Calculating Concentrations with Units and Dilutions

Calculating Concentrations with Units and Dilutions Calculating the concentration of a chemical  solution  is a basic skill all students of chemistry must develop early in their studies. What is concentration? Concentration refers to the amount of solute that is dissolved in a solvent. We normally think of a solute as a solid that is added to a solvent (e.g., adding table salt to water), but the solute could easily exist in another phase. For example, if we add a small amount of ethanol to water, then the ethanol is the solute, and the water is the solvent. If we add a smaller amount of water to a larger amount of ethanol, then the water could be the solute! How To Calculate Units of Concentration Once you have identified the solute and solvent in a solution, you are ready to determine its concentration. Concentration may be expressed several different ways, using percent composition by mass, volume percent, mole fraction, molarity, molality, or normality. Percent Composition by Mass (%)This is the mass of the solute divided by the mass of the solution (mass of solute plus mass of solvent), multiplied by 100.Example:Determine the percent composition by mass of a 100 g salt solution which contains 20 g salt.Solution:20 g NaCl / 100 g solution x 100 20% NaCl solutionVolume Percent (% v/v) Volume percent or volume/volume percent most often is used when preparing solutions of liquids. Volume percent is defined as:v/v % [(volume of solute)/(volume of solution)] x 100%Note that volume percent is relative to the volume of the solution, not the volume of solvent. For example, wine is about 12% v/v ethanol. This means there is 12 ml ethanol for every 100 ml of wine. It is important to realize liquid and gas volumes are not necessarily additive. If you mix 12 ml of ethanol and 100 ml of wine, you will get less than 112 ml of solution.As another example, 70% v/v rubbing alcohol may be prepared by taking 700 ml of isopropyl alcohol and adding su fficient water to obtain 1000 ml of solution (which will not be 300 ml). Mole Fraction (X) This is the number of moles of a compound divided by the total number of moles of all chemical species in the solution. Keep in mind, the sum of all mole fractions in a solution always equals 1.Example:What are the mole fractions of the components of the solution formed when 92 g glycerol is mixed with 90 g water? (molecular weight water 18; molecular weight of glycerol 92)Solution:90 g water 90 g x 1 mol / 18 g 5 mol water92 g glycerol 92 g x 1 mol / 92 g 1 mol glyceroltotal mol 5 1 6 molxwater 5 mol / 6 mol 0.833x glycerol 1 mol / 6 mol 0.167Its a good idea to check your math by making sure the mole fractions add up to 1:xwater xglycerol .833 0.167 1.000Molarity (M) Molarity is probably the most commonly used unit of concentration. It is the number of moles of solute per liter of solution (not necessarily the same as the volume of solvent!).Example:What is the molarity of a solution made when water is added to 11 g CaCl2 to make 100 mL of solution ? (The molecular weight of CaCl2 110)Solution:11 g CaCl2 / (110 g CaCl2 / mol CaCl2) 0.10 mol CaCl2100 mL x 1 L / 1000 mL 0.10 Lmolarity 0.10 mol / 0.10 Lmolarity 1.0 M Molality (m) Molality is the number of moles of solute per kilogram of solvent. Because the density of water at 25 °C is about 1 kilogram per liter, molality is approximately equal to molarity for dilute aqueous solutions at this temperature. This is a useful approximation, but remember that it is only an approximation and doesnt apply when the solution is at a different temperature, isnt dilute, or uses a solvent other than water.Example:What is the molality of a solution of 10 g NaOH in 500 g water? (Molecular weight of NaOH is 40)Solution:10 g NaOH / (40 g NaOH / 1 mol NaOH) 0.25 mol NaOH500 g water x 1 kg / 1000 g 0.50 kg watermolality 0.25 mol / 0.50 kgmolality 0.05 M / kgmolality 0.50 mNormality (N) Normality is equal to the gram equivalent weight of a solute per liter of solution. A gram equivalent weight or equivalent is a measure of the reactive capacity of a given molecule. Normality is the only concentration unit that is reaction dependent.Example:1 M sulfuric acid (H2SO4) is 2 N for acid-base reactions because each mole of sulfuric acid provides 2 moles of H ions. On the other hand, 1 M sulfuric acid is 1 N for sulfate precipitation, since 1 mole of sulfuric acid provides 1 mole of sulfate ions. Grams per Liter (g/L)This is a simple method of preparing a solution based on grams of solute per liter of solution.Formality (F)A formal solution is expressed regarding formula weight units per liter of solution.Parts per Million (ppm) and Parts per Billion (ppb)Used for extremely dilute solutions, these units express the ratio of parts of solute per either 1 million parts of the solution or 1 billion parts of a solution.Example:A sample of water is found to contain 2 ppm lead. This means that for every million parts, two of them are lead. So, in a one gram sample of water, two-millionths of a gram would be lead. For aqueous solutions, the density of water is assumed to be 1.00 g/ml for these units of concentration. How To Calculate Dilutions You dilute a solution whenever you add solvent to a solution. Adding solvent results in a solution of lower concentration. You can calculate the concentration of a solution following a dilution by applying this equation: MiVi MfVf where M is molarity, V is volume, and the subscripts i and f refer to the initial and final values. Example:How many milliliters of 5.5 M NaOH are needed to prepare 300 mL of 1.2 M NaOH? Solution:5.5 M x V1 1.2 M x 0.3 LV1 1.2 M x 0.3 L / 5.5 MV1 0.065 LV1 65 mL So, to prepare the 1.2 M NaOH solution, you pour 65 mL of 5.5 M NaOH into your container and add water to get 300 mL final volume

