Concentration is a fundamental property of solutions used to quantify the amount of a substance dissolved within a liquid medium. The standard method for expressing this concentration is molarity, which provides a precise measure for laboratory work and industrial processes. Calculating the volume of a solution required to contain a specific amount of dissolved substance is a common task derived directly from this concentration relationship. This calculation is essential for accurately preparing solutions and performing chemical reactions.
Defining Molarity and Moles
Molarity, symbolized by a capital M, is a unit of concentration that specifically relates the quantity of a dissolved substance to the total volume of the solution. It is defined as the number of moles of a solute per liter of solution and is often read as “molar.” This unit, mol/L, makes it easy to compare the concentrations of different solutions directly.
The term “mole,” represented by \(n\), is the standard SI unit for the amount of a substance in chemistry. In this context, it refers to the amount of the solute, the substance being dissolved. Volume, represented by \(V\), is the total space the solution occupies. Volume must be measured in liters (L) for the molarity formula to be mathematically correct.
Deriving the Volume Formula
The foundational mathematical relationship connecting these three variables is the definition of molarity: \(M = n/V\). To find the volume in liters from the known molarity and moles, this equation must be rearranged through simple algebra.
The goal is to isolate \(V\) on one side of the equation. Start by multiplying both sides of the equation (\(M = n/V\)) by \(V\), resulting in \(M \times V = n\). The final step is to divide both sides of this new equation by the molarity (\(M\)).
Dividing both sides by \(M\) yields the final derived formula: \(V = n/M\). This shows that the volume of the solution in liters is equal to the moles of solute divided by the solution’s molarity. Using this formula ensures the resulting unit will be liters, as the units for moles (mol) and molarity (mol/L) cancel out.
Step-by-Step Calculation Example
To apply the derived formula, consider a scenario where a chemist needs a specific amount of sodium chloride (table salt) from a stock solution. Suppose the chemist requires 0.45 moles of sodium chloride, and the available stock solution has a concentration of 1.5 M. The objective is to calculate the precise volume in liters of the solution needed.
First, identify the known values: the number of moles (\(n\)) is 0.45 mol, and the molarity (\(M\)) is 1.5 M. The rearranged formula, \(V = n/M\), is then used for the calculation, yielding \(V = 0.45 \text{ mol} / 1.5 \text{ mol/L}\).
The calculation involves dividing 0.45 by 1.5, which results in 0.3. Because the unit for moles appears in both the numerator and the denominator, they cancel out, leaving the volume unit of liters. Therefore, the required volume (\(V\)) is 0.3 L.