Question

Phosphorus is present in seawater to the extent of 0.07 ppm by mass. If the phosphorus is present as phosphate, \(\mathrm{PO}_{4}{ }^{3-}\), calculate the corresponding molar concentration of phosphate in seawater.

Short answer

The corresponding molar concentration of phosphate in seawater is \(2.258 \times 10^{-6}\,\text{mol/L}\).

Step-by-step solution

Convert ppm to mass concentration

To convert the concentration of phosphorus from ppm to a mass concentration, we can use the following relationship: 1 ppm = 1 mg/L So, 0.07 ppm of phosphorus corresponds to 0.07 mg of phosphorus per liter of seawater.

Convert mass of phosphorus to moles

To find the moles of phosphorus, we need to convert the mass of phosphorus to moles using the molar mass. The molar mass of phosphorus (\(\mathrm{P}\)) is approximately 31 g/mol: Number of moles = \(\frac{\text{mass of P}}{\text{molar mass of P}}\) Plugging in the values, we get: Number of moles of P = \(\frac{0.07\,\text{mg}}{31\,\text{g/mol}}\) = \(\frac{0.07 \times 10^{-3}\,\text{g}}{31\,\text{g/mol}}\) Number of moles of P = \(2.258 \times 10^{-6}\) mol

Calculate the moles of phosphate ions

Since there is 1 phosphorus atom in each phosphate ion (\(\mathrm{PO}_{4}{ }^{3-}\)), the number of moles of phosphate ions is equal to the number of moles of phosphorus: Number of moles of \(\mathrm{PO}_{4}{ }^{3-}\) = \(2.258 \times 10^{-6}\) mol

Calculate the molar concentration of phosphate ions

To calculate the molar concentration of phosphate ions, we can use the following relationship: Molar concentration = \(\frac{\text{number of moles}}{\text{volume}}\) Since the mass concentration given was per liter of seawater, the volume is 1 L: Molar concentration of \(\mathrm{PO}_{4}{ }^{3-}\) = \(\frac{2.258 \times 10^{-6}\,\text{mol}}{1\,\text{L}}\) Molar concentration of \(\mathrm{PO}_{4}{ }^{3-}\) = \(2.258 \times 10^{-6}\,\text{mol/L}\) Therefore, the corresponding molar concentration of phosphate in seawater is \(2.258 \times 10^{-6}\,\text{mol/L}\).

Key concepts

Parts Per Million (PPM)

Understanding the measure of parts per million (ppm) is crucial when dealing with very dilute substances, as is often the case in chemistry and environmental science. It represents the mass of a substance compared to the mass of the overall solution or mixture. To put it into perspective, 1 ppm is akin to measuring one drop of dye in a giant tanker truck carrying 50 liters of water - it's a proportion used to represent minute concentrations.

When we say that a substance has a concentration of 0.07 ppm, it means that for every million parts (by mass) of the solution, there are 0.07 parts of the substance. This unit of measure is convenient for analyzing trace amounts of substances, such as measuring the phosphorus content in seawater in the given exercise. It's a good segue into learning how to convert ppm to a mass concentration, which is a foundational skill in environmental chemistry.

Mole Concept

The mole concept is a bridge between the micro world of atoms and molecules and the macro world we can measure, and forms the basis for stoichiometry in chemistry. One mole of any substance contains an Avogadro's number of entities, which is approximately 6.022 x 10²³.

It's essential to grasp the mole concept since it helps in quantifying chemical reactions. For example, knowing the number of moles of phosphorus allows us to determine the number of moles of phosphate ions. This is because there's a direct relationship in stoichiometry: one mole of phosphorus atoms would form one mole of phosphate ions, assuming complete conversion. In the exercise, we see how the mass of phosphorus is converted into moles, which is a critical step for finding the molar concentration.

Molar Mass

Next, let's dive into the concept of molar mass. The molar mass is the weight of one mole (6.022 x 10²³ particles) of a substance and is expressed in grams per mole (g/mol). This property is inherent to each substance and is essential to quantifying how much of a substance is present.

To illustrate, the molar mass of phosphorus is approximately 31 g/mol. With this figure, we can convert the mass of phosphorus in grams to the number of moles, which is a pivotal step in the problem-solving process. In the given exercise, by multiplying the tiny mass of phosphorus (in mg) with the inverse of its molar mass, we ascertain the moles present in the seawater. Molar mass is an indispensable part of stoichiometry because it connects the mass of a substance to the amount in moles.

Stoichiometry

Finally, stoichiometry is the art and science of measuring and calculating the relative quantities of reactants and products in chemical reactions. Using the mole concept and molar masses, stoichiometry allows chemists to predict the outcomes of chemical reactions, and quantify the proportions in which chemicals combine.

In the case of the exercise, converting ppm to moles involves stoichiometry. We used the molar mass of phosphorus to find the moles from a given mass. Then, understanding the stoichiometric relationship between phosphorus and phosphate ions, we could equate their moles directly as they are in a 1:1 ratio. Finally, stoichiometry guided us to the calculation of the molar concentration of phosphate ions by dividing the number of moles of phosphate by the volume of the seawater solution. The critical takeaway here is that stoichiometry encompasses all these steps to deduce the desired molar concentration.