Stoichiometry is the accounting, or math, behind chemistry. Given enough information, one deserve to use stoichiometry to calculate masses, moles, and also percents within a chemical equation.

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What is a chemistry EquationThe MoleBalancing chemical EquationsLimiting ReagentsPercent CompositionEmpirical and Molecular FormulasDensityConcentrations the Solutions

## What is a chemistry equation?

In chemistry, us use signs to stand for the various chemicals. Successin chemistry depends upon emerging a solid familiarity v these an easy symbols. Because that example, the symbol "C"represents one atom that carbon, and "H" represents an atom that hydrogen. To represent a molecule the table salt, salt chloride, we would usage the notation "NaCl", where "Na" represents sodium and "Cl" to represent chlorine. We call chlorine "chloride" in this case since of its link to sodium. Girlfriend will have actually a chance to evaluation naming schemes, or nomenclature
, in a later on reading.A chemistry equation is one expression the a chemical process. Because that example:AgNO3(aq) + NaCl(aq) ---> AgCl (s) + NaNO3(aq)In this equation, AgNO3 is blended with NaCl. The equation reflects that the reactants (AgNO3 and also NaCl) react through some process (--->) to kind the commodities (AgCl and also NaNO3). Due to the fact that they undergo a chemistry process, castle are changed fundamentally. Frequently chemical equations room written mirroring the state the each substance is in. The (s) sign way that the link is a solid. The (l) sign means the problem is a liquid. The (aq) authorize stands for aqueous in water and method the compound is liquified in water. Finally, the (g) sign method that the compound is a gas. Coefficients are used in all chemical equations to present the relative amounts of each substance present. This amount deserve to represent either the relative variety of molecules, or the relative number of moles (described below). If no coefficient is shown, a one (1) is assumed. On part occasions, a variety of information will it is in written above or listed below the arrows. This information, such as a worth for temperature, present what problems need come be current for a reaction to occur. Because that example, in the graphic below, the notation over and below the arrows shows that we require a chemical Fe2O3, a temperature the 1000 levels C, and a press of 500 atmospheres for this reaction come occur.The graphic listed below works to capture most the the principles described above: ## The Mole

Given the equation above, we can tell the variety of moles that reactants and products. A mole just represents Avogadro"s number (6.023 x 1023) of molecules. A mole is comparable to a term like a dozen. If you have actually a dozen carrots, you have twelve of them. Similarily, if you have actually a mole the carrots, you have actually 6.023 x 1023 carrots. In the equation above there are no numbers in prior of the terms, so each coefficient is presume to be one (1). Thus, you have actually the same variety of moles the AgNO3, NaCl, AgCl, NaNO3.Converting between moles and also grams the a problem is often important.This conversion can be quickly done when the atomic and/or molecularweights of the substance(s) are known. The atomic or molecularweight of a problem in grams provides up one mole of the substance.For example, calcium has actually an atomic load of 40 grams. So, 40grams that calcium makes one mole, 80 grams provides two moles, etc.

## Balancing chemistry Equations

Sometimes, however, we have to do part work before using the coefficients the the state to stand for the relative number of molecules of each compound. This is the situation when the equations are not effectively balanced. We will think about the following equation:Al + Fe3O4---> Al2O3Since no coefficients are in front of any of the terms, that is basic to assume the one (1) mole of Al and one (1) mole of Fe304 react to form one (1) mole that Al203. If this to be the case, the reaction would be quite spectacular: an aluminum atom would show up out the nowhere, and also two (2) stole atoms and also one (1) oxygen atom would magically disappear. We recognize from the legislation of conservation of fixed (which states that matter can neither be developed nor destroyed) that this simply cannot occur. We need to make certain that the number of atoms that each details element in the reactants amounts to the number of atoms of the same element in the products. To do this we have to figure out the relative number of molecules of every term expressed by the term"s coefficient.Balancing a chemical equation is basically done through trial and also error. Over there are many different ways and systems of act this, yet for every methods, it is necessary to know exactly how to counting the number of atoms in one equation. For example we will look in ~ the following term.2Fe3O4This hatchet expresses two (2) molecules of Fe3O4. In every molecule that this substance there room three (3) Fe atoms. Thus in 2 (2) molecule of the substance there have to be six (6) Fe atoms. An in similar way there are 4 (4) oxygen atom in one (1) molecule the the substance so there have to be eight (8) oxygen atoms in two (2) molecules. Now let"s shot balancing the equation discussed earlier:Al + Fe3O4---> Al2O3+ Fe emerging a strategy can be difficult, but here is one way of approaching a difficulty like this. count the number of each atom ~ above the reactant and also on the product side. Identify a term to balance first. As soon as looking in ~ this problem it shows up that the oxygen will certainly be the most difficult to balance so we"ll shot to balance the oxygen first. The simplist method to balance the oxygen state is:Al +3 Fe3O4---> 4Al2O3+Fe it is crucial that you never readjust a subscript. Only adjust the coefficient as soon as balancing an equation. Also, be sure to notice that the subscript time the coefficient will give the number of atoms of that element. On the reactant side, we have a coefficient of three (3) multiply by a subscript of 4 (4), providing 12 oxygen atoms. On the product side, we have a coefficient of four (4) multiplied by a subscript of 3 (3), offering 12 oxygen atoms. Now, the oxygens room balanced. Choose one more term to balance. We"ll choose iron, Fe. Since there space nine (9) iron atom in the ax in i beg your pardon the oxygen is balanced we include a nine (9) coefficient in prior of the Fe. We currently have:Al +3 Fe3O4---> 4Al2O3+9Fe Balance the critical term. In this case, because we had eight (8) aluminum atom on the product side we need to have eight (8) top top the reactant next 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

