The mole (mol) and the liter (L) are fundamental measurements in chemistry, but they describe different properties of matter. The mole is the International System of Units (SI) base unit for the amount of substance, representing a specific quantity of particles, such as atoms or molecules. The liter, by contrast, is a unit of volume, indicating the amount of three-dimensional space a substance occupies. Converting from moles to liters is not a direct, fixed ratio for all substances. The conversion method depends entirely on the state of the substance—whether it is a gas under specific conditions or a solute dissolved in a solution.
The Simplest Conversion: Gases at Standard Conditions
The most straightforward conversion applies exclusively to gases under Standard Temperature and Pressure (STP). STP is defined as a temperature of \(0^\circ \text{C}\) (\(273.15 \text{ K}\)) and a pressure of \(1 \text{ atm}\). Under these specific conditions, all ideal gases exhibit a uniform behavior, a principle derived from Avogadro’s Law.
This principle establishes a constant relationship between moles and volume for gases at STP: one mole of any gas occupies \(22.4 \text{ L}\) of space. This fixed value, \(22.4 \text{ L/mol}\), is known as the molar volume of a gas at STP. To find the volume in liters from a known number of moles, multiply the number of moles by this constant. For example, \(5 \text{ moles}\) of oxygen gas at STP would occupy \(5 \text{ mol} \times 22.4 \text{ L/mol}\), resulting in a volume of \(112 \text{ L}\).
Conversion for Solutions: Using Molarity
When dealing with a substance dissolved in a liquid, the conversion from moles to liters is determined by the solution’s concentration, not a fixed gas constant. This requires the concept of molarity (\(M\)). Molarity is defined as the number of moles of the dissolved substance (solute) per liter of the total solution.
The standard units for molarity are moles per liter (\(\text{mol/L}\)), abbreviated as \(M\). This relationship provides the necessary conversion factor between moles of solute and the volume of the solution. The defining formula is \(M = \text{moles} / \text{liters}\), which is rearranged to solve for the volume: \(\text{Liters} = \text{Moles} / \text{Molarity}\).
Using this formula, if one has \(0.75 \text{ moles}\) of salt dissolved in a solution with a known concentration of \(0.5 \text{ M}\), the volume of the solution needed is \(0.75 \text{ mol} / 0.5 \text{ mol/L}\), which equals \(1.5 \text{ L}\).
Conversion for Gases Under Variable Conditions
For gases not held at Standard Temperature and Pressure, the conversion from moles to liters requires the Ideal Gas Law. This law mathematically describes gas behavior under a wide range of pressures and temperatures using the equation \(PV = nRT\).
In this formula, \(P\) is the pressure, \(V\) is the volume in liters, \(n\) is the number of moles, and \(T\) is the absolute temperature in Kelvin. \(R\) is the Ideal Gas Constant, a universal value that links the other four properties. A commonly used value for \(R\) is \(0.08206 \text{ L} \cdot \text{atm} / (\text{mol} \cdot \text{K})\).
To find the volume (\(V\)) from a known number of moles (\(n\)), rearrange the equation to \(V = nRT/P\). If, for example, one has \(2.0 \text{ moles}\) of gas at \(3.0 \text{ atm}\) and \(25^\circ \text{C}\), the temperature must first be converted to Kelvin by adding \(273.15\), yielding \(298.15 \text{ K}\). Substituting these values allows for the calculation of the volume, demonstrating that a change in environmental variables affects the final volume.