five steps to the solution

Faculty of Chemistry and Technology in Split

First published: 2012/01/03

Stoichiometric calculations are based on the equalization between the ratio of the amount of substance we're interested in, and the ratio of the corresponding absolute values of the stoichiometric numbers. Almost every single stoichiometric task can be solved in five easy steps, and with only a basic knowledge of mathematics.

- Extracting measurement data from the task
- Converting all units of measurement to the same base units
- Writing a balanced reaction
- Determining the stoichiometry of species
- Calculating the desired quantity

Let us demonstrate this on a simple example:

* Task: Calculate the concentration of hydrochloric acid if the titration of* 0.2451 g

Let's start from the beginning - step by step.

As before, the path to the solution begins with the first (and hardest) step, which requires of you to not only keep your eyes sharp, but also your mind. Before you even begin, make sure to carefully read the task itself. Once you understand what is required of you, separate that from all of the other data, and then rearrange the data by the species it relates to. Don't be too crude about this, however, as the only purpose of this step is to help you succeed in the task, or rather to help you find the formulas you need.

When writing physical quantities make sure to *always* mark (in brackets or as an index) which species the quantity relates to (remember that a species can be an atom, molecule, ion, apple, etc.). A physical quantity without a species it relates to has absolutely no meaning.

-------------------------

Note that the last piece of information is not found in the task itself. But you probably already know that whenever you need it, and you usually do when you're working with masses, you can find the mass of one mole of an element or compound in the periodic table.

*A word of advice:* if you have been given a compound of something (in either a ratio or percentages), it's enough to say (and you can even lie, it doesn't matter) that you have one kilogram, mole, or liter of that something (depending on whether we're talking about a mass, volume, or molar ratio). After that the ratios will automatically become a quantity you can work with (parts of a kilogram, mole, or liter).

It often happens that the units in a task are mixed with their multiples or submultiples (like in our task since the volume is given in cm^{3}, and the required concentration in mol dm^{-3}). It is necessary to convert them all into the same unit of measurement (it is best to convert everything into mole, dm, g). Be careful and remember: whenever you perform a mathematical operation on a unit, you must also do the same to the number before the unit (and vice versa).

For example, if 1 dm has 10 cm, then (1 dm)^{3} has (10 cm)^{3}, and conversely 1 dm^{3} has 1000 cm^{3}, which written mathematically looks like

1 dm^{3} = 1000 cm^{3} or

1 dm^{3}
/
1000 cm^{3}

= 1 which can be written a little shorter as
1 dm^{3}
/
10^{3} cm^{3}

= 1
You can also a write a reciprocal relationship without much of an issue (1000 cm^{3}/1 dm^{3}) if that's your preference - in both cases the result will be the same (1). Select the form whose right side will, once everything is shortened, contain only the unit to which we are converting.

23.09 cm^{3} = ? dm^{3}

23.09 cm^{3} ·
^{-3} dm^{3}

1 dm^{3}
/
10^{3} cm^{3}

= 23.09·10or 23.09 cm^{3} = 23.09·10^{-3} dm^{3}

Do note that 1 mL = 1 cm^{3}, and conversely 1 L = 1 dm^{3}. Which quantities, units, and prefixes you are allowed to use you can look up in the The International system of units.

On a more complex example you can see why this is called a simple dimensional analysis. Let's see what the speed of a car driving 45 km/h is in meters per second.

45 km/h = ? m/s

We need to convert kilometers into meters, and hours into seconds. Each unit requires its own conversion factor: 1 km = 1000 m and 1 h = 3600 s (since an hour has 60 minutes, and a minute 60 seconds)

45 km/h ·

1000 m
/
1 km

·
1 h
/
3600 s

= 12.5 m/s (Simple, isn't it?)
If the unit in the result (the unit on the right side) is not a multiple or submultiple of the unit on the left side, then you have chosen the wrong conversion factor.

