measure a spatula of sugar for a reaction, we’d have a very small number measuring the mass in kilograms. It’s inconvenient to say 0.004 kilograms. It’s much easier and more convenient to say four grams of sugar. We can adjust the unit size, which will in turn adjust the number or measurement. The k in kilogram is called a prefix. Prefixes adjust or convert a unit to a multiple or submultiple. In other words, prefixes make a unit larger or smaller by factors of 10. And this is much more convenient.

Now, let’s learn about the different prefixes and how to convert between them. The table shows a list of prefixes, their symbols, and what the prefix means. This mnemonic will help us remember the order of the prefixes. The Great Mighty King Henry died by drinking chocolate milk under-neath pier. The first letter of each word indicates the prefix. The T in the word the reminds us of the prefix tera-, G in the next word reminds us of giga-, M in the next word for mega-, et cetera. The only thing we need to remember is the u in the word under stands for or reminds us of the unit symbol for micro-, which looks like a letter u but is in fact a Greek letter. Some of the prefix symbols are uppercase, some are lowercase, and some have more than one letter, and again micro- uses a Greek letter.

If we take the base unit, we can adjust it by using a suitable prefix according to what we are measuring. For example, if we want to measure the distance between two cities, kilometers is more convenient than the base unit meters. One kilometer is 1000 times bigger than one meter or 10 to the three meters. Another example is nanoparticles, which are measured in nanometers. A nanometer is 0.000000001 meters or 10 to the negative nine meters. The relationship between a base unit and a prefixed unit, as shown here, is called a conversion factor.

Let’s have a look at some examples of converting between units with different prefixes. Let’s convert 543 grams of iron to kilograms of iron. How we do this is we take the measured or given value and multiply by a conversion factor to convert to the desired unit. The conversion factor must be written as a ratio of 𝑥 over 𝑦. In this example, we take our measured or given value of 543 grams and we multiply by the conversion factor. If we use our prefix table from earlier, we would work out that the conversion factor here is 1000 grams equals one kilogram. We can write that as a ratio of 1000 grams over one kilogram or 1000 grams per kilogram or one kilogram over 1000 grams. It does not matter which way we write the ratio. The value of the numerator means the same as the value of the denominator, except that they have different units and so the numbers have been adjusted.

Which ratio do we pick to use in our calculation? We are going to choose the one that will allow this grams to cancel out. So we will choose the conversion factor with grams in the denominator. The grams can now cancel out because one is in the numerator and one is in the denominator. And we get 543 times one kilogram divided by 1000, which gives 0.543 kilograms. Now, 543 grams and 0.543 kilograms means exactly the same thing just expressed with different units. It’s still the same mass of iron.

In this example, we want to convert from centimeters to kilometers. We have our measured or given value, and we need a conversion factor to relate the two units. Notice that here we are going from centimeters to kilometers straight past the base unit meters. This problem is a bit more complex than the previous one. The best thing to do is to convert from centimeters to meters using a conversion factor and then from meters to kilometers using another conversion factor.

The conversion factor for centimeters to meters is 100 centimeters equals one meter. We can write that as 100 centimeters over one meter or one meter over 100 centimeters; they mean the same thing. And the conversion factor between meters and kilometers is 1000 meters equals one kilometer, which we can write as 1000 meters over a kilometer or one kilometer over 1000 meters.

So we write down our measured or given value and multiply it by a conversion factor. In the first conversion factor, which we will write here, we want to convert centimeters to meters. So which ratio will we use? We will use the one with centimeters as in the denominator. This is so that we can eliminate the unit centimeters. The two centimeter units can cancel. Remember, this number is actually over one. So it is in the numerator.

Now we need to multiply by another conversion factor to convert meters to kilometers. We want our final answer to be in kilometers. So our aim is to get rid of this meter unit in the numerator, which means again we must choose this conversion factor where meters is in the denominator. There is our conversion factor. And the meters cancel with the meters because one is in the numerator and one is in the denominator. When we simplify our equation and solve for the answer, we get 0.45562 kilometers. In summary, we must use the conversion factor that allows us to cancel the units that we do not want.

Now let’s have a look at predicting units. We can predict the units of a calculation when we know the equation used for that calculation. For example, using this equation for concentration concentration equals number of moles of a volume or 𝑛 over 𝑣, where the unit of moles is mole and the unit for volume is often expressed as dm cubed or liters, we will have a number in moles over a number in decimeters cubed, giving us an answer with the unit moles per decimeter cubed. So even if you did not know the units for concentration, as you do the calculation, you will be able to figure out what the final unit will be.

What will the units be for this equation, number of moles equals mass divided by molar mass? The mass unit is grams. And the molar mass unit is grams per mole, which can be expressed in two different ways on paper, giving us grams divided by grams per mole. Notice that the grams units can cancel, and the answer will have the unit moles. This minus-one exponent changes to a plus one when the unit is taken into the numerator. More on this in another video.

Let’s now turn our attention to rearranging simple algebraic equations. Sometimes we are given an equation, and we need to rearrange it to solve for one of the variables. Using this example, density equals mass of a volume or 𝑑 equals 𝑚 over 𝑣, what if we want to solve for mass? The aim is to get mass all by itself on one side of the equal sign, which means on the right-hand side of this equal sign or the right-hand side of this equation, we need to get rid of 𝑣, volume. Volume is in the denominator, so we need to multiply by volume in the numerator so that the two volumes can cancel. But the golden rule is what we do to one side of an equation, we must also do to the other side. This is to ensure that the equal sign still is true. One side must still equal the other side. And so we also multiply by volume on the left-hand side of the equation.

Now the two volumes on the right-hand side of the equation can cancel. And we are left with 𝑣 times 𝑑 equals 𝑚, which is the same as 𝑚 equals 𝑣 times 𝑑. But what if we want to make 𝑣 the subject of the formula? In other words, what if we want to solve for 𝑣? We want volume all alone by itself. And we don’t want it in the denominator. We can multiply both sides of the equation by 𝑣. These two volumes will cancel, and we get 𝑣𝑑 equals 𝑚 as before. Volume is no longer in the denominator, but it is still not by itself. To get rid of the 𝑑 on the left-hand side, we divide both sides by density. These two densities can cancel, and we get volume by itself equals mass divided by density.

Before we summarize everything we have learnt, let’s very briefly have a look at the different units used for volume because, in chemistry, there are several different units that we use. Volume units used in chemistry are centimeters cubed, decimeters cubed, milliliters, and liters. The conversion factor between centimeters and decimeters is 10 centimeters equals one decimeter. Cubing both sides of the equation, we change from length to volume and we get the conversion factor of 1000 centimeters cubed equals one decimeter cubed. Also, 1000 milliliters is the same as one liter and one centimeter cubed is the same as one millimeter.

We won’t go into explaining why this is so in this video, but we can deduce that 1000 centimeters cubed would thus be equal to 1000 milliliters. Summarizing all this into one statement, we get 1000 centimeters cubed is the same as a decimeter cubed, which is the same as 1000 milliliters, which is the same as one liter. Knowing and understanding this conversion factor will help you greatly in your chemistry calculations. You can convert between any of these units. You can relate these two or these two or these two and so on.

Now let’s summarize everything we have learnt. In this lesson, we have learned that the SI units are standard units of measure used internationally. The seven base units are for time, seconds; length, meters; mass, kilograms; electrical current, amperes; temperature, kelvin; amount of substance, mole; and luminous intensity, candela. We learnt about unit prefixes and how to convert between them and a mnemonic for remembering their order, as well as how to predict units and rearrange simple algebraic equations.

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