Solutions in chemistry often need to be prepared at specific concentrations for laboratory experiments, manufacturing processes, or medical applications. Concentrated solutions are frequently stored as a “stock” and then modified to achieve a lower concentration before use. This process of reducing the concentration is known as dilution, and it requires a simple, reliable mathematical tool to manage the change in concentration and volume accurately. The relationship between the initial and final states of a solution is described by a fundamental equation.
Identification and Underlying Principle
The equation \(M_1V_1 = M_2V_2\) is formally known as the Dilution Equation or the Dilution Formula. The equation is based on the fundamental principle of the conservation of matter, specifically the conservation of moles of solute. When a solution is diluted, only the solvent, typically water, is added, while the amount of the dissolved substance, the solute, remains unchanged.
The left side, \(M_1V_1\), represents the initial state of the concentrated or “stock” solution, while \(M_2V_2\) represents the final state of the diluted solution. The product of concentration (\(M\)) and volume (\(V\)) mathematically yields the number of moles of solute. Because the amount of solute does not change during dilution, the quantity of solute in the initial solution must equal the quantity in the final solution, which explains why the two sides of the equation are equal.
Defining Molarity and Volume
The variables in the Dilution Equation represent two fundamental properties of the solution: concentration and volume. The letter \(M\) stands for Molarity, which is the standard unit of concentration used in this context. Molarity is defined as the number of moles of solute dissolved per liter of solution. This unit, abbreviated as a capital “M,” is widely used because it relates directly to the chemical amount of the dissolved substance.
The letter \(V\) represents the volume of the solution. \(V_1\) is the starting volume of the concentrated solution, and \(V_2\) is the total final volume of the diluted solution. A requirement for using the equation correctly is that the units of volume must be consistent on both sides. For example, if \(V_1\) is measured in milliliters (mL), \(V_2\) must also be in milliliters, and the concentration units for \(M_1\) and \(M_2\) must match.
Practical Application in Dilution Calculations
The Dilution Equation is routinely used in laboratory settings to prepare solutions of a desired concentration from a pre-existing, more concentrated stock solution. The concentrated starting material is labeled with the subscript “1,” and the target, less concentrated solution is designated with the subscript “2.” Scientists often rearrange the equation to solve for the one unknown variable, typically the volume of the stock solution (\(V_1\)) needed or the final concentration (\(M_2\)) of the diluted solution.
Calculating Stock Volume
For example, if a chemist needs to know the volume of a 6.0 M stock solution (\(M_1\)) required to make 500 mL (\(V_2\)) of a 0.5 M solution (\(M_2\)), they rearrange the formula to \(V_1 = (M_2V_2) / M_1\). Substituting the known values and solving the calculation provides the exact volume of the concentrated material to be measured. Once the required volume of the stock solution is determined, that amount is carefully measured. Solvent is then added until the total volume reaches the desired final volume (\(V_2\)). This simple algebraic manipulation allows for the precise and reproducible preparation of countless solutions in various scientific disciplines.