## Limiting Reagents

Sometimes when reactions occur in between two or an ext substances, onereactant operation out before the other. That is dubbed the "limitingreagent." Often, that is important to identify the limiting reagent in a problem. Example: A chemist only has 6.0 grams the C2H2 and also an unlimitted it is provided of oxygen and also desires to create as much CO2 together possible. If she offers the equation below, exactly how much oxygen must she add to the reaction?2C2H2(g) + 5O2(g) ---> 4CO2(g) + 2 H2O(l) To settle this problem, that is vital to determine just how much oxygen shouldbe added if every one of the reaction were provided up (this is the means to produce the maximum lot of CO2). First, we calculate the variety of moles that C2H2 in 6.0 grams that C2H2. To have the ability to calculate the moles we need to look in ~ a regular table and see the 1 mole that C weighs 12.0 grams and also H weighs 1.0 gram. Therefore we recognize that 1 mole that C2H2 weighs 26 grams (2*12 grams + 2*1 gram). Because we only have actually 6.0 grams the C2H2 we must find out what fraction of a mole 6.0 grams is. To perform this, we use the following equation. Then, due to the fact that there are five (5) molecule of oxygen to every 2 (2) molecules of C2H2, we should multiply the moles of C2H2 by 5/2 to gain the total moles that oxygen that would certainly be supplied to react through all the C2H2. We then transform the mole of oxygen come grams in stimulate to find the amount of oxygen that needs to it is in added: ## Percent Composition

It is possible to calculate the mole ratios (also called mole fractions) between terms in a chemistry equation when provided the percent by fixed of products or reactants. Percent by massive = massive of part/ massive of wholeThere space two types of percent ingredient problems-- problems in which you are given the formula (or the weight of every part) and asked to calculation the percentage of every elementand troubles in which you are provided the percentages and asked to calculate the formula.In percent ingredient problems, there room many possible solutions. It is always possible to dual the answer. Because that example, CH and C2H2 have the exact same proportions, but they are various compounds. The is typical to offer compounds in their most basic form, where the ratio in between the facets is asreduced as it can be-- called the empirical formula. Once calculating the empirical formula indigenous percent composition, one can transform the percentages to grams. Because that example, that is generally the most basic to i think you have 100 grams therefore 54.3% would become 54.3 grams. Then we can convert the masses to mole which gives us mole ratios. The is vital to alleviate to whole numbers. A good technique is to divide all the state by the smallest variety of moles. Climate the ratio of the moles deserve to be transfered to write the empirical formula.Example: If a compound is 47.3% C (carbon), 10.6% H (hydrogen) and also 42.0% S (sulfur), what is that is empirical formula? To do this trouble we have to transfer all of our percents to masses. Us assume that we have actually 100 g the this substance. Then we convert to moles: Now we shot to obtain an even ratio in between the aspects so we divide by the variety of moles of sulfur, since it is the smallest number: So us have: C3H8 SExample: figure out the portion by massive of hydrogen sulfate, H2SO4.In this problem we need to very first calculate the full weight that the compound by looking at the routine table. This provides us:(2(1.008) + 32.07 + 4(16.00) grams/mol = 98.09 g/mol Now, we have to take the weight fraction of each aspect over the complete mass (which we just found) and also multiply by 100 to obtain a percentage. Now, we can examine that the percentages add up to 100% 65.2 + 2.06 + 32.7 = 99.96This is essentially 100 so we recognize that everything has worked, and we probably have actually not made any type of careless errors. therefore the price is that H2SO4 is comprised of 2.06% H, 32.7% S, and also 65.2% O through mass.

## Empirical Formula and also Molecular Formula

While the empirical formula is the simplest form of a compound, themolecular formula is the kind of the term as it would appear in a chemicalequation. The empirical formula and the molecule formula deserve to be thesame, or the molecule formula deserve to be any kind of multiple the the empiricalformula.Examples that empirical formulas: AgBr, Na2S, C6H10O5. Instances of molecule formulas: P2, C2O4, C6H14S2, H2, C3H9.One can calculate the empirical formula native the masses or percent composition of any compound. We have already discussed percent composition in the ar above. If us only have mass, every we space doing is essentially eliminating the step of convertingfrom percentage to mass. Example: calculate the empirical formula for a compound that has 43.7 g p (phosphorus) and also 56.3 grams that oxygen.First we transform to moles: Next we division the mole to shot to get a even ratio. When we divide, us did no get entirety numbers therefore we have to multiply by two (2). The answer=P2O5Calculating the molecular formula when we have the empirical formula is easy. If we understand the empirical formula that a compound, all we need to do is divide the molecular mass that the link by the fixed of the empirical formula.It is also possible to perform this with one of the elements in the formula;simply division the mass of that facet in one mole of compound by the massof that facet in the empirical formula. The result should always be awhole number. Example: if we recognize that the empirical formula the a compound is HCN and we are told that a 2.016 grams that hydrogen room necesary to make the compound, what is the molecule formula? In the empirical formula hydrogen weighs 1.008 grams. Dividing 2.016 by 1.008 we see that the amount of hydrogen necessary is twice as much. Because of this the empirical formula demands to be enhanced by a aspect of 2 (2). The prize is: H2C2N2.

## Density

Densityrefers come the mass every unit volume of a substance. It is a really commonterm in chemistry.

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## Concentrations the Solutions

The concentration that a equipment is the "strength" the a solution. A solution commonly refers come the dissolve of part solid substance in a liquid, such together dissolving salt in water. It is likewise often necessary to figure out how much water to add to a equipment to readjust it to a certain concentration. The concentration of a solution is typically given in molarity.Molarity is defined as the number of moles that solute (what is actually dissolved in the solution) separated by the liters of equipment (the full volume that what is dissolved and also what it has been dissolved in). Molarity is more than likely the most frequently used term since measuring a volume of fluid is a fairly easy thing to do.Example: If 5.00 grams the NaOH are dissolved in 5000 mL the water, what is the molarity of the solution?One the our very first steps is to convert the amount of NaOH offered in grams right into moles: Now we simply use the definition of molarity: moles/liters to acquire the answer So the molarity (M) the the equipment is 0.025 mol/L.Molality is one more common measure up of concentration. Molality is defined as moles of solute divided by kilograms that solvent (the problem in which it is dissolved, choose water). Molality is occasionally used in ar of molarity at extreme temperatures since the volume deserve to contract or expand. Example: If the molality that a systems of C2H5OH dissolved in water is 1.5 and the load of the water is 11.7 kg, number out how much C2H5OH must have been included in grams come the solution? Our very first step is to instead of what us know into the equation. Then we shot to deal with for what us don"t know: moles of solute. Once we know the mole of solute we can look at the regular table and figure out the counter from moles to grams. It is possible to convert in between molarity and also molality. The only information needed is density.Example: If the molarity of a equipment is 0.30 M, calculate the molalityof the solution discovering that the thickness is 3.25 g/mL.To do this problem we have the right to assume one (1) liter of systems to do thenumbers easier. We require to acquire from the molarity units of mols/Liter tothe molality systems of mols/kg. We job-related the problem as follows,remembering the there space 1000 mL in a Liter and 1000 grams in a kg. Thisconversion will only be exact at small molarities and molalities. It is also feasible to calculate colligative properties, such together boiling suggest depression, using molality. The equation for temperature depression or expansion is adjust in T= K * mWhere:T is temperature depression (for freezing point) or temperature development (for cook point) (°C)K is the freezing point continuous (kg °C/moles)m is molality in moles/kgExample: If the freezing suggest of the salt water placed on roadways is -5.2 C, what is the molality the the solution? (The Kf for water is 1.86 C/m.) This is a basic problem where we simply plug in numbers right into the equation. One item of details we do have to know is that water commonly freezes in ~ 00C. T=K * m T/K= mm = 5.2/1.86m = 2.8 mols/kg

## Practice Problems

1. If only 0.25 molar NaOH and water room available, exactly how much NaOH demands to be added to do 10 liters that 0.2 molar equipment of NaOH? check your work2. If 2.0 mole of sucrose weighing 684 grams is put in 1000 grams that water and also is climate dissolved, what would certainly be the molality the the solution?Check your work. 3. If you have a 0.25 molar systems of benzene with a density of 15 grams/liter, calculate the molality that the solution. Check your work4. If the density of mercury is 13.534 g/cm2 and also you have actually 62.5 cm3 the mercury, how plenty of grams, moles, and also atoms that mercury carry out you have? (Mercury has actually a mass of 200.6 g/mol.) inspect your occupational developed by 