Solution concentration is commonly expressed using molarity, which describes the amount of a substance dissolved in a specific volume of liquid. While molarity and volume characterize a solution, they do not directly represent the physical quantity of the material itself. To prepare a solution or inventory the solid material used, chemists must know the mass, typically measured in grams, of the dissolved substance. This conversion links the solution’s concentration and volume to the substance’s molecular properties.
Step One: Calculating the Number of Moles
The first step in determining the mass of a solute is to calculate the number of moles present. Molarity is defined as the number of moles of solute dissolved per liter of solution (\(\text{mol/L}\)).
To find the number of moles, multiply the molarity (concentration) by the total volume of the solution. The volume used in this calculation must be expressed in liters (\(\text{L}\)). If the volume is initially provided in milliliters (\(\text{mL}\)), convert it by dividing the milliliter value by 1,000.
Step Two: Determining the Molar Mass
To convert the calculated number of moles into a measurable mass, the molar mass of the substance must be known. Molar mass represents the mass of one mole of a substance and is expressed in units of grams per mole (\(\text{g/mol}\)). This value is unique to every chemical compound.
The molar mass is determined by examining the compound’s chemical formula and consulting the atomic masses of its constituent elements on the Periodic Table. The atomic mass for each element is multiplied by the number of times that atom appears in the molecule.
Summing these weighted atomic masses yields the molar mass. For example, in water (\(\text{H}_2\text{O}\)), the mass of two hydrogen atoms is added to the mass of one oxygen atom.
Step Three: Converting Moles to Grams
The final step uses the calculated moles and molar mass to find the total mass of the solute in grams. This is achieved by multiplying the number of moles by the molar mass of the compound: \(\text{Mass} = \text{Moles} \times \text{Molar Mass}\).
Multiplying moles (\(\text{mol}\)) by grams per mole (\(\text{g/mol}\)) results in the desired unit of mass through unit cancellation, leaving the final result in grams (\(\text{g}\)).
A Worked Example Problem
Consider finding the mass of sodium chloride (\(\text{NaCl}\)) required to prepare \(0.5 \text{ L}\) of a \(0.1 \text{ M}\) solution. First, calculate the number of moles by multiplying the molarity by the volume in liters. Multiplying \(0.1 \text{ mol/L}\) by \(0.5 \text{ L}\) yields \(0.05 \text{ moles}\) of \(\text{NaCl}\).
Next, determine the molar mass of sodium chloride from its constituent elements, Sodium (\(\text{Na}\)) and Chlorine (\(\text{Cl}\)). The atomic mass of sodium is \(22.99 \text{ g/mol}\), and chlorine is \(35.45 \text{ g/mol}\). Adding these values together gives a molar mass of \(58.44 \text{ g/mol}\) for \(\text{NaCl}\).
Finally, calculate the total mass by multiplying the \(0.05 \text{ moles}\) by the molar mass of \(58.44 \text{ g/mol}\). This multiplication results in a required mass of \(2.922 \text{ grams}\) of sodium chloride.