Stoichiometry Summary

Solution Terminology

The solute is the substance that is present in the smaller amount. The solvent is the substance that is present in the larger amount. Either may be a solid, liquid or gas although some solute/solution combinations are more common. A concentrated solution has a relatively large quantity of s specific solute per unit amount of solution, a dilute solution has a relatively small quantity of the same solute per unit ammount of solution. Solubility is a measure of how much solute will dissolve in a given amount of solvent and a given temperature. A solution that can exist in equilibrium with undissolved solute is a saturated solution. A solution whose concentration corresponds to the solubility limit is therefore saturated. If the concentration of solute is less than the solubility limit, it is unsaturated. Under carefully controlled conditions, a solution can be produced in which the concentration of solute is greater than the normal solubility limit. such a solution is said to be supersaturated. Miscible and immiscible are terms usually limited to solutions of liquids in liquids. If two liquids dissolve in each other in all proportions they are said to be miscible. If two liquids are insoluble in each other, they are said to be immiscible.

Formation of a Solution:

When a soluble ionic crystal is placed in water, the negatively charged ions at the surface are attracted by the positive region of the polar water molecules. A “tug-of-war” for the negative ions begins. Water molecules tend to pull them from the crystal, while neighboring positive ions tend to hold them to the crystal. In a similar way, positive ions at the surface are attacked by the negative portion of hte water molecules and are torn from the crystal. Once released, the ions are surrounded by the polar water molecules. Such ions are said to be hydrated. The time required to dissolve a given amount of solute – or to reach equilibrium, if excess solute is present – depends on several factors:

  1. The dissolving process depends on surface area. A finelydivided solid offers more surface area per unit of mass than a coarsly divided solid. Therefore a finely divided solid dissolves more rapidly.

  2. In a still solution, concentration builds up around the solute surface, causing a higher re-crystallization rate than would be present ifthe solute were uniformly distributed. Stirring or agitating the solution prevents this build-up and maximizes the net dissolving rate.

  3. At higher temperatures particle movement is more rapid, thereby speeding up all physical processes.

Factors that Determine Solubility:

The extent to which a particular solute dissolves in a given solvent depends on three things:

  1. Strength of intermolecular forces within the solute, within the solvent, and between the solute and solvent.

  2. The partial pressure of a solute gas over a liquid solvent.

  3. The temperature.

Intermolecular forces:

Generally speaking, if the forces between A molecules are about the same as the forces between B molecules, A and B will probably dissolve in each other.

Partial Pressure:

Changes in partial pressure of a solute gas over a liquid solution have a pronounced effect on the solubility of the gas. As the partial pressure is increased, the solubility is increased.


Solubility depends on temperature. As a general rule, solubility increases with increasing temperature. However, with gases. the solubility decreases with increasing temperature.

Solution Concentration:

Concentration of a solution tells us how much solute is present per given amount of solution or a given amount of solvent. As a “per” expression, concentration has the form of a fraction, or a concentration ratio. Amount of solute appears in the numerator and may be in grams, moles or equivalents. Quantity of solvent or solution is in the denominator and may be in mass or volume units.

Percentage (%):

If a solution concentration is given as a percentage, you can generally assume it is a mass percentage unless otherwise stated. By definition, percentage by mas is grams of solute per 100g of solution.

A better way to calculate solution percentage is to multiply the concentration ratio g solute/g solution by 100:

Be very careful with the denominator. If you are quoted a mass of solvent and a mass of solute, you will need to add them together to get the mass of solution.

Example 1: When 25g of solute is dissolved in 75g of solvent. What is the percentage concetration?

Concentration of a solution tells us how much solute is present per given amount of solution or a given amount of solvent. As a “per” expression, concentration has the form of a fraction, or a concentration ratio. Amount of solute appears in the numerator and may be in grams, moles or equivalents. Quantity of solvent or solution is in the denominator and may be in mass or volume units.

Molarity (M):

When working with liquids, it is often easier to measure volume rather than mass. Therefore, a solution concentration bsed on volume is usually more convenient than one based on mass. Molarity (M) is defined as the number of moles of solute per liter of solution, and is expressed as:

Example 1: What is the molarity of a solution prepared with 0.50 moles of solute dissolved in enough solvent to give 1.00 Liters of solution?

