Our equation for calculating the molarity of a diluted solution becomes:. The solution has been diluted by a factor of five, since the new volume is five times as great as the original volume. Consequently, the molarity is one-fifth of its original value.
Another common dilution problem involves deciding how much a highly concentrated solution is required to make a desired quantity of solution with a lower concentration. The highly concentrated solution is typically referred to as the stock solution. Concentration is important in healthcare because it is used in so many ways. It's also critical to use units with any values to ensure the correct dosage of medications or report levels of substances in blood, to name just two. Another way of looking at concentration such as in IV solutions and blood is in terms of equivalents.
One equivalent is equal to one mole of charge in an ion. The value of the equivalents is always positive regardless of the charge. Equivalents are used because the concentration of the charges is important than the identity of the solutes. For example, a standard IV solution does not contain the same solutes as blood but the concentration of charges is the same.
What mass of sodium did the patient receive? Note that if this problem had a different ion with a different charge, that would need to be accounted for in the calculation. Allison Soult , Ph. Department of Chemistry, University of Kentucky. Learning Outcomes Define concentration. Use the terms concentrated and dilute to describe the relative concentration of a solution. Calculate the molarity of a solution. Use concentration units in calculations. Determine equivalents for an ion.
Complete calculations relating equivalents to moles, volumes, or mass. Complete dilution calculations. There are approximately times as many moles of water as moles of acetic acid, so the ratio should be approximately 0. The concentration of a solution can also be described by its molality m , the number of moles of solute per kilogram of solvent:. Molality, therefore, has the same numerator as molarity the number of moles of solute but a different denominator kilogram of solvent rather than liter of solution.
For dilute aqueous solutions, the molality and molarity are nearly the same because dilute solutions are mostly solvent. Thus because the density of water under standard conditions is very close to 1. Another common way of describing concentration is as the ratio of the mass of the solute to the total mass of the solution.
The result can be expressed as mass percentage, parts per million ppm , or parts per billion ppb :. In the health sciences, the concentration of a solution is often expressed as parts per thousand ppt , indicated as a proportion. For example, adrenalin, the hormone produced in high-stress situations, is available in a solution, or one gram of adrenalin per g of solution.
The labels on bottles of commercial reagents often describe the contents in terms of mass percentage. Parts per million and parts per billion are used to describe concentrations of highly dilute solutions. These measurements correspond to milligrams and micrograms of solute per kilogram of solution, respectively. For dilute aqueous solutions, this is equal to milligrams and micrograms of solute per liter of solution assuming a density of 1. Several years ago, millions of bottles of mineral water were contaminated with benzene at ppm levels.
This incident received a great deal of attention because the lethal concentration of benzene in rats is 3. A mL sample of mineral water has Because the contaminated mineral water is a very dilute aqueous solution, we can assume that its density is approximately 1. Given : volume of sample, solute concentration, and density of solution.
Asked for : molarity of solute and mass of solute in mL. A To calculate the molarity of benzene, we need to determine the number of moles of benzene in 1 L of solution. We know that the solution contains Because The molarity is therefore. B We are given that there are Hence the mass of benzene in mL g of solution is. How do chemists decide which units of concentration to use for a particular application?
Although molarity is commonly used to express concentrations for reactions in solution or for titrations, it does have one drawback—molarity is the number of moles of solute divided by the volume of the solution, and the volume of a solution depends on its density, which is a function of temperature.
For many applications this may not be a problem, but for precise work these errors can become important. In contrast, mole fraction, molality, and mass percentage depend on only the masses of the solute and solvent, which are independent of temperature. Mole fraction is not very useful for experiments that involve quantitative reactions, but it is convenient for calculating the partial pressure of gases in mixtures, as discussed previously.
Mole fractions are also useful for calculating the vapor pressures of certain types of solutions. Molality is particularly useful for determining how properties such as the freezing or boiling point of a solution vary with solute concentration.
Because mass percentage and parts per million or billion are simply different ways of expressing the ratio of the mass of a solute to the mass of the solution, they enable us to express the concentration of a substance even when the molecular mass of the substance is unknown.
Units of ppb or ppm are also used to express very low concentrations, such as those of residual impurities in foods or of pollutants in environmental studies. The following formula is very useful, as it relates the molarity of the solution, the total volume of the solution in liters , and the number of moles solute:.
A student pipettes a mL sample of a 1. How many moles of potassium bromide are contained in the sample? You might notice that the above formula bears some resemblance to our dilution formula:. After all, in any dilution, what changes is the amount of solvent, while the number of moles of solute remains constant throughout.
Molarity Practice Problems — YouTube : This video demonstrates practice problems with molarity, calculating the moles and liters to find the molar concentration. It also uses conversion factors to convert between grams and moles and between milliliters and liters. This video looks at how to use molarity as a conversion factor.
If you know the molarity, you can solve for either the number of moles or the volume of a solution. Also, molarity is a ratio that describes the moles of solute per liter of solution. Stoichiometry can be used to calculate the quantitative relationships between species in aqueous solution.
Calculate concentrations of solutions in molarity, molality, mole fraction and percent by mass and volume. Recall that a solution consists of two components: solute the dissolved material and solvent the liquid in which the solute is dissolved. The amount of solute in a given amount of solution or solvent is known as the concentration. The two most common ways of expressing concentration are molarity and molality. The molar concentration M of a solution is defined as the number of moles of solute n per liter of solution i.
For example, the number of moles of NaCl in 0. The molal concentration m of a solution is defined as the number of moles of solute n per kilogram of solvent i.
For example, the number of moles of NaCl dissolved in 0. We can perform stoichiometric calculations for aqueous phase reactions just as we can for reactions in solid, liquid, or gas phases. Almost always, we will use the concentrations of the solutions as conversion factors in our calculations.
Crystals of silver chloride AgCl : Stoichiometry deals with the relative quantities of reactants and products in chemical reactions. It can be used to find the quantities of the products from given reactants in a balanced chemical reaction, as well as percent yield.
The next step, as in any calculation involving stoichiometry, is to determine our limiting reactant. We can do this by converting both of our reactants into moles:. Because there are fewer moles of NaCl present in solution, NaCl is our limiting reactant.
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