Basics 6--page 1 Basics 6: Solutions
Basics 6--page 2 Solutions: A Reprise A solution is a homogeneous mixture of 2 or more pure substances. What makes a mixture homogeneous/ We understand that the word homogeneous implies uniformity, but what precisely do we mean by this? What makes something uniform, and how do we tell? For example, from a distance, a picture printed on an ink jet printer may appear to have an area that is colored uniformly red. Yet, when we look at it up close, we find that it is, in reality, composed of many dots of red color. Is the picture uniformly red? Apparently not. In the same sense, a mixture is considered to be uniform only if its composition is uniform no matter how microscopically we view it. If you look at a rock, it is pretty easy to see that it is a heterogeneous mixture of many different minerals...you can see small differently colored areas that indicate this in most rocks. On the other hand, a bottle of milk appears to be uniform. It turns out, however, that it is not...if looked at closely enough, it turns out that milk consists of tiny globules of fat and protein suspended in water. If you dissolve salt in water, however, you get an even distribution of salt in water no matter how closely you look at the solution...up to a limit...that limit is the limit of the separate atoms and ions that make up that solution. In other words, when we say "uniformity" we mean uniformity down to the smallest possible subunit...this smallest subunit being an atom, ion, or molecule, depending on what substances are mixed together to form the solution. So when we say that a homogeneous mixture is one that is uniform in composition no matter how closely you look at it, we have to include one very important proviso, and that is that we mean "no matter how closely you look at it down to the inherent limitations in the atomic/molecular structure of matter". Most of the chemistry that occurs in the human body occurs in aqueous solution. This means that one of the solution components is water. In general, we refer to the component of a solution which is in excess as the solvent, and the substances that are dispersed in it as solutes. Thus, in an aqueous saline solution (salt water), the solvent is water, and sodium chloride is the solute. Solutions can be quite complex containing many components. For example, during heart surgery, it is common to administer an aqueous solution (water is the solvent) containing the following solutes: potassium chloride, sodium chloride, insulin and glucose.
Basics 6--page 3 Obviously the concentration of a solution is going to be critical in determining its chemical and biological effects. A dilute (5%) solution of acetic acid in water is called vinegar, and is consumed as food. A more concentrated solution (say 50%) would lead to burns and tissue damage in the mouth, esophagus and stomach. Solutions: Molarity If 1 mole of a substance is dissolved in a solvent so that the volume of the entire solution is 1 liter, the the solution is said to be 1 molar in that solute. If 2 moles are dissolve in 1 liter of solution, then the solution is 2 molar. If 1 mole of solute is dissolved in 2 liters of solution, then that solution is said to be 0.5 molar in that solute. Can you infer the general definition of Molarity from this information? The Molarity of a solute is the number of moles of solute contained in each liter of a solution. This means that, to find the Molarity of any solution, we need to find (or know) the number of moles of solute and the number of liters of solution that contains it, and then divide the number of moles of solute by the number of liters of solution. Thus if we knew that we had 20 grams of NaOH dissolved in a two liters of solution, we could easily calculate the molarity. We know that the formula weight of NaOH is 40 grams (if you don't know this, then get your periodic table out and add up the atomic masses to find the FW right now). This means that 20 grams corresponds to 1/2 of a mole of NaOH dissolved in 2 liters of solution. To find the molarity, we would simply divide 0.5 moles by 2 liters. The answer is that we have a 0.25 Molar solution, which is often written as 0.25M. We can summarize the relationships between Molarity, number of moles, and volume in the algebraic definition of molarity:
Basics 6--page 4 In the above box, we have written out the definition in words, and then condensed it to the familiar algebraic form that is used in scientific textbooks and research papers. As we learned in the algebra pages, we can express the relationships between these three variables in three ways, enabling us to solve for any one of these quantities if the other two are known. In the next few pages, we will present examples of numerical calculations which illustrate the uses of these equations. But we remind you that your core objective is NOT to learn how to perform calculations; it is to understand the meaning of
Basics 6--page 5 concentration, and the methods people use to calculate it and the uses to which it can be put. So please be sure that you can follow the logic of these calculations, but keep your conceptual objectives in mind,. Molarity is a measure of how concentrated a solute is, and, indirectly, of how chemically effective a solution is likely to be. Concentration and volume can be used to determine the dose of solute that is contained in a given volume of solution. Concentration can be used to determine the volume of a solution needed to deliver a given dosage of solute. Concentration is a property of an entire sample of a solution. If you know the concentration of a 2 liter bottle of a solution, this will be the concentration of any portion of that solution, no matter how small, that you use. Concentration and amount are not the same. A dilute solution may contain a great deal of solute if the amount of solution is large enough, and, conversely, a small amount of a concentrated solution will not contain much solute--but it is still concentrated. An interesting illustration of this last point is in the area of treatment for poisoning. The advice for many instances of ingestion of toxic substances,especially when they are water soluble, is to immediately drink large amounts of water. The reason for this is that absorption by the body depends strongly on concentration. Sometimes a poison can be rendered ineffective simply by reducing its concentration (i.e., by diluting it). Flushing chemicals from our skin and eyes also utilizes this phenomenon. The purpose of an eye wash station in the lab is to dilute any chemical that may have entered the eye, and then to wash this dilute solution away with the flowing water of the eyewash. How to Calculate Molarity How to calculate molarity. Here are some examples: If I add 43.87 grams of NaCl to a flask and then dilute this with water to 500 ml, what is the molarity?
