In chemistry, solutions are mixtures where a solute is dissolved in a solvent, and concentration is often measured using molarity. Molarity quantifies how much solute is present in a given volume of the solution. This calculation links the measurable properties of a solution—volume and concentration—to the fundamental unit of chemical quantity, moles.
Defining the Variables
The relationship between concentration, quantity, and volume is expressed by a fundamental mathematical equation. Molarity, represented by the capital letter \(M\), is defined as the amount of solute in moles divided by the volume of the entire solution in liters. This establishes molarity as a standard concentration unit, consistently expressed as moles per liter (\(\text{mol}/\text{L}\)).
The amount of substance being solved for is represented by the variable \(n\), which stands for moles. The mole is a defined unit representing a specific, large number of particles, providing a practical count of the dissolved chemical substance.
The third variable in the relationship is the volume of the solution, represented by \(V\). For the molarity equation to function correctly and yield standard units, this volume must be universally expressed in liters (L). Therefore, the entire mathematical relationship is summarized by the concise equation: Molarity equals moles divided by volume, or \(M = n/V\).
Crucial Preparation: Unit Consistency
Before any calculation, unit consistency is required because the definition of molarity relies specifically on volume being measured in liters. Any volume provided in smaller units, such as milliliters (mL), must be converted first. Using milliliters directly in the equation would yield an incorrect numerical result.
Since one liter contains 1000 milliliters, the conversion process requires dividing the milliliter value by 1000. For example, a measured volume of 500 milliliters becomes 0.5 liters, ensuring the volume variable \(V\) is properly aligned with the units of molarity. This preparatory step guarantees that the subsequent calculation will produce the correct quantity of moles.
The Step-by-Step Calculation
To isolate the quantity we are seeking, the foundational equation \(M = n/V\) must be algebraically rearranged to solve directly for moles (\(n\)). This manipulation is achieved by multiplying both sides of the equation by the volume (\(V\)). The resulting formula clearly shows that the amount of substance is the direct product of its concentration and its volume: \(n = M \times V\).
The calculation steps are defined by the rearranged formula \(n = M \times V\). First, identify the given molarity (\(M\)). Second, confirm the volume (\(V\)) is in liters, converting from milliliters if required. Third, multiply the molarity value by the volume value to find the result in moles.
The final answer must be stated with the correct chemical unit, moles. The multiplication of the units (moles/liter) by (liters) results in the cancellation of the volume unit, leaving only the mole unit for the final answer.
Applying the Method (Worked Example)
Consider a scenario where a scientist needs to find the moles of sodium hydroxide (\(\text{NaOH}\)) present in 250 milliliters of a 0.5 \(M\) solution. This example integrates the algebraic steps and unit preparation. The initial step requires converting the given volume of 250 mL into liters.
Dividing the 250 mL by 1000 correctly yields a volume of 0.250 L. With the volume now prepared, the calculation \(n = M \times V\) can be executed.
The known molarity (\(M\)) is \(0.5\) mol/L, and the prepared volume (\(V\)) is \(0.250\) L. Multiplying these values, \(0.5 \times 0.250\), results in a product of \(0.125\). Therefore, the specific solution contains 0.125 moles of sodium hydroxide.