Spanish Phrases and Idioms Using ‘Ojo’

Spanish Phrases and Idioms Using ‘Ojo’ Sight is one of the most important senses, the one most of us use most to learn whats happening around us. So it shouldnt be surprising that a number of phrases refer to the organ of sight. This is especially true in Spanish, which has over two dozen phrases using the word ojo. Following are some of the most common ones, along with some examples of their use. Many of the definitions below include a literal translations. These are word-for-word translations of the phrase rather than how the phrases would be used or understood by a native speaker. Spanish Phrases Referring to Eyes abrir/cerrar los ojos (to open/close ones eyes): Es un ejercicio que consiste en abrir y cerrar los ojos. (Its an exercise that consists of opening and closing the eyes.) ojo a la funerala, ojo a la virulà ©, ojo morado (bruised or black eye; literally ) ojos saltones (bulging eyes; literally eyes that jump) poner los ojos en blanco (to roll ones eyes; literally to make the eyes white): Cuando no saben de quà © hablar, ponen los ojos en blanco. (When they dont know what to say, they roll their eyes.) Names of Things Using Ojo ojo de buey (porthole; literally crabs eye or oxs eye) ojo de la cerradura (keyhole; literally eye of the lock) ojo de la escalera (stairwell; literally eye of the stairway) ojo de gallo (corn, a type of growth on a foot; literally roosters eye) ojo de pez (fish-eye lens; literally fishs eye) ojo de la tormenta (eye of the storm) Idioms Using Ojo abrir los ojos a alguien, abrirle los ojos a alguien (to open someones eyes): El curso me abrià ³ los ojos a cosas que nunca se me habà ­an ocurrido antes. (The course opened my eyes to things that never had occurred to me before.) a ojos vistas (in plain sight, clearly, obviously; vista comes from the past participle of ver, to see): Antonio progresaba a ojos vistas en todos los aspectos. (Antonio clearly progressed in all aspects.) andar con ojo, andar con mucho ojo, andar con cien ojos (to be careful; literally to walk with an eye, to walk with much eye, and to walk with 1,000 eyes): Anda con ojo con el coche. (Be careful with the car.) a ojo de buen cubero (by rule of thumb, approximately, roughly; literally by the eye of a good barrel maker): La capacidad de la bandeja de papel, a ojo de buen cubero, no supera las 150 hojas. (The capacity of a tray of paper, as a rule of thumb, doesnt exceed 150 sheets.) comerse con los ojos a alguien (to figuratively drool over someone, to stare at someone): Andrea se comà ­a con los ojos a mi amigo Luis. (Andrea drooled over my friend Luis.) costar algo un ojo de la cara (to cost an arm and a leg; literally to cost an eye of the face): Este perro le costà ³ un ojo de la cara. (That dog cost him an arm and a leg.)  ¡Dichosos los ojos que te ven! (How great it is to see you! Literally, happy the eyes that see you!) en un abrir y cerrar de ojos (in the twinkling of an eye; literally in the opening and closing of eyes): En un abrir y cerrar de ojos la vida nos cambià ³. (Life changed us in the twinkling of an eye.) mirar algo con buenos/malos ojos (to look at something favorably/unfavorably, to approve/disapprove of; literally to look at something with good/bad eyes): Esa religià ³n miraba con malos ojos la comunicacià ³n con los antepasados. (That religion looks unfavorably on communication with the dead.) no pegar ojo (to not get any sleep; literally to not seal the eye shut): Hace dos noches que no pegà ³Ã‚  ojo Antonio. (Two nights ago Antonio didnt sleep) poner los ojos a/en alguien/algo (to set ones sights on someone/something): Pinochet puso los ojos en Sudfrica. (Pinochet set his sights on South Africa.) ser todo ojos (to be all eyes): Martà ­n era todo ojos y todo oà ­dos para aprender. (Martin was all eyes and ears for learning.) tener ojo clà ­nico para algo (to be a good judge of something, to have a good eye for something; literally to have a clinical eye for something): No tiene ojo clà ­nico para elegir a quienes le acompaà ±an. (He doesnt have good judgment in picking who goes with him.) tener ojos de lince (to have extremely good eyesight, to have eagle eyes; literally to have the eyes of a lynx): Si tiene ojos de lince posiblemente pueda ver los pequeà ±os loros verdes. (If you can see really well, you might be able to see the small green parrots.) Proverbs and Sayings Ojo por ojo, diente por diente. (An eye for an eye, a tooth for a tooth.) Ojos que no ven, corazà ³n que no siente. (What the eye doesnt see, the heart doesnt feel.) Cuatro ojos ven ms que dos. (Two heads are better than one. Literally, four eyes are better than two.)  ¡Ojo! can also be used by itself as an interjection to mean Watch out! or Be careful!