What is the molarity of a phosphoric acid solution if the solution is \(85 \%\) by mass \(\mathrm{H}_{3} \mathrm{PO}_{4}\) and has a density of \(1.7 \mathrm{~g} / \mathrm{mL}\) ?

Molarity, often represented by the symbol 'M', is a measure of concentration that expresses the number of moles of a solute in one liter of solution. The molarity formula is a straightforward equation:

\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]
This is a fundamental concept in chemistry, especially when preparing solutions for experiments. When calculating molarity, it's essential to ensure that the volume of the solution is expressed in liters, as the formula is based on moles per liter.

For our phosphoric acid example, after determining the number of moles of \(\mathrm{H}_{3}\mathrm{PO}_{4}\) present, we simply divide by the volume of the solution to find the molarity. This calculation is critical in fields like analytical chemistry, where precise concentrations are necessary.

The process of converting moles to liters is tied closely with the concept of molarity. Since molarity is moles per liter, if we know the molarity and the number of moles, we can find the volume of the solution in liters. Conversely, if we have a certain volume and molarity, we can calculate the number of moles.

The conversion is straightforward in the context of molarity:
\[ \text{Liters of solution} = \frac{\text{moles of solute}}{\text{Molarity}} \]
This represents an inverse relationship between the volume of the solution and the concentration, given a fixed amount of solute. Understanding this relationship is necessary when you have to dilute or concentrate a solution by adding more solvent or evaporating it, respectively.

The mass percent solution is another way to express concentration, defined as the mass of solute in a solution divided by the total mass of the solution, multiplied by 100. It is represented by the equation:

\[ \text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100\% \]
When you are given a mass percent, you can determine the mass of solute in a specific volume of solution if you also know the solution's density. In the phosphoric acid example, with an 85% mass percent and a density of 1.7 g/mL, we are provided the necessary details to calculate the solute's mass in one liter of the solution. The mass percent is a simple yet powerful piece of information that aids chemists in calculating concentrations, especially when preparing solutions of a desired strength.

Determining the number of moles from a given mass is a fundamental task in chemistry, achieved by using the molar mass of the substance. The molar mass is the mass of one mole of a substance (in grams per mole) and can be found on the periodic table. The formula for calculating moles from mass is:

\[ \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \]
For instance, in our exercise, we need to find the mass of \(\mathrm{H}_{3}\mathrm{PO}_{4}\) present in a liter of solution. Once the mass is obtained, the number of moles of phosphoric acid can be calculated by dividing the mass by its molar mass, which is 98 g/mol. Consequently, this step is critical in the sequence of calculations needed to determine molarity, allowing scientists to gauge the amount of substance involved in chemical reactions and solutions.