Question

In the extraction of bromine from seawater (reaction 22.3), seawater is first brought to a pH of 3.5 and then treated with \(\mathrm{Cl}_{2}(\mathrm{g}) .\) In practice, the \(\mathrm{pH}\) of the seawater is adjusted with \(\mathrm{H}_{2} \mathrm{SO}_{4},\) and the mass of chlorine used is \(15 \%\) in excess of the theoretical. Assuming a seawater sample with an initial pH of 7.0 a density of \(1.03 \mathrm{g} \mathrm{cm}^{-3}\), and a bromine content of 70 ppm by mass, what masses of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and \(\mathrm{Cl}_{2}\) would be used in the extraction of bromine from \(1.00 \times 10^{3} \mathrm{L}\) of seawater?

Short answer

The detailed solution of each step involving multiple chemical and mathematical calculations will provide the exact masses of \(H_{2}SO_{4}\) and \(Cl_{2}\) used in the extraction of bromine from the seawater.

Step-by-step solution

Calculate mass of seawater

The first step is to calculate the mass of the seawater sample using the provided volume and density. \n Given the density \(\rho = 1.03 \, \mathrm{g/cm^3}\) and the volume \(V = 1.00 \times 10^{3} \, \mathrm{L} = 1.00 \times 10^{6} \, \mathrm{cm^3}\), the mass \(m\) of the seawater can be calculated with the formula \(m = \rho \times V\).

Calculate mass of bromine

Next, determine the mass of bromine in the seawater. The bromine content is given as 70 ppm by mass, which means there are 70 g of bromine in \(1 \times 10^{6} \) g of seawater. Use the mass of seawater calculated in Step 1 to determine the mass of bromine.

Find moles of bromine

Now, find the moles of bromine in the seawater using its molar mass. The molar mass of bromine (\(Br\)) is approximately 79.9 g/mol. Divide the mass of bromine obtained in Step 2 by the molar mass of bromine to obtain the number of moles.

Calculate moles of \(Cl_2\)

The procedure involves treating the seawater with chlorine gas (\(Cl_2\)). Since chlorine and bromine both belong to Group 7 elements, they react in a 1:1 ratio. Therefore, the number of moles of \(Cl_2\) needed is equal to the moles of bromine. As per the question, we need to take \(Cl_2\) 15% in excess of the theoretical requirement. Hence calculate 15% more of the moles of \(Cl_2\) obtained.

Find mass of \(Cl_{2}\)

Next, calculate the mass of \(Cl_2\) using its molar mass and the moles of \(Cl_2\) calculated in Step 4. The molar mass of \(Cl_2\) is 70.9 g/mol. Multiply the moles of \(Cl_2\) from Step 4 by the molar mass to get the mass of \(Cl_2\) that would be used in the extraction of bromine.

Find moles of \(H_{2}SO_{4}\)

To adjust the pH of the seawater to 3.5, \(H_{2}SO_4\) is used. For that, figure out the moles of \(H^+\) required to adjust the pH. pH is defined as \(-\log[H^+]\), where \(H^+\) is the concentration of hydrogen ions in moles per liter. Therefore, to find \(H^+\), apply the anti-log formula. Then multiply by the volume of the seawater to find the required moles of \(H^+\) ions.

Find mass of \(H_{2}SO_{4}\)

Sulfuric acid (\(H_{2}SO_4\)) is a strong acid and it dissociates completely in water to give two \(H^+\) ions. Therefore, the number of moles of \(H_{2}SO_{4}\) is half of the moles of \(H^+\) ions. Finally, the molar mass of \(H_{2}SO_{4}\) is approximately 98 g/mol. Multiply the moles of \(H_{2}SO_4\) by its molar mass to get the mass.

Key concepts

Calculating Mass with Density and Volume

Understanding the relationship between mass, density, and volume is foundational in chemistry and plays an essential role in various calculations. Mass is typically represented by the symbol 'm' and is measured in grams (g). Density (\(\rho\)) is a measure of how much mass is contained within a unit volume of a substance and is commonly expressed in grams per cubic centimeter (g/cm³). Volume 'V' refers to the space that a substance occupies and is measured in cubic centimeters (cm³) or liters (L).
To find the mass of an object or substance when the density and volume are known, you use the formula: \(m = \rho \times V\). This formula is fundamental when dealing with problems where you must extract a substance, like bromine, from a solution like seawater. For example, with a density of seawater being \(1.03 \text{ g/cm}^3\) and a volume of \(1.00 \times 10^3 \text{ L}\), which is \(1.00 \times 10^6 \text{ cm}^3\) when converted, you can calculate the mass of the seawater necessary for the extraction process. It's clear, concise and crucial for steps that follow in many chemical procedures.

Moles and Molar Mass Calculations

Moles and molar mass are integral concepts in chemistry, helping scientists quantify the amount of a substance. A mole is a unit that measures the amount of a chemical substance and is defined by Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities (atoms, molecules, etc.). Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol).
To convert the mass of a substance to moles, you can use the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\). In extracting bromine from seawater, once you've determined the mass of bromine present, you divide that by bromine's molar mass to get moles. This step establishes a bridge that links the physical mass of bromine to its moles, allowing for further stoichiometric calculations, such as determining reactant amounts or yields in a reaction.

Chemical Stoichiometry

Chemical stoichiometry is the calculation of reactants and products in chemical reactions. It is based on the conservation of mass and the concept of the mole. Stoichiometry revolves around the use of balanced chemical equations to determine the ratios in which chemicals react or form products.
In the context of bromine extraction, stoichiometry is employed to calculate the exact amount of chlorine gas needed to react with the bromine ions present in seawater. Since bromine and chlorine belong to the same group on the periodic table and have similar chemical properties, they react in a 1:1 mole ratio. However, we take into account the practical excess of chlorine used in the process, 15% more than the stoichiometrically calculated amount. This ensures the complete reaction of all bromine ions, taking real-world conditions such as incomplete reactions and losses into consideration.

Acid-Base Chemistry

Acid-base chemistry is a fundamental concept referring to the chemical reactions that take place between acids and bases. One of the critical parameters in acid-base chemistry is the pH value, which measures the acidity or basicity of a solution. The pH scale ranges from 0 to 14, where 7 is neutral, values less than 7 indicate acidity, and values greater than 7 indicate basicity.
In relation to the extraction of bromine, the acid used to adjust the pH of seawater is sulfuric acid (\(H_2SO_4\)). The pH adjustment is crucial because certain reactions only occur under specific pH conditions. By calculating the moles of \(H^+\) ions required to achieve the desired pH, and knowing that sulfuric acid releases two \(H^+\) ions per molecule, we can find out how much sulfuric acid is needed to acidify the seawater to pH 3.5. This step demonstrates the interplay between pH control and the amount of acid needed for a desired chemical environment.