君たちは化学が好きでしょうか? 僕は良い文章を見付けた。その文章は基本化学に教えているんだ,ストイキオメトリ。何か思い出すのか? 我々が中学にあった時, ストイキオメトリを勉強した でしょう. じゃあ, 読みましょう。。。 ^_^
Stoichiometry is branch of chemistry that deals with the quantitative relationships that exist among the reactants and products in chemical reactions. Given enough information, one can use stoichiometry to calculate masses, moles, and percents within a chemical equation.
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.
Limiting Reagents
Sometimes when reactions occur between two or more substances, one reactant runs out before the other. That is called the "limiting reagent". Often, it is necessary to identify the limiting reagent in a problem.
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.
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.
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.
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 . This is probably the most commonly used term because measuring a volume of liquid is a fairly easy thing to do.
| Molarity = | moles of solute liters of solution |
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.
| Molality = | moles solute kg solvent |
It is also possible to calculate colligative properties, such as boiling point depression, using molality. The equation for temperature depression or expansion is ΔT= Kf × m Where: ΔT is temperature depression (for freezing point) or temperature expansion (for boiling point) (°C) Kf is the freezing point constant (kg °C/mol) m is molality in mol/kg.
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