Example 2: What is the molarity of a solution prepared with 16g of oxygen gas (R.M.M = 32 g/mol) dissolved in enough water to give 0.5 liters of solution?

There are two steps in this calculation. first you must determine the number of moles of oxygen and then determine the concentration.


Many pysical properties are related to solution concentration expressed as molality, m, the number of moles of solute dissolved in one kilogram of solvent. Again the concentration ratio is the defining equation:

Example: If a solution is prepared with 0.5 moles of ethanol dissolved in 1.00kg of solvent, what is its molality?


Ionic Compounds in Solution: Electrolytes.

Earlier in this chapter I showed &Deltaa diagram of how an ionic solid dissolvves in water. What I want to talk about now is how the dissolution of ionic compounds in solution affect their properties, in particular there electrical properties. Totally pure water (H2O) does not conduct electricity AT ALL. When you drop the toaster in the bath and try to kill yourself, it is the ions in solution and not the water itself that are conducting the electricity. So, if you want to go quicker, add lots of Ions!!!!!! Not all solids that dissolve in water form electrolytes, the ones that do so must be able to dissociate into ions (dissociate means separate into their ions). Some copounds will dissociate very well and some will not, this gives us different types of electrolytes. The more a solid dissociates in solution, the stronger the electrolyte. The stronger the electrolyte, the better the solution conducts electricity.

            Most ionic compounds dissociate into their component ions, in solution and are generally referred to as electrolytes. Most molecular compounds, however, do not dissociate into their component ions in solution and are generally referred to as non-electrolytes. There are however several groups of molecular compounds that are electrolytes, these are the acids such as HNO, HCl, H2SO4, H3PO4. This occurs because this type of molecular compounds is easilt ionizable.


Electrolytes can be grouped into three main categories:

  1. STRONG ELECTROLYTES: These compounds exist almost completely as ions in solution. Nearly all ionic compounds are strong electrolytes. e.g. NaCl, NaOH, Na2NO3, HCl, H2SO4.

  2. WEAK ELECTROLYTES: These compounds ionize only slightly when dissolved in water and so there are fewer ions available to conduct electricity. For example in a 1.0M solution of acetic acid (vinegar), HC2H3O2, moste of the molecule remains as HC2H3O2 and only a very small amount (about 1%) ionizes to forrm H+ and C2H3O2– . This amount of dissociation is independent of the solubility of the compound. Acetic acid is extremely soluble in water. The interesting thing about weak electrolytes is that they DO NOT just dissociate to 1% and stop, they are constantly dissociating and re-associating in a process known as dynamic equilibrium, often called chemical equilibrium and are represented in the chemical equation by a double arrow:

The double arrow is used to represent the ionization of weak electrolytes, a single arrow would represent the ionization of a strong electrolyte.

The single arrow indicates that th species have no tendencey to recombine in water to form the original compound.

  1.  NON-ELECTROLYTES: These compouds do not ionize in solution at all.

Acids, Bases and Salts:

This group of compounds are very familiar to most people and are encountered daily in one form or another.


These are substances that are able to ionize in solution to form a hydrogen ion and thereby increase the concentration of H+ ions in and aqueous solution. Hydrogen as an element contains only one proton and one electron. The hydrogen ion, has lost that electron and so is just a proton, because of this, acids are often known as proton donors. Acids that contain one hydrogen are called monoprotic (HCl), those with two are called diprotic (H2SO4) and those with three are called triprotic (H3PO4). Each of these acids can lose one or all of their hydrogens as acidic protons. Loss of more than one proton often requires a lot of energy and so loss of the second hyrdogen is often an equilibrium process. These acids are still strong electrolytes because they have already lost one proton in a non-equilibrium process.


These are substances that can react with or accept H+ ions. Hydroxide ions (OH– ) are basic because they react with H+ ions to form water. We can define a base as any substance that increases the concentration of OH ions in aqueous solution. Ionic hydroxides such as NaOH, KOH and Ca(OH)2 are among the most common bases. When dissolved into water they dissociate to form the separate ions and releasing OH into solution. One other common base that does not contain hydroxide ions, is ammonia. Ammonia reacts with water to form the ammonium ion and a hydroxide ion.

