Question

Seawatercontains \(0.13 \%\) magnesium by mass, and has a density of \(1.025 \mathrm{~g} / \mathrm{mL}\). What fraction of the magnesium can be removed by adding a stoichiometric quantity of \(\mathrm{CaO}\) (that is, one mole of \(\mathrm{CaO}\) for each mole of \(\mathrm{Mg}^{2+}\) )?

Short answer

The fraction of magnesium that can be removed by adding a stoichiometric quantity of CaO is 1, or 100%.

Step-by-step solution

Calculate the mass of magnesium in 1L of seawater

Given the density of seawater, \(1.025\, \mathrm{g/mL}\), we can calculate the mass of seawater in 1L. 1L = 1000mL so, Mass_Seawater = Volume × Density Mass_Seawater = \(1000\,\mathrm{mL} \times 1.025\,\mathrm{g/mL} = 1025\,\mathrm{g}\) Since seawater contains 0.13% magnesium by mass, we can find the mass of magnesium in this 1L of seawater. Mass_Magnesium = Mass_Seawater × (Percentage Magnesium / 100) Mass_Magnesium = \(1025\,\mathrm{g} \times (0.13 / 100) = 1.3325\,\mathrm{g}\)

Calculate the moles of magnesium and CaO needed

Now we can calculate the moles of magnesium in the seawater using its molar mass (24.305 g/mol). Moles_Magnesium = Mass_Magnesium / Molar_Mass_Magneisum Moles_Magnesium = \(1.3325\,\mathrm{g} / 24.305\,\mathrm{g/mol} = 0.0548\,\mathrm{mol}\) Since the problem states that we need one mole of CaO for each mole of magnesium, we also need 0.0548 moles of CaO.

Calculate the fraction of magnesium that can be removed by CaO

To find the fraction of magnesium that can be removed by CaO, we can use the moles of magnesium calculated in Step 2 and compare it with the total moles of magnesium in 1L of seawater. We already have the moles of magnesium that can be removed, 0.0548 moles, so we just need to find the total moles of magnesium in the seawater. Since the mass of magnesium is 1.3325 g, we can use the molar mass of magnesium to find the total moles. Total_Moles_Magnesium = Mass_Magnesium / Molar_Mass_Magnesium Total_Moles_Magnesium = \(1.3325\,\mathrm{g} / 24.305\,\mathrm{g/mol} = 0.0548\,\mathrm{mol}\) Fraction = Moles_Magnesium / Total_Moles_Magnesium Fraction = \(0.0548\,\mathrm{mol} / 0.0548\,\mathrm{mol} = 1\) So, the fraction of magnesium that can be removed by adding a stoichiometric quantity of CaO is 1, or 100%.

Key concepts

Stoichiometric Calculation

Stoichiometric calculations are the cornerstone of chemical reactions, enabling chemists to quantify the relationship between reactants and products in a chemical equation. In the context of seawater chemistry, it allows us to determine how much of a compound is needed to react with a certain amount of another substance. For instance, when adding calcium oxide (CaO) to seawater, a stoichiometric calculation helps to ascertain the precise amount required to react with the magnesium (Mg²⁺) present.

To perform these calculations, you need to find the molar ratio of the reactants and products from the balanced chemical equation. In the case of removing magnesium from seawater by adding CaO, the ratio is 1:1—this means one mole of CaO reacts with one mole of Mg²⁺. Then, you would calculate the number of moles of magnesium in seawater using its mass and molar mass, and since the ratio is 1:1, the moles of CaO required would be equal to the moles of magnesium, leading you to the fraction of magnesium that could be removed.

Molar Mass

The molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a vital concept in stoichiometry, as it links the mass of a substance to the amount in moles, facilitating the conversion between these two units.

For practical calculations like those needed for seawater chemistry, the molar mass of magnesium—which is 24.305 g/mol—is used to convert the mass of magnesium in a certain volume of seawater to the number of moles. Knowing the molar mass allows us to work out the stoichiometric relationships in a reaction. It is important to always use the molar mass specific to the element or compound in question; this is found on the periodic table or in a list of standard molar masses.

Chemistry of Seawater

The chemistry of seawater is complex, involving various dissolved salts, minerals, and gases, with magnesium (Mg²⁺) being one of the many ions present. Understanding seawater's composition is essential for marine chemistry applications, such as removing certain ions or managing the ecosystem's health.

Seawater's unique chemistry plays a pivotal role in global chemical cycles and has specific properties like density, which is influenced by the type and amount of dissolved substances. When solving chemical problems related to seawater, considering these physical and chemical characteristics ensures accurate results, as seen in our example where the density of seawater was used to calculate the mass of seawater, and hence, the mass of magnesium. This kind of stoichiometric application in seawater chemistry can also have practical implications, for example, in desalination processes or environmental remediation.