Basics 6--page 6 500 ml = 1/2 liter. You try this one: If I dilute 81.10 grams of iron (III) chloride to 750 ml, what is the molarity? The answer to be found in the next section.
Basics 6--page 7 Answer for Calculating Molarity If I dilute 81.10 grams of iron (III) chloride to 750 ml, what is the molarity? Molarity: Calculating the Number of Moles How many grams of Na 2 SO 4 are in 5.5 liters of 0.1 Molar Solution? Strategy: first use the molarity formula to calculate the number of moles, then use the result to find the number of grams.
Basics 6--page 8 The molecular weight of Na 2 SO 4 is... So we have... You try: How many grams of sodium sulfide will be needed to prepare 4 liters of 0.5 molar solution? See the next section for the solution.
Basics 6--page 9 Answer: Calculating the Number of Moles How many grams of sodium sulfide will be needed to prepare 4 liters of 0.5 molar solution? The molecular weight of Na 2 S is... So we have...
Basics 6--page 10 Molarity: Calculating the Volume To what volume should I dilute 3.09 g of KOH so that I will get a 0.1 M solution? You try: to what volume should I dilute 3 grams of sodium hydride (NaOH) to obtain a 0.5 M solution? See the next section for the solution.
Basics 6--page 11 Answer: Calculating the Volume To what volume should I dilute 3 grams of sodium hydride (NaOH) to obtain a 0.5 M solution? Solution Dilution We can make concentrated stock solution into a more dilute solution by diluting with water. Usually we have a final target in mind. "I want so many ml of such and such molarity...how much of the concentrated stuff do I need?" The key to understanding this is to recognize that the moles of solute doesn't change during dilution. If we take some of solution 1 (to gain a name) and dilute it...let us denote the dilute solution by calling it solution 2.
Basics 6--page 12 Then... However---- Why? n 1 =n 2 because we have only added water...no solute...in diluting solution 1. So... Let's make this more concrete. I want to prepare 5 liters of 0.3 M HCl. My starting material is stock, off-the-shelf, 12 M HCl. What should I do?
Basics 6--page 13 The idea is this. We label our starting solution as solution "1", and our final (desired) solution as solution "2". We want to know exactly how much of "1" (the concentrated stuff) we need to make, in this case, 5 liters of "2" (the dilute stuff). Thinking this way, allows us to assign specific values to the variables in our molarity equation. Remember, this equation only works when you are only adding water. If we were adding (or removing) HCl, the equation would not be applicable. It assumes the number of moles of HCl stays the same throughout our process of diluting the solution. The answer tells us that, if we want to make 5 liters of 0.3M HCl, we should take 125 ml of 12 M HCl and dilute it with water to 5 liters. Now You try this: How much 5M KOH do I need to make 2 liters of 0.25 M KOH? See the next section for the answer
Basics 6--page 14 Dilution Answer How much 5M KOH do I need to make 2 liters of 0.25 M KOH?
Basics 6--page 15 Per Cent by Mass There is another concentration measure that is worth mentioning, mass per cent. The mass per cent is simply the mass of one component, divided by the mass of the entire solution, with the whole ratio multiplied by 100 to convert it to a percent. We can illustrate the use of this definition by means of a simple example. Suppose 50 grams of sodium chloride is dissolved in 500ml of water? What is the mass per cent of this solution in NaCl. Since the density of water is close to 1g/ml, we immediately conclude that we have 500g of water. The mass per cent is then calculated as shown below: