Molarity (M) serves as a fundamental measure of concentration in chemistry. This value indicates how much of a dissolved substance is present within a specific volume of liquid. Understanding molarity is necessary for chemists to accurately prepare solutions and control chemical reactions in a laboratory setting. Calculating this concentration requires a systematic approach that links the mass of a substance to the volume of the solution it creates.
Defining the Necessary Components
A solution is a homogeneous mixture formed when one substance dissolves completely into another. The two primary components are the solute, the substance that is dissolved, and the solvent, the dissolving medium, usually the component in the largest quantity.
The calculation of molarity relies on two specific measurements: the amount of solute and the total volume of the solution. The amount of solute must be expressed in moles (n), which is the standard unit for the amount of substance in chemistry.
The total volume of the final solution must be measured in liters (L). If the volume is initially measured in milliliters (mL), it must be converted to liters by dividing the milliliter value by 1,000. This ensures the final molarity value is expressed in the correct units of moles per liter (mol/L), abbreviated as M.
Determining the Moles of Solute
Before the final molarity calculation can be performed, the mass of the solute must be converted into the unit of moles. This conversion is achieved by using the substance’s molar mass, which is the mass in grams of one mole of that compound. The molar mass is determined by summing the atomic masses of all the individual atoms that constitute the chemical formula of the solute.
For instance, to find the molar mass of sodium chloride (NaCl), one would look up the atomic masses for sodium (Na) and chlorine (Cl) on the periodic table. The atomic mass of sodium is approximately \(22.99 \text{ g/mol}\), and chlorine is about \(35.45 \text{ g/mol}\), which sums to a molar mass of \(58.44 \text{ g/mol}\) for NaCl.
Once the molar mass is known, the number of moles (n) is calculated by dividing the measured mass (m) of the solute by its molar mass. The mathematical relationship is Moles (n) = Mass (g) / Molar Mass (g/mol).
Applying the Molarity Formula Step-by-Step
The final calculation for molarity (M) is determined by the quotient of the moles of solute (n) and the volume of the solution in liters (V). The formula is expressed simply as M = n / V.
Consider a practical example where \(5.85 \text{ g}\) of sodium chloride (NaCl) is dissolved to make a \(500 \text{ mL}\) solution.
Step 1: Convert Mass to Moles
The first step involves converting the mass of NaCl into moles using its molar mass of \(58.44 \text{ g/mol}\). Dividing the mass \(5.85 \text{ g}\) by the molar mass \(58.44 \text{ g/mol}\) yields approximately \(0.100 \text{ moles}\) of NaCl.
Step 2: Convert Volume to Liters
The second step requires converting the solution volume from milliliters to liters. The \(500 \text{ mL}\) volume is converted by dividing by \(1,000\), which results in a volume of \(0.500 \text{ L}\).
Step 3: Calculate Molarity
Dividing the \(0.100 \text{ moles}\) of solute by the \(0.500 \text{ L}\) of solution volume gives a result of \(0.200 \text{ M}\). This final concentration indicates that every liter of this solution contains \(0.200 \text{ moles}\) of dissolved NaCl.
Finding Molarity Through Dilution
A different situation arises when a solution is prepared by diluting a more concentrated stock solution rather than weighing out a solid solute. Dilution involves adding more solvent, usually water, to decrease the concentration without changing the total amount of solute present.
The molarity is calculated using the dilution equation: \(M_1V_1 = M_2V_2\). Here, \(M_1\) and \(V_1\) represent the initial molarity and volume of the stock solution, while \(M_2\) and \(V_2\) represent the final molarity and volume of the diluted solution. The equation works because the product of molarity and volume (\(M \times V\)) represents the total moles of solute (n).
This formula is useful for finding an unknown final molarity (\(M_2\)). By rearranging the equation to solve for the final molarity, \(M_2 = (M_1V_1) / V_2\), the concentration of the new solution can be determined accurately.