Problem 32 - Chemistry: The Central Science

Question

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

Step-by-Step Solution

Answer

The corresponding molar concentration of phosphate in seawater is approximately \(0.000737 \, mol/L\).

Step 1: Convert phosphorus concentration from ppm to grams per liter

Phosphorus is present in seawater at 0.07 ppm, which means there are 0.07 grams of phosphorus in every 1 million grams of seawater. We can convert this to grams per liter by assuming the density of seawater is 1 g/mL (it's actually slightly higher, but this is a reasonable approximation). 0.07 ppm = \(\frac{0.07 \, grams}{1,000,000 \, grams}\)\(\times \frac{1,000,000 \, grams}{1,000 \, Liters}\) = \(\frac{0.07 \, grams}{1,000 \, Liters}\) So, the concentration of phosphorus is 0.07 g/L in seawater.

Step 2: Determine the molar mass of the phosphate ion, PO4^{3-}

To find the molar mass of the phosphate ion PO4^{3-}, we need to add the atomic masses of the constituent elements. Molar mass of PO4^{3-} = 1(atomic mass of P) + 4(atomic mass of O) Using the periodic table, the atomic mass of P is ~31 g/mol, and the atomic mass of O is ~16 g/mol. Molar mass of PO4^{3-} = 31 + 4(16) = 31 + 64 = 95 g/mol

Step 3: Calculate the moles of phosphate in one liter of seawater

Now, we know the concentration of phosphorus in seawater (0.07 g/L) and the molar mass of the phosphate ion (95 g/mol). We can use this information to find the moles of phosphate in one liter of seawater. Moles of phosphate = \(\frac{mass\,of\,phosphorus}{molar\,mass\,of\,phosphate}\) Moles of phosphate = \(\frac{0.07\,g}{95\,g/mol}\) = 0.0007368 mol

Step 4: Calculate the molar concentration of phosphate in seawater

Since we know the moles of phosphate in one liter of seawater, we can find the molar concentration of phosphate. Molar concentration of phosphate = \(\frac{moles\,of\,phosphate}{volume\,of\,seawater}\) Molar concentration of phosphate = \(\frac{0.0007368\,mol}{1\,L}\) = 0.0007368 mol/L So, the corresponding molar concentration of phosphate in seawater is approximately 0.000737 mol/L.

Key Concepts

PPM to Molarity Conversion

When dealing with solutions, one of the essential skills in chemistry is converting different units of concentration. Parts per million (ppm) is a unit commonly used to express very dilute concentrations of substances. One ppm indicates one part of a substance per million parts of the total solution. To convert ppm to molarity, which is expressed as moles per liter (mol/L), one must understand both concepts deeply.

Molarity is a more chemically informative unit because it reflects the number of moles, which directly relates to the number of particles or molecules in a given volume. Converting ppm to molarity requires two main steps:

• First, you convert ppm to a mass concentration (e.g., g/L), considering the density of the solution, which for many aqueous solutions is close to that of water, approximately 1 g/mL.
• Next, you divide this mass concentration by the molar mass of the solute to get the molarity.

The direct conversion can be formulated as follows:
\[Molarity (mol/L) = \frac{ppm \times Density\text{ of solution (g/mL)}}{Molar\text{ Mass (g/mol)} \times 10^{6}}\]
This formula is extremely useful when dealing with the dilute solutions encountered in environmental chemistry or biological contexts.

Molar Mass of Ions

The molar mass is a fundamental property of a substance, defined as the mass of one mole of that substance, typically measured in grams per mole (g/mol). Knowing the molar mass is pivotal for various calculations in chemistry, including converting between mass and moles.

For ions, such as the phosphate ion (PO4^{3-}), the molar mass calculation is quite similar to that of neutral atoms or molecules. One should sum the atomic masses of all the atoms in the ion, as the charge does not affect the molar mass. For instance:

• Phosphorus (P) has an atomic mass of approximately 31 g/mol.
• Oxygen (O) has an atomic mass of approximately 16 g/mol.

Therefore, the molar mass of the phosphate ion (PO4^{3-}) is calculated by adding the mass of one phosphorus atom to the mass of four oxygen atoms:
\[Molar\text{ Mass of } PO4^{3-} = (1 \times 31 g/mol) + (4 \times 16 g/mol) = 95 g/mol\]
This calculation reveals that the molar mass plays a crucial role in converting concentrations from mass-based units (like ppm or g/L) to molarity (mol/L).

Stoichiometry in Solution Chemistry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. In the context of solution chemistry, stoichiometry is used to determine the concentrations of solutes in a solution and to calculate the volume or mass of solutions required to react completely with a given amount of reactant.

Applying stoichiometry involves understanding the mole concept, which relates the mass of a substance to its number of particles (atoms, molecules, or ions). It's based on balanced chemical equations where the coefficients represent the ratio of moles of each substance involved.
When working with solutions, the molar concentration (also known as molarity) is the most commonly used unit of concentration. It provides a direct way of knowing how many moles of a solute are present in a given volume of solution, making it a critical concept in stoichiometric calculations.
For example, if you want to know how much of a reagent is required to react with a substance in solution, you would use the molarity of the solution and the stoichiometric ratio from the balanced equation to calculate the necessary volume or mass of the reagent. Stoichiometry in solutions is therefore not only about understanding concentrations but also about using this knowledge to perform precise chemical manipulations and reactions.