Stoichiometry

What is a Chemical Equation?

In chemistry, we use symbols to represent the various chemicals. Success in chemistry depends upon developing a strong familiarity with these basic symbols. For example, the symbol "C"represents an atom of carbon, and "H" represents an atom of hydrogen. To represent a molecule of table salt, sodium chloride, we would use the notation "NaCl", where "Na" represents sodium and "Cl" represents chlorine. We call chlorine "chloride" in this case because of its connection to sodium. You should have reviewed naming schemes, or nomenclature, in earlier readings.

A chemical equation is an expression of a chemical process. For example:

AgNO₃(aq) + NaCl(aq) ---> AgCl(s) + NaNO₃(aq)

In this equation, AgNO₃ is mixed with NaCl. The equation shows that the reactants (AgNO₃ and NaCl) react through some process (--->) to form the products (AgCl and NaNO₃). Since they undergo a chemical process, they are changed fundamentally.

Often chemical equations are written showing the state that each substance is in. The (s) sign means that the compound is a solid. The (l) sign means the substance is a liquid. The (aq) sign stands for aqueous in water and means the compound is dissolved in water. Finally, the (g) sign means that the compound is a gas.

Coefficients are used in all chemical equations to show the relative amounts of each substance present. This amount can represent either the relative number of molecules, or the relative number of moles (described below). If no coefficient is shown, a one (1) is assumed.

On some occasions, a variety of information will be written above or below the arrows. This information, such as a value for temperature, shows what conditions need to be present for a reaction to occur. For example, in the graphic below, the notation above and below the arrows shows that we need a chemical Fe₂O₃, a temperature of 1000° C, and a pressure of 500 atmospheres for this reaction to occur.

The graphic below works to capture most of the concepts described above:

The Mole

Given the equation above, we can tell the number of moles of reactants and products. A mole simply represents Avogadro's number (6.022 x 1023) of molecules. A mole is similar to a term like a dozen. If you have a dozen carrots, you have twelve of them. Similarly, if you have a mole of carrots, you have 6.022 x 1023 carrots. In the equation above there are no numbers in front of the terms, so each coefficient is assumed to be one (1). Thus, you have the same number of moles of AgNO3, NaCl, AgCl, NaNO3. Converting between moles and grams of a substance is often important. This conversion can be easily done when the atomic and/or molecular mass of the substance(s) are known. Given the atomic or molecular mass of a substance, that mass in grams makes a mole of the substance. For example, calcium has an atomic mass of 40 atomic mass units. So, 40 grams of calcium makes one mole, 80 grams makes two moles, etc.

Balancing Chemical Equations

Sometimes, however, we have to do some work before using the coefficients of the terms to represent the relative number of molecules of each compound. This is the case when the equations are not properly balanced. We will consider the following equation:

Al + Fe₃O₄---> Al₂O₃
+ Fe

Since no coefficients are in front of any of the terms, it is easy to assume that one (1) mole of Al and one (1) mole of Fe₃O₄ react to form one (1) mole of Al₂O₃. If this were the case, the reaction would be quite spectacular: an aluminum atom would appear out of nowhere, and two (2) iron atoms and one (1) oxygen atom would magically disappear. We know from the Law of Conservation of Mass (which states that matter can neither be created nor destroyed) that this simply cannot occur. We have to make sure that the number of atoms of each particular element in the reactants equals the number of atoms of that same element in the products. To do this we have to figure out the relative number of molecules of each term expressed by the term's coefficient.

Balancing a simple chemical equation is essentially done by trial and error. There are many different ways and systems of doing this, but for all methods, it is important to know how to count the number of atoms in an equation. For example we will look at the following term.

2Fe₃O₄

This term expresses two (2) molecules of Fe₃O₄. In each molecule of this substance there are three (3) Fe atoms. Therefore in two (2) molecules of the substance there must be six (6) Fe atoms. Similarly there are four (4) oxygen atoms in one (1) molecule of the substance so there must be eight (8) oxygen atoms in two (2) molecules.

Now let's try balancing the equation mentioned earlier:

Al + Fe₃O₄---> Al₂O₃+ Fe

Developing a strategy can be difficult, but here is one way of approaching a problem like this.

