# Formulas and Equations

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## The Atom

Atoms are made up of protons, neutrons and electrons. Most of the mass of an atom is in the nucleus, where you find protons and neutrons. Electrons orbit the nucleus in orbitals, which take up most of the volume of the atom. Nuclear symbols show numbers of subatomic particles. The top number is the mass number, the number of protons and neutrons. The lower number is the number of protons in the element. The number of electrons is the same as the protons in an atom with no overall charge. Ions have different numbers of protons and electrons. Negative ions have more electrons than protons, whilst positive ions have more protons. Isotopes are atoms of the same element with different number of neutrons. Different mass numbers mean different numbers of neutrons. The atomic number is the same. Isotopes have virtually the same chemical properties due to same numbers of electrons, but their physical properties are slightly different because physical properties depend more on the mass of the atom.

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## Atoms and Moles

Relative masses are masses of atoms compared to carbon-12. The relative atomic mass is the average mass of an atom of an element on a scale where an atom of carbon-12 is 12. Relative isotopic mass is the mass of an atom of an isotope of an element on a scale where carbon-12 is 12. The relative molecular mass is the average mass of a molecule on a scale where an atom of carbon-12 is 12. A mole is just a (very large) number of particles. Amount of substance is measured using a unit called the mole (mol for short) and given the symbol n. One mole is roughly 6x10 to the power of 23 particles (The Avogadro constant, L). Number of moles = Number of particles you have divided by the number of particles in a mole. Molar mass is the mass of one mole. Molar mass is the same as the relative molecular mass, but measured in grams per mole. The mole is the number of particles for which the weight in grams is the same as the relative molecular mass. Number of moles = Mass of substance divided by molar mass. In a solution the concentration is measured in mols per decimetre cubed. Number of moles = concentration x volume in cm cubed divided by 1000 or simply concentration x volume in dm cubed. A solution that has more moles per dm cubed than another is more concentrated, and vice versa. For really low concentrations, you end up with tiny mols per dm cubed. Parts per million is used for really small quantities. E.g if there is 0.000009 parts of xenon in every 100 parts of air, then to calulate this in parts per million you multiply it all by 10000 to make the quantity large enough to work with. For xenon, this becomes 0.09 parts per million.

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## Empirical and Molecular Formulas

Empirical and Molecular formulas are ratios. The empirical formulas gives the smallest whole number ratio of atoms in a compound. The molecular formulas gives the actual number of atoms in a molecule. The molecular formula is made up of a whole number of empirical units. To work out molecular formula from an empirical formula and mass in g, you compare the empirical and molecular mass by working out the empirical mass and dividing the actual mass by the empirical mass. Empirical formulas are calculated from experiments. To work out the empirical formula from masses, you work out how many moles of the products you have using mass divided by molecular mass for each product, then work out the ratios of the reactants to one another and divide by the smallest number. For percentages, you work out how many moles of each element you have in 100g of compound by using moles = mass divided by molecular mass. Then divide each number of moles by the smallest number. If the measurements are wrong you could get the formula wrong. There is a limit to how accurate you can get. Molecular formulas are calculated from experimental data too. Once you know the empirical formula, you just need a bit more info and you can work out the molecular formula. E.g 4.6g of an alcohol with molar mass 46g is burnt in excess oxygen. It produces 8.8g of carbon dioxide and 5.4g of water. You first work out the empirical formula with mass divided by molecular mass for each product. Once you have the empirical formula, you compare the empirical and molecular masses, then divide molecular mass by empirical mass to give the formula.

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## Equations and Calculations

Balanced equations have equal numbers of each atom on both sides. You add more compounds by adding more numbers in front of a compound or changing one thats already there. You can't change the formula to balance it, ever. In ionic equations the charges must balance too. In ionic equations only the reacting particles are included. You balance it like a normal equation, then you check the charges balance. If not add electrons so the charges do balance. Balanced equations can be used to work out masses. E.g calculate the mass of iron produced if 28g of iron is burnt in air. You take the molar mass and use mass divided by molecular mass to work out the number of moles, in this case 0.5. From the equation, 2 moles of iron produces 1 mole of iron(II) oxide, so 0.5 moles of Fe produces 0.25 moles of iron(II) oxide. Then you take the molecular mass of iron(II) oxide and work out the mass, in this case 0.25x160 = 40g. That's not all... balanced equations can be used to work out gas volumes. If temperature and pressure stay the same, one mole of any gas has the same volume. At room temperature (298K) and pressure (101.3KPa) this happens to be 24 decimetres cubed. Number of moles = Volume in dm cubed divided by 24 or Volume in cm cubed divided by 24000. It's handy to be able to work out how much gas a reaction will produce, so that you can use large enough apparatus. Or else there might be a rather large bang. State symbols give a bit more information about the substances. State symbols tell you what state an element is in in a reaction where s=solid, g=gas, l=liquid and aq=aqueous (solution in water).