Acids ans bases fall into two categories bases on their level of dissociation. If they are strong electrolytes then they will be known as Strong acids or Strong bases. However, if they are weak electrolytes, they will be called Weak acids or Weak bases. This has nothing at all to do with the concentration of the acid. Weak acids are generally less reactive than strong acids although there are exceptions to this rule. Hydrofluoric acid is a weak acid but it is very reactive and will even attack glass. This is because of the anion, F which is highly reactive in combination with the H+.


These are ionic compounds formed by replacing one or more of the hydrogen ions in an acid, with a different ion. This very often comes about by reacting an acid with a base in a process known as neutralization. Almost all salts are strong electrolytes (the excption being those made from heavy metals such as mercury and lead).


Neutralization Reactions:

When we mix solutions of acids and bases, a neutralization reaction occurs that generally produces a salt composed of the bases cation and the acids anion together with water. Exceptions to this would be carbonates which often produce carbon dioxide plus a salt.

Ionic Equations:

Often when working with reactions in solutions it is neccessary to clearly outline what ions are present and how they might interact to give products that may themselves be ionic or may be solids, liquids and gases. The equations that we have written so far have mostly been molecular equations that show just the reactants and products. In order to get a full icture of the story, we must use ionic equations. This involves, writing all ionic components of a reaction as their ions. In these kinds of reactions, any species designated as (aq), can be designated in terms of its ions. species designated as (s)(l), or (g) are not. When ions appear on both sides of the equation, they are said to be SPECTATOR IONS as they do not take part in the overall reaction, they just “watch” like a sports spectator, they are required to be present but dont change permanently. Because the spectator ions dont actually take part in the reaction, they can be omitted from the reaction equation for simplicity. When this occurs, the remaining equation is called the NET IONIC EQUATION.

If we consider the reaction between HCl and NaOH:

You can see that HCl, NaOH and NaCl show an (aq) symbol but H2O shows a (l) symbol. What this tells us is that some of the reactants have combined to form water which has been “lost” from the overall reaction. The remaining ions are still “in-solution”. We can start to represent this by writing out all the ions. This is called the COMPLETE IONIC EQUATION. From here you can see that Na+ and Cl appear in both the reactants and products. These are spectator ions and we can choose to omit them and obtain the NET IONIC EQUATION. The net ionic equation contains only those ions and molecules that are directly involved in the reaction. Net Ionic equations are great (OK, I know you dont think so but . . . ) because they can highlight the similarities and differences between a group of seemingly identical reactions.

 According to the textbook, in order to write an ionic equation, you must first ask yourself a few questions:

  1. Is the substance soluble?

  2. If it is soluble, is it a strong electrolyte.

            Only if the answer to both questions is yes, can you write the substance in an Ionic form. That means, acetic acid, HF and all other weak electrolytes must remain in their molecular form.

 Metathesis Reactions:

What a wonderful name, it is a greek word for “to transpose”. In molecular equations for many aqueous reactions, positive ions (cations) and negative ions (anions) appear to exchange partners. These reactions have the following general format:

An example of this is given in the text book as:

We can convert metathesis reactions into net ionic equations, ions must be removed from solution. In general, three chemical processes can lead to the removal of ions from solution, thus serving as a driving force for metathesis reactions (see Le Chatleliers Principle):

  1. The formation of an insoluble solid (called a precipitate).

  2. The formation of either a soluble weak electrolyte or a soluble non-electrolyte.

  3. The formation of a gas that escapes from the solution.

We now need to investigate the factors which might influence precipitation, gas formation and so on. A lot of this falls into the category of solubility and solubility rules.

Solubility and Solubility Rules:

The solubility of a substance is the amount of that substance that can be dissolved in a given quantity of solvent. The textbook refers to any substance with a maximum solubility of less than 0.01 moles per liter as being insoluble. Because of the wealth of research that has been done on various compounds we are able to draw on information available and draw-up a table that expresses what kinds of compounds will be soluble. These “solubility rules are as follows:


Solubility Rule

Mainly Water Soluble Ionic Compounds
NO3 All nitrates are soluble
C2H3O2 All acetates are soluble
Cl All chlorides are soluble, except AgCl, Hg2Cl2, and PbCl2
Br All bromides are soluble except, AgCl, Hg2Cl2, HgCl2 & PbCl2
I All iodides are soluble except, AgI, Hg2I2, HgI2 & PbCl2
SO42- All sulfates are soluble except CaSO4, SrSO4, BaSO4, PbSO4, Hg2SO4, & Ag2SO4.
Mainly Water Insoluble Ionic Compounds.
S2- All sulfides are insoluble except those of the 1A and 2A elements and (NH4)2S.
CO32- All carbonates are insoluble except those of the 1A elements and (NH4)2CO3
PO43- All phosphates are insoluble except those of the 1A elements and (NH4)2PO4
OH All hydroxides are insoluble except those of the 1A elements, Ba(OH)2, Sr(OH)2, and Ca(OH)2.

There are plenty of examples in the textbook that you can look at and get an idea of what to look for.

Reactions in which a Weak or Non-Electrolyte Forms:

We have already talked about this kind of reaction, indirectly. Ions can interact to form a soluble weak or non-electrolyte which remains in solution. The most common example of this is the formation of liquid water during an acid-base neutralization reaction. Another example of this would be the reaction of a metal oxide with an acid such as HNO3 or for an example where a non-water weak electrolyte is formed, look to the reaction between hydrochloric acid and sodium acetate (the salt of acetic acid) too form sodium chloride and acetic acid.

Which can be written as a net ionic equation:

Reactions in which as Gas Forms:

We have mentioned this a little previously when the evolution of carbon dioxide during a neutralization reaction was talked about. This is most significant when a gas with low solubility is produced during the reaction. The book gives the example of hydrochloric acid reacting with sodium sulfide to produce hydrogen sulfide and sodium chloride. Hydrogen sulfide is a gas with the odor of rotton eggs. Other reactions that produce gases include the reaction of carbonates and sulfites with acids. If you have ever made wine or beer, one of the sterilizing solutions contains sodium bisulfite (NaHSO3) which can decompose under acid conditions to give sulfur dioxide. When you add citric acid to the sterilizing solution, the amount of sulfur dioxide evolved during the reaction is quite impressive and sure to clear your apartment of friends for almost as long as if you released hydrogen sulfide. But hey, at least you your apartment will be sterilized.

Reactions of Metals:

Dont we all love the oxidation of metals! That day you spot the first rust blemish on the wing of your car. You give it a prod to see if it is real and your hand goes though the wing leaving a whole so big that you could get the whole gearbox though it. We call this corrosion. You can take solace that you are just a pawn in the chemical cycle of your average metal and its desire to lose those electrons. When a metal corrodes, it loses electrons and forms cations. for example if you add acid to calcium (Ca) it reacts vigorously to give calcium cations (Ca2+) and hydrogen gas. when an atom, ion or molecule loses electrons it becomes positively charged and we say it has been OXIDIZED. The loss of electrons is called oxidation. The term oxidation is used because this type of behavior was firs identified in reactions with oxygen. An example of this would be: When an atom, ion or molecule gains electrons it becomes more negatively charged and we say that it has been REDUCED. The gain of electrons is called reduction. In an oxidation reaction, when one species is oxidized, the other specied must be reduced. It is logical that if one species (usually the metal) gives away electrons, the other species (usually the non-metal) must accept them. Electrons do not like to float around on their own. Oxidations and reductions always occur together, in the same reaction, at the exact same time. The electron is transferred from one species directly to the other. The species which is oxidized is called the reducing agent because it reduces the OTHER species. The species which is rediced is called the oxidizing agent because it oxidizes the OTHER species. A little acronym to help you learn the difference between oxidation and reduction in terms of electron loss and electron gain.

Oxidation of Metals by Acids and Salts:

Many metals react with acids to form salts and hydrogen gas. For example, magnesium metal reacts with hyrochloric acid to form margnesium chloride and hydrogen gas: In each case, the metal os oxidized by the acid to form the metal cation, and the acid is reduced from H+ to hydrogen gas. The acid anion (Cl in this case) is a spectator. Metals can also be oxidized by aqueous solutions of salts of other metals in a metathesis reaction where the elemental metal and the metal in the salt exchange places.

For example:

The big question is how do we know which metals replace each other. To answer this, we turn to the “Activity Series” which is a table that lists the important metals in order of decreasing ease of oxidation. What this tells us is that if you add a metal to a metallic salt and the metal is above the salt in the list then a reaction will occur, if it is below the salt then no reaction will occur. The activity series for metals of interest to us are shown below. You will notice that magnesium (Mg) is much higher in the list than silver (Ag) is and so, magnesium will DISPLACE silver from any salts in which silver is present and deposit metallic silver.


Oxidation Reaction



Li  àLi + + e


K   à K + + e


Ba à Ba 2+ + 2e


Ca à Ca 2+ + 2e


Na à Na + + e


Mg à Mg 2+ + 2e


Al  à Al 3+ + 3e


Mn à Mn 2+ + 2e


Zn  à Zn 2+ + 2e


Cr  à Cr 3+ + 3e


Fe  à Fe 2+ + 2e


Co à Co 2+ + 2e


Ni à Ni 2+ + 2e


Sn à Sn 2+ + 2e


Pb à Pb 2+ + 2e


H2  à 2H + + 2e


Cu à Cu 2+ + 2e


Ag à Ag + + e


Hg à Hg 2+ + 2e


Pt  à Pt 2+ + 2e

Au à Au 3+ + 3e

You will see that there are only five metals below hydrogen. Only those metals above hydrogen are able to react with acids to form H2. Copper does react with Nitric acid (HNO3) but this is not a simple reaction between the copper and the hydrogen ions. Instead the metal is oxidized by the nitrate ion to give copper nitrate, water and nitrogen dioxide (a smelly brown gas).


Solution Stoichiometry:


Solution stoichiometry is very much like the stoichiometry you have encountered previously, except that the given compound, wanted compound or both are in solutions with a concentration (usually moles/Liter).

There are three main steps to solving stoichiometry problems:

  1. Convert the quantity of given species to moles.

  2. Convert the moles of given species to moles of wanted species.

  3. Convert the moles of wanted species to the required quantity units.

Using molarity as a conversion factor, we have another way to convert between a measurable quantity – volume of solution – and moles.

Example 1: How many liters of 1.5M sodium hydroxide are required to react with 0.5 liter of 2.0M hydrochloric acid?

Example 2: How many liters of 1.5M sodium hydroxide are required to react with 0.5 grams of hydrogen chloride?

There are several possible combinations for this type of calculation, all of which you need to be able to figure out. You should net memorize each combination but learn to decide what comes next. For example in this problem I start off with grams of HCl and so must use RMM (molecular weight) to obtain the number of moles. I then look at the balanced equation for my coefficients so that I know the molar ratio of sodium hydroxide to hydrogen chloride. I then notice that I use molarity to obtain the final number of liters from the number of moles.

Learn to manipulate the information given, it will make life a lot easier. You may be given or asked to determine, grams, volume of gas, pressure of gas, temperature of gas, volume of solution, concentration of solution, density of solution or relative molecular mass (molecular weight).

We use the concept of stoichiometry a lot as an anylitical tool called titration. In a titration we accurately measure the amount of a known concentration of solution is required to EXACTLY react with a known volume of a solution of unknown concentration and so determine that concentration. This kind of experiment might be used to estimate the amount of blood in your alcohol stream after you have been pulled over for the sixth time because you were driving down the skunk river in your roommates new Mustang.. . . Or it can be used for Laboratory science!!!

I dont want to spend a lot of time on titration and its techniques, that is something you will learn in the lab. One thing that I should point out is that titration does not neet to be between two solutions, solids and gases can also be titrated. Titration is basically a method for determining the exact amount of two substances required for a complete reaction. There are several terms that we need to be familiar with:

  1. Standard Solution: This is the solution of known concentration.

  2. Equivalence Point: This is the point at which the stoichiometrically equivalent quantities are brought together. I.E. This is the point where the exact amount of each substance has been added to obtain a complete reaction. If you add anymore of the standard solution beyond this point the experiment will be ruined and you will need to start again.

  3. Indicators: You must have some way of determining when the equivalence point has been reached. With Acids and bases we can use an acid-base indicator. With other types of reaction, appropriate indicators such as conductivity, color, turbidity and so on can be used.

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