1. Count the number of each atom on the reactant and on the product side.
   
2. Determine a term to balance first. When looking at this problem, it appears that the oxygen will be the most difficult to balance so we'll try to balance the oxygen first. The simplest way to balance the oxygen terms is:
   Al + 3 Fe₃O₄---> 4 Al₂O₃+ Fe

   Be sure to notice that the subscript times the coefficient will give the number of atoms of that element. On the reactant side, we have a coefficient of three (3) multiplied by a subscript of four (4), giving 12 oxygen atoms. On the product side, we have a coefficient of four (4) multiplied by a subscript of three (3), giving 12 oxygen atoms. Now, the oxygens are balanced.
   

3. Choose another term to balance. We'll choose iron, Fe. Since there are nine (9) iron atoms in the term in which the oxygen is balanced we add a nine (9) coefficient in front of the Fe. We now have:
   Al +3 Fe₃O₄---> 4Al₂O₃+ 9Fe

4. Balance the last term. In this case, since we had eight (8) aluminum atoms on the product side we need to have eight (8) on the reactant side so we add an eight (8) in front of the Al term on the reactant side.
   Now, we're done, and the balanced equation is:

8Al + 3Fe₃O₄ ---> 4Al₂O₃ + 9 Fe

Percent Composition

It is possible to calculate the mole ratios (also called mole fractions) between terms in a chemical equation when given the percent by mass of products or reactants. percentage by mass = mass of part/ mass of whole
There are two types of percent composition problems-- problems in which you are given the formula (or the weight of each part) and asked to calculate the percentage of each element and problems in which you are given the percentages and asked to calculate the formula.

In percent composition problems, there are many possible solutions. It is always possible to double the answer. For example, CH and C₂H₂ have the same proportions, but they are different compounds. It is standard to give compounds in their simplest form, where the ratio between the elements is as reduced as it can be-- called the empirical formula. When calculating the empirical formula from percent composition, one can convert the percentages to grams. For example, it is usually the easiest to assume you have 100 g so 54.3% would become 54.3 g. Then we can convert the masses to moles; this gives us mole ratios. It is necessary to reduce to whole numbers. A good technique is to divide all the terms by the smallest number of moles. Then the ratio of the moles can be transferred to write the empirical formula.

Example: If a compound is 47.3% C (carbon), 10.6% H (hydrogen) and 42.0% S (sulfur), what is its empirical formula?
To do this problem we need to transfer all of our percents to masses. We assume that we have 100 g of this substance. Then we convert to moles:

Carbon:	47.3 grams 1	x	1 mole 12.01 grams	= 3.94 moles
Hyrdrogen:	10.6 grams 1	x	1 mole 1.008 grams	= 10.52 moles
Sulfur:	42.0 grams 1	x	1 mole 32.07 grams	= 1.310 moles

Now we try to get an even ratio between the elements so we divide by the number of moles of sulfur, because it is the smallest number:

Carbon:	3.94 1.310	= 3
Hydrogen:	10.52 1.310	= 8
Sulfur:	1.310 1.310	= 1

So we have: C₃H₈ S

Example: Figure out the percentage by mass of hydrogen sulfate, H₂SO₄.
In this problem we need to first calculate the total mass of the compound by looking at the periodic table. This gives us:
2(1.008) + 32.07 + 4(16.00) g/mol = 98.09 g/mol
Now, we need to take the weight fraction of each element over the total mass (which we just found) and multiply by 100 to get a percentage.

hydrogen:	2(1.008) 98.09	=	2.016 98.09	= 0.0206 ∗ 100 = 2.06%
sulfur:	32.07 98.09	= 0.327 ∗ 100 = 32.7%
oxygen:	4(16.00) 98.09	=	64.00 98.09	= 0.652 ∗ 100 = 65.2%

Now, we can check that the percentages add up to 100%

65.2 + 2.06 + 32.7 = 99.96
This is essentially 100 so we know that everything has worked, and we probably have not made any careless errors.
So the answer is that H₂SO₄ is made up of 2.06% H, 32.7% S, and 65.2% O by mass.

Empirical Formula and Molecular Formula

While the empirical formula is the simplest form of a compound, the molecular formula is the form of the term as it would appear in a chemical equation. The empirical formula and the molecular formula can be the same, or the molecular formula can be any positive integer multiple of the empirical formula. Examples of empirical formulas: AgBr, Na₂S, C₆H₁₀O₅. Examples of molecular formulas: P₂, C₂O₄, C₆H₁₄S₂, H₂, C₃H₉.

One can calculate the empirical formula from the masses or percentage composition of any compound. We have already discussed percent composition in the section above. If we only have mass, all we are doing is essentially eliminating the step of converting from percentage to mass.

Example: Calculate the empirical formula for a compound that has 43.7 g P (phosphorus) and 56.3 grams of oxygen. First we convert to moles:

43.7 grams P 1	x	1 mol 30.97 grams	= 1.41 moles
56.3 grams O 1	x	1 mol 16.00 grams	= 3.52 moles

Next we divide the moles to try to get an even ratio.

Phosphorus:	1.41 1.41	= 1.00
Oxygen:	3.52 1.41	= 2.50

When we divide, we did not get whole numbers so we must multiply by two (2). The answer = P₂O₅

Calculating the molecular formula once we have the empirical formula is easy. If we know the empirical formula of a compound, all we need to do is divide the molecular mass of the compound by the mass of the empirical formula. It is also possible to do this with one of the elements in the formula; simply divide the mass of that element in one mole of compound by the mass of that element in the empirical formula. The result should always be a natural number.

Example: if we know that the empirical formula of a compound is HCN and we are told that a 2.016 grams of hydrogen are necessary to make the compound, what is the molecular formula? In the empirical formula hydrogen weighs 1.008 grams. Dividing 2.016 by 1.008 we see that the amount of hydrogen needed is twice as much. Therefore the empirical formula needs to be increased by a factor of two (2). The answer is:
H₂C₂N₂.

Density

Density refers to the mass per unit volume of a substance. It is a very common term in chemistry.

Concentrations of Solutions

The concentration of a solution is the "strength" of a solution. A solution typically refers to the dissolving of some solid substance in a liquid, such as dissolving salt in water. It is also often necessary to figure out how much water to add to a solution to change it to a specific concentration.

The concentration of a solution is typically given in molarity. Molarity is defined as the number of moles of solute (what is actually dissolved in the solution) divided by the volume in liters of solution (the total volume of what is dissolved and what it has been dissolved in).

Molarity =

moles of solute liters of solution

Molarity is probably the most commonly used term because measuring a volume of liquid is a fairly easy thing to do.

Example: If 5.00 g of NaOH are dissolved in 5000 mL of water, what is the molarity of the solution?
One of our first steps is to convert the amount of NaOH given in grams into moles:

5.00g NaOH 1

x

1 mole (22.9 + 16.00 + 1.008)g

= 0.125 moles

Now we simply use the definition of molarity: moles/liters to get the answer

Molarity =

0.125 moles 5.00 L of soln

= 0.025 mol/L

So the molarity (M) of the solution is 0.025 mol/L.

Molality is another common measurement of concentration. Molality is defined as moles of solute divided by kilograms of solvent (the substance in which it is dissolved, like water).

Molality =

moles of solute kg of solvent

Molality is sometimes used in place of molarity at extreme temperatures because the volume can contract or expand.

Example: If the molality of a solution of C₂H₅OH dissolved in water is 1.5 and the mass of the water is 11.7 kg, figure out how much C₂H₅OH must have been added in grams to the solution.
Our first step is to substitute what we know into the equation. Then we try to solve for what we don't know: moles of solute. Once we know the moles of solute we can look at the periodic table and figure out the conversion from moles to grams.

Molality = moles solute kg solvent

Now we simply use the definition of molarity: moles/liters to get the answer

Molality = moles solute kg solvent

1.5 mols kg = moles solute 11.7 kg

1.5 moles kg x 11.7 kg = 17.55 moles

17.55 moles 1 x (2 ∗ 12.01) + (6 ∗ 1.008) + 16 1 moles = 808.5 g C2H5OH

It is possible to convert between molarity and molality. The only information needed is density.

Example: If the molarity of a solution is 0.30 M, calculate the molality of the solution knowing that the density is 3.25 g/mL.
To do this problem we can assume one (1) liter of solution to make the numbers easier. We need to get from the molarity units of mol/L to the molality units of mol/kg. We work the problem as follows, remembering that there are 1000 mL in a Liter and 1000 grams in a kg. This conversion will only be accurate at small molarities and molalities.

0.3 mol 1 L

x

1 mL 3.25 g

x

1 L 1000 mL

x

1000 g 1 kg

= 0.09 mols / kg

It is also possible to calculate colligative properties, such as boiling point depression, using molality. The equation for temperature depression or expansion is

ΔT= K_f × m

Where:

ΔT is temperature depression (for freezing point) or temperature expansion (for boiling point) (°C)
K_f is the freezing point constant (kg °C/mol)
m is molality in mol/kg

Example: If the freezing point of the salt water put on roads is -5.2° C, what is the molality of the solution? (The K_f for water is 1.86 °C/m.)
This is a simple problem where we just plug in numbers into the equation. One piece of information we do have to know is that water usually freezes at 0° C.