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## Confirming Equations

A balanced equation can be confirmed by experimental data. A balanced equation tells you how many moles of products you should expect from given amounts of reactants. You can check by doing a experiment to measure the amount of product you get, using measuring cylinders, balances or titrations. The experimental data is used to calculate the number of moles. To confirm the equation, you need to know how many moles of reactants and products there were. It's just a matter of using the right formulas. Use number of moles = mass of substance divided by molar mass or number of moles = volume in dm cubed divided by 1000 or volume in cm cubed divided by 24000. You can find out the number of moles of an alkali from the result of a titration. The accuracy of experimental data is always limited by the methods used. There are several problems that can cause the result to be inaccurate, such as unwanted reactions or oxidising, unwanted mass in a reactant, and gas escaping in the transferral of gas. These are systematic errors, and can be minimised, but the only way to remove them is to do a different method, which may have problems of its own. And the equipment used can affect it too. With all measurements there's a limit to the precision that is possible. For example a measuring cylinder has a limited number of markings to it. You usually have to estimate what the amount actually is. Errors by equipment are random errors and affect your result differently each time. There's no good having equipment that is precise but inaccurate. And there's always human error, that can be systematic (always reading above the true value) or random.

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## Making Salts

Salts can be hydrated. All solid salts consist of a lattice of positive and negative ions. In some salts, there is water molecules too. A solid salt with water in it is hydrated. The formula of a hydrated salt shows how many water molecules are in the lattice. A double salt contains two cation or two anions. If you mix two different solutions of two different salts and crystallise them you get a double salt with two cations or anions. But you can also prepare it from raw ingredients. Preparing a salt - Mix the right stuff, crystallise, filter. For example to prepare hydrated ammonium iron(II) sulfate from iron, ammonia and sulfuric acid, you add a known mass of iron filings to an excess of warm sulfuric acid and stir until they have all reacted. You now have iron(II) sulfate solution. Add just enough ammonia solution to react completely with the iron. Leave the solution to evaporate - blue-green crystals of the salt will from. Some solution will remain because you started with an excess of acid. Collect the crystals by filtering then wash them using distilled water. To dry the crystals press them between two pieces of filter paper to absorb as much water as possible. Percentage yield is never 100%. The theoretical yield is the mass of product that should be formed. It assumes no chemicals are lost in the process. You can use the masses of reactants and a balanced equation to calculate the theorectical yield. Once you have it, to work out percentage yield you divide your actual yield by the theoretical yield and multiply by 100.

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## Atom Economy and Percentage Yield

Atom economy is a measure of the efficiency of a reaction. The percentage yield can tell you how wasteful the process is, but doesn't tell how wasteful the reaction itself is. Atom economy is a measure of the proportion of reactant atoms that become part of the desired product (rather than by products) in the balanced chemical equation. %Atom economy = molecular mass of desired product divided by the sum of molecular masses of all products x 100. Addition reactions have a 100% atom economy, as they only have one product from two reactants. No atoms are wasted. Substitution reactions have a lower atom economy than addition reactions because in a substitution reaction some atoms from one reactant are swapped with another reactant, resulting in at least two products. A reaction can have a high percentage yield and a low atom economy. E.g 0.475g of bromomethane reacts with excess NaOH in this reaction: Bromomethane + sodium hydroxide makes methanol and sodium bromide. 0.153g of methanol is produced. The percentage yield works out to be 0.153 divided by 160 x 100 = 95.6%. but the atom economy is only 23.7%. It is important to develop reactions with high atom economies. Companies in the chemical industry will often choose to use reactions with high atom economies. Keeping atom economy as high as possible has environmental and economic benefits. A low atom economy means there's lots of waste product, which has to go somewhere. It costs money to seperate the desired product from the other products and more money to dispose of the waste products. If a large proportion of products are going to waste the reactants are being used inefficiently. This is costly to the company (who have to buy a lot of reactant to get the product). It also lowers the sustainability of the process.

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