Let's get back to our task. In order to avoid confusion, copy the new units behind the data in step 1. Add an equality sign (=) after the old value and write the new value and its unit behind it. For example:

Now that you know what exactly is required of you and what you can calculate with its time to move on to the most important step - equalizing the chemical equation. You'll find a brief guide on how to easily balance chemical equations on the Balancing redox reactions page.

Na_{2}CO_{3} + 2HCl
→
H_{2}O + CO_{2} + 2NaCl

Don't even try to solve the task without first balancing the chemical equation. Once you manage to balance the equation of the chemical reaction you will be able to determine the relationship (stoichiometry) between the substances (species) that interest you.

This is a small step for you, but a giant leap towards solving the task. Its purpose is to connect what you are searching for with what you currently have. The procedure is simple. By looking at the balanced equation you need to write down the relationship between two species on one side, and the relationship between the numbers that stand beside them (also known as stoichiometric numbers or stoichiometric coefficients) on the other side of the equal sign. If there is no number before the formula of a species the stoichiometric coefficient is 1. It doesn't matter who is going to be in the numerator and who in the denominator position (the calculation will be slightly simpler if you put what you're looking for into the numerator).

Na_{2}CO_{3}
/
HCl

=
1
/
2

is the same as
HCl
/
Na_{2}CO_{3}

=
2
/
1

The above expression can be read as follows: *The ratio between the number of sodium carbonate molecules and the number of hydrochloric acid molecules is 1:2.* You can apply the same rules to this relation as you would to numbers in algebra. Move HCl to the right side by simply multiplying both fractions with HCl (with the number of hydrochloric acid molecules).

Na_{2}CO_{3} =

1
/
2

HClAnd if you know the number of molecules divided by the Avogadro number gives the number of moles, you can write the expression above in a much more elegant way and transform it into a magical formula to solve our task

1
/
2

Believe it or not, at this point you already have the solved task in front of you - it's just that you haven't presented it very well. You only need to express the number of moles on the left and right side of the equation by using relations that contain the values given in the task itself. You can also combine several formulas (for example, use volume and density to determine mass, and then use that to determine the amount) or you can use the ideal gas equation (*pV = nRT*).

Until you gain a bit of experience always work with only two species. If you have two (or more) related reactions, the stoichiometric number of the shared species must be the same in both relationships, or rather in both reactions (even if this means we need to multiply one of the reactions with some number).

We have finally reached the end. You can find which data you need in order to get the amount of a specific species on the Quantitative expression of composition of mixtures and solutions page.

Once you recover from the shock due to the mountain of formulas you will notice that each unit is hiding the formula from which it was created: the molar mass unit is kg/mol (mass/amount), the unit of concentration is mol/dm^{3} (amount/volume), the unit of density is kg/L (mass/volume), etc.

From our data we can immediately see that our units for concentration (mol/dm^{3}) and molar mass (g/mol) already have moles within them. Let's write those formulas down

Whether you calculate each equation separately or you include all of them into the magical equation from the previous step is completely irrelevant. Both of them are elementary mathematics.

1
/
2

1
/
2

Move *c*(HCl) to one side, and the rest to the other side of the equality sign. You don't know how? Simply multiply both sides of the equation with 2 and then divide with *V*(HCl).

Enter your data (arranged in step 3), take a calculator and compute.

2 · 0.2451 g
/
23.09·10^{-3} dm^{3} · 105.99 gmol^{-1}

= 0.2003 moldmWhile you marvel at your success, make sure to check if the result makes any sense (it's unlikely that you'll get 3 kg of product from 4 g of a reagent) and if the unit matches the physical quantity. It does? Excellent, you can now take a well-deserved rest!

Finally, remember that this is not the only way you can solve your task. There are many of them, and you can find an example based on dimensional analysis at the Department of General and Inorganic Chemistry at the Faculty of Chemistry and Technology at Split.

Citing this page:

Generalic, Eni. "Stoichiometric calculations - five steps to the solution." *EniG. Periodic Table of the Elements*. KTF-Split, 25 Jan. 2022. Web. {Date of access}. <https://www.periodni.com/stoichiometric_calculations.html>.

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