Question

The average concentration of bromide ion in seawater is \(65 \mathrm{mg}\) of bromide ion per \(\mathrm{kg}\) of seawater. What is the molarity of the bromide ion if the density of the seawater is \(1.025 \mathrm{~g} / \mathrm{mL}\) ?

Short answer

The molarity of bromide ions in seawater is approximately \(8.34 \times 10^{-4} \mathrm{M}\).

Step-by-step solution

Convert mass of bromide ions to moles.

Since we have 65 mg of bromide ions per kg of seawater, first we need to convert the mass of bromide ions to grams: \(65 \mathrm{mg} = 0.065 \mathrm{g}\) Next, we need to find the molar mass of bromide ions, which can be found in the periodic table: Molar mass of Br⁻ = 79.90 g/mol Now, we can convert the mass of bromide ions to moles: \(\mathrm{moles~of~bromide~ions} = \frac{0.065 \mathrm{g}}{79.90 \mathrm{g/mol}} = 8.14 \times 10^{-4} \mathrm{mol}\)

Determine the volume of one kg of seawater in liters.

We are given the density of seawater as 1.025 g/mL. We know that 1 kg of seawater contains 65 mg of bromide ions. First, we need to convert 1 kg of seawater to grams: \(1 \mathrm{kg} = 1000 \mathrm{g}\) Next, we can use the density to find the volume of 1000 g of seawater in milliliters: \(\mathrm{Volume} = \frac{\mathrm{Mass}}{\mathrm{Density}} = \frac{1000 \mathrm{g}}{1.025 \mathrm{g/mL}} = 975.61 \mathrm{mL}\) Finally, we can convert the volume to liters: \(975.61 \mathrm{mL} = 0.97561 \mathrm{L}\)

Calculate the molarity of bromide ions.

Now we have all the necessary information to calculate the molarity of bromide ions in seawater. Molarity is defined as moles of solute per liter of solution. Thus, we can calculate the molarity as follows: \(\mathrm{Molarity~of~bromide~ions} = \frac{8.14 \times 10^{-4} \mathrm{mol}}{0.97561 \mathrm{L}} = 8.34 \times 10^{-4} \mathrm{M}\) So, the molarity of bromide ions in seawater is approximately \(8.34 \times 10^{-4} \mathrm{M}\).

Key concepts

Mole Concept

The mole concept is a fundamental aspect of chemistry that deals with quantities of substances. A mole represents Avogadro's number (\(6.022 \times 10^{23}\) atoms, molecules, or ions), which is the number of particles in a substance. Understanding the mole concept is crucial because it bridges the gap between the microscopic world of atoms and molecules and the macroscopic world we can measure.

When we say we have one mole of bromide ions (\text{Br}^-), we mean we have Avogadro's number of those ions. This mole concept allows us to convert between the mass of a substance and the number of particles it contains. By knowing the molar mass (the mass of one mole) of bromide ions, we use the mass to mole conversion:
\text{moles of bromide ions} = \frac{\text{mass of bromide ions in grams}}{\text{molar mass of bromide ions}}
The calculation above is a typical application of the mole concept in solution preparation.

Solution Concentration

Solution concentration describes how much solute is present in a given amount of solvent. Molarity, often symbolized by 'M', is a common unit of concentration used in chemistry. It is defined as the number of moles of solute per liter of solution.

In the bromide ion problem, we're looking to find its molarity in seawater. To reach that, we consider the mass of bromide in a known mass of seawater and then convert it into a volume-based concentration. These steps help us understand the real-world applications of chemistry, such as determining the concentration of ions in oceanography or salt content in food sciences. The steps in the solution above illustrate how to transition from knowing the mass of a solute in a certain mass of solvent to finding its molarity.

Unit Conversion

Unit conversion is the process of converting one type of unit to another to measure the same quantity. In chemistry, unit conversion is essential because it allows for communication and calculations using standard units.

For example, we converted milligrams of bromide ions to grams, kilograms to grams, and milliliters to liters in the given exercise. This is because calculations in chemistry are typically done in grams and liters, making it necessary to convert the given units into these standard units. Being fluent with unit conversion is invaluable, not just in chemistry, but in any scientific problem-solving situation.

Without accurate unit conversions, calculations for the molarity could lead to incorrect results, thus it's a key skill in solving chemistry problems.

Stoichiometry

Stoichiometry is the part of chemistry that concerns the relative quantities of reactants and products in chemical reactions. It can also apply to other calculations in chemistry, like figuring out concentrations of solutions.

In the context of calculating molarity, stoichiometry helps us relate the quantity of solute (bromide ions) to the volume of the solution (seawater). By using the molar mass of the bromide ions and the molarity formula, we perform stoichiometric calculations to determine how much of a substance is present in a certain volume of solution. It's a concept that encapsulates the quantitative relationships within chemical formulas and reactions, crucial for making precise measurements in all branches of chemistry.