Concentration is a fundamental concept representing how much of one substance is contained within another. This measurement applies to a solution, which is a uniform mixture created when a solute dissolves completely into a solvent.
The solute is typically the substance present in the smaller amount, while the solvent is the substance present in the largest amount that does the dissolving. For example, when mixing sugar into water, the sugar is the solute and the water is the solvent. Concentration is a quantitative measure of the amount of solute dissolved in a given amount of solution or solvent.
Calculating Concentration Using Percentages and Ratios
The most intuitive way to express concentration uses percentages and ratios, comparing the amount of solute to the total solution. These methods are frequently used on product labels and in non-scientific settings.
Mass percent (\(\% m/m\)) is calculated by dividing the mass of the solute by the total mass of the solution and multiplying by 100. This requires both the solute and the solution to be measured using the same mass unit. Volume percent (\(\% v/v\)) is used when both the solute and the solvent are liquids, such as alcohol in water. It is calculated by dividing the volume of the solute by the total volume of the solution and multiplying by 100.
A third common expression is mass/volume percent (\(\% m/v\)), which divides the mass of the solute (in grams) by the volume of the solution (in milliliters) and then multiplies by 100. This ratio is useful when a solid is dissolved in a liquid, common in laboratory and pharmaceutical preparations.
For extremely dilute solutions, such as monitoring trace contaminants, parts per million (PPM) and parts per billion (PPB) are used. These are extensions of percentage calculation, representing a ratio of parts of solute to one million or one billion parts of the total solution. The PPM value is calculated by dividing the mass or volume of the solute by the total mass or volume of the solution and then multiplying the result by \(10^6\). Similarly, PPB involves multiplying the solute-to-solution ratio by \(10^9\).
Understanding Molarity and Mole Calculations
In scientific and laboratory settings, the standard unit of concentration is molarity (\(M\)). Molarity is defined as the number of moles of solute per liter of the solution, calculated using the formula \(M = \text{moles of solute} / \text{liters of solution}\). This unit is preferred because it relates directly to the number of particles involved in a chemical reaction.
To use molarity, one must understand the concept of a mole, which is a way of counting a specific, large number of particles. One mole of any substance contains approximately \(6.022 \times 10^{23}\) particles, known as Avogadro’s number.
The number of moles of a substance is calculated by dividing its mass in grams by its molar mass. Molar mass is the mass of one mole of that substance, found by summing the atomic masses of all the atoms in the compound’s chemical formula. For instance, to find the molar mass of table salt (\(\text{NaCl}\)), you add the atomic mass of sodium (Na) to the atomic mass of chlorine (Cl). Once the mass is converted into moles, this value is divided by the volume of the solution in liters to find the molarity.
Preparing Solutions of Known Concentration
Preparing a solution with a precise, known concentration requires a careful, sequential process. This process begins with calculating the required mass of solute based on the desired molarity and final volume. The calculated mass of the solid solute must be weighed out precisely, typically using an analytical balance.
The weighed solute is transferred to a beaker and dissolved completely in a small amount of the solvent. The liquid solution is then carefully transferred into a specialized piece of glassware called a volumetric flask. A volumetric flask is calibrated to hold one specific, exact volume, making it the preferred tool for high-precision preparation.
The beaker and transfer equipment are thoroughly rinsed multiple times with small volumes of solvent to ensure all solute is moved into the flask. The flask is then filled with solvent until the liquid level is close to the etched calibration mark. Finally, the last few drops of solvent are added carefully until the bottom of the meniscus rests exactly on the calibration line, ensuring the solution reaches its intended volume.