ΔT = K_f * m
ΔT/K_f = m
m = 5.2/1.86
m = 2.8 mols/kg

Can You Drink Too Much Water?

Can You Really Drink Too Much Water?

In a word, yes. Drinking too much water can lead to a condition known as water intoxication and to a related problem resulting from the dilution of sodium in the body, hyponatremia. Water intoxication is most commonly seen in infants under six months of age and sometimes in athletes. A baby can get water intoxication as a result of drinking several bottles of water a day or from drinking infant formula that has been diluted too much. Athletes can also suffer from water intoxication. Athletes sweat heavily, losing both water and electrolytes. Water intoxication and hyponatremia result when a dehydrated person drinks too much water without the accompanying electrolytes.

What Happens During Water Intoxication?

When too much water enters the body's cells, the tissues swell with the excess fluid. Your cells maintain a specific concentration gradient, so excess water outside the cells (the serum) draws sodium from within the cells out into the serum in an attempt to re-establish the necessary concentration. As more water accumulates, the serum sodium concentration drops -- a condition known as hyponatremia. The other way cells try to regain the electrolyte balance is for water outside the cells to rush into the cells via osmosis. The movement of water across a semipermeable membrane from higher to lower concentration is called osmosis. Although electrolytes are more concentrated inside the cells than outside, the water outside the cells is 'more concentrated' or 'less dilute' since it contains fewer electrolytes. Both electrolytes and water move across the cell membrane in an effort to balance concentration. Theoretically, cells could swell to the point of bursting.

From the cell's point of view, water intoxication produces the same effects as would result from drowning in fresh water. Electrolyte imbalance and tissue swelling can cause an irregular heartbeat, allow fluid to enter the lungs, and may cause fluttering eyelids. Swelling puts pressure on the brain and nerves, which can cause behaviors resembling alcohol intoxication. Swelling of brain tissues can cause seizures, coma and ultimately death unless water intake is restricted and a hypertonic saline (salt) solution is administered. If treatment is given before tissue swelling causes too much cellular damage, then a complete recovery can be expected within a few days.

It's Not How Much You Drink, It's How Fast You Drink It!

The kidneys of a healthy adult can process fifteen liters of water a day! You are unlikely to suffer from water intoxication, even if you drink a lot of water, as long as you drink over time as opposed to intaking an enormous volume at one time. As a general guideline, most adults need about three quarts of fluid each day. Much of that water comes from food, so 8-12 eight ounce glasses a day is a common recommended intake. You may need more water if the weather is very warm or very dry, if you are exercising, or if you are taking certain medications. The bottom line is this: it's possible to drink too much water, but unless you are running a marathon or an infant, water intoxication is a very uncommon condition.

Elements named

There are 13 elements named after people, although only 12 of the names are formally accepted by the International Union of Pure and Applied Chemistry (IUPAC).

* bohrium (Bh, 107) – Niels Bohr
* curium (Cm, 96) – Pierre and Marie Curie
* einsteinium (Es, 99) – Albert Einstein
* fermium (Fm, 100) – Enrico Fermi
* gallium (Ga, 31) – both named after Gallia (Latin for France) and its discoverer, Lecoq de Boisbaudran (le coq, the French word for 'rooster' translates to gallus in Latin)
* hahnium (105) – Otto Hahn (Dubnium, named for Dubna in Russia, is the IUPAC-accepted name for element 105)
* lawrencium (Lr, 103) – Ernest Lawrence
* meitnerium (Mt, 109) – Lise Meitner
* mendelevium (Md, 101) – Dmitri Mendeleev
* nobelium (No, 102) – Alfred Nobel
* roentgenium (Rg, 111) – Wilhelm Roentgen (formerly Ununumium)
* rutherfordium (Rf, 104) – Ernest Rutherford
* seaborgium (Sg, 106) – Glenn T. Seaborg
This is an alphabetical list of element toponyms or elements named for places or regions. Ytterby in Sweden has given its name to four elements: Erbium, Terbium, Ytterbium and Yttrium.

* Americium – America, the Americas
* Berkelium – University of California at Berkeley
* Californium – State of California and University of California at Berkeley
* Copper - probably named for Cyprus
* Darmstadtium – Darmstadt, Germany
* Dubnium – Dubna, Russia
* Erbium – Ytterby, a town in Sweden
* Europium – Europe
* Francium – France
* Gallium – Gallia, Latin for France. Also named for Lecoq de Boisbaudran, the element's discoverer (Lecoq in Latin is gallus)
* Germanium – Germany
* Hafnium – Hafnia, Latin for Copenhagen
* Hassium – Hesse, Germany
* Holmium – Holmia, Latin for Stockholm
* Lutetium – Lutecia, ancient name for Paris
* Magnesium – Magnesia prefecture in Thessaly, Greece
* Polonium – Poland
* Rhenium – Rhenus, Latin for Rhine, a German province
* Ruthenium – Ruthenia, Latin for Russia
* Scandium – Scandia, Latin for Scandinavia
* Strontium – Strontian, a town in Scotland
* Terbium – Ytterby, Sweden
* Thulium – Thule, a mythical island in the far north (Scandinavia?)
* Ytterbium – Ytterby, Sweden
* Yttrium – Ytterby, Sweden

Egg in a Bottle Demonstration The Power of Air Pressure

The egg in a bottle demonstration is an easy chemistry or physics demonstration you can do at home or in the lab. You set an egg on top of a bottle (as pictured). You change the temperature of the air inside the container either by dropping a piece of burning paper into the bottle or by directly heating/cooling the bottle. Air pushes the egg into the bottle.

Egg in a Bottle Materials

* peeled hard-boiled egg (or soft-boiled, if a yolk mess interests you)
* flask or jar with opening slightly smaller than the diameter of the egg
* paper/lighter or very hot water or very cold liquid

In a chemistry lab, this demonstration is most commonly performed using a 250-ml flask and a medium or large egg. If you are trying this demonstration at home, you can use a glass apple juice bottle. I used a Sobe™ soft drink bottle. If you use too large of an egg, it will get sucked into the bottle, but stuck (resulting in a gooey mess if the egg was soft-boiled). I recommend a medium egg for the Sobe™ bottle. An extra-large egg gets wedged in the bottle.

Perform the Demonstration

* Method 1: Set a piece of paper on fire and drop it into the bottle. Set the egg on top of the bottle (small side pointed downward). When the flame goes out, the egg will get pushed into the bottle.
* Method 2: Set the egg on the bottle. Run the bottle under very hot tap water. Warmed air will escape around the egg. Set the bottle on the counter. As it cools, the egg will be pushed into the bottle.
* Method 3: Set the egg on the bottle. Immerse the bottle in a very cold liquid. I have heard of this being done using liquid nitrogen, but that sounds dangerous (could shatter the glass). I recommend trying ice water. The egg is pushed in as the air inside the bottle is chilled.

How It Works

If you just set the egg on the bottle, its diameter is too large for it to slip inside. The pressure of the air inside and outside of the bottle is the same, so the only force that would cause the egg to enter the bottle is gravity. Gravity isn't sufficient to pull the egg inside the bottle.

When you change the temperature of the air inside the bottle, you change the pressure of the air inside the bottle. If you have a constant volume of air and heat it, the pressure of the air increases. If you cool the air, the pressure decreases. If you can lower the pressure inside the bottle enough, the air pressure outside the bottle will push the egg into the container.

It's easy to see how the pressure changes when you chill the bottle, but why is the egg pushed into the bottle when heat is applied? When you drop burning paper into the bottle, the paper will burn until the oxygen is consumed (or the paper is consumed, whichever comes first). Combustion heats the air in the bottle, increasing the air pressure. The heated air pushes the egg out of the way, making it appear to jump on the mouth of the bottle. As the air cools, the egg settles down and seals the mouth of the bottle. Now there is less air in the bottle than when you started, so it exerts less pressure. When the temperature inside and outside the bottle is the same, there is enough positive pressure outside the bottle to push the egg inside.

Heating the bottle produces the same result (and may be easier to do if you can't keep the paper burning long enough to put the egg on the bottle). The bottle and the air are heated. Hot air escapes from the bottle until the pressure both inside and outside the bottle is the same. As the bottle and air inside continue to cool, a pressure gradient builds, so the egg is pushed into the bottle.

How to Get the Egg Out

You can get the egg out by increasing the pressure inside the bottle so that it is higher than the pressure of the air outside of the bottle. Roll the egg around so it is situated with the small end resting in the mouth of the bottle. Tilt the bottle just enough so you can blow air inside the bottle. Roll the egg over the opening before you take your mouth away. Hold the bottle upside down and watch the egg 'fall' out of the bottle. Alternatively, you can apply negative pressure to the bottle by sucking the air out, but then you risk choking on an egg, so that's not a good plan.