Question

The most abundant element in sea water is chlorine (Cl, atomic weight \(=35.5 \mathrm{~g} / \mathrm{mole})\), which is present as chloride ion, \(\mathrm{Cl}^{-}\), in a concentration of \(19 \mathrm{~g} \mathrm{Cl}^{-}\) per \(1 \mathrm{~kg}\) of sea water. If the volume of the earth's oceans is \(1.4 \times 10^{21}\) liters, how many moles of \(\mathrm{Cl}^{-}\) are present in the oceans? Assume that the density of sea water is \(1.0 \mathrm{~g} / \mathrm{cm} 3\).

Short answer

There are approximately \(7.49 \times 10^{21}\) moles of Cl⁻ ions in the Earth's oceans.

Step-by-step solution

Convert volume of oceans to mass using density

First we need to convert the volume of the oceans from liters to grams using the density of sea water. We know that the volume of Earth's oceans is \(1.4 \times 10^{21} \mathrm{~L}\) and that the density of sea water is \(1.0 \mathrm{~g}/\mathrm{cm}^3 \). 1 L is equal to 1000 cm³, so the total volume of the oceans in cm³ is: \(1.4 \times 10^{21} \mathrm{~L} \times \frac{1000 \mathrm{~cm}^3}{1 \mathrm{~L}} = 1.4 \times 10^{24} \mathrm{~cm}^3\) Now we can calculate the mass of the oceans using the density formula: Density = Mass / Volume Mass = Density × Volume Mass = \(1.0 \mathrm{~g}/\mathrm{cm}^3 \times 1.4 \times 10^{24} \mathrm{~cm}^3 = 1.4 \times 10^{24}\) grams

Calculate the mass of Cl⁻ ions in the oceans

Now that we have the mass of the oceans, we can calculate the mass of Cl⁻ ions in the oceans using the given concentration. We are told that there are \(19 \mathrm{~g}\) of Cl⁻ ions per \(1 \mathrm{~kg}\) of sea water. 1 kg is 1000 g, so there are \(19 \mathrm{~g} / 1000 \mathrm{~g} = 0.019 \mathrm{~g}\) of Cl⁻ ions per gram of sea water. Now we can calculate the mass of Cl⁻ ions in the oceans: Mass of Cl⁻ ions = Mass of oceans × Concentration of Cl⁻ ions Mass of Cl⁻ ions = \(1.4 \times 10^{24} \mathrm{~g} \times 0.019 \mathrm{~g} / \mathrm{g} = 2.66 \times 10^{23} \mathrm{~g}\)

Calculate the number of moles of Cl⁻ ions

Finally, we can calculate the number of moles of Cl⁻ ions in the oceans by dividing the mass of Cl⁻ ions by the atomic weight. We are given that the atomic weight of Cl is 35.5 g/mole. Number of moles of Cl⁻ ions = Mass of Cl⁻ ions / Atomic weight Number of moles of Cl⁻ ions = \(2.66 \times 10^{23} \mathrm{~g} / 35.5 \mathrm{~g}/\mathrm{mole} = 7.49 \times 10^{21} \mathrm{~moles}\) So, there are approximately \(7.49 \times 10^{21}\) moles of Cl⁻ ions in the Earth's oceans.

Key concepts

Density of Sea Water

Sea water, a complex solution, is composed of various salts, dissolved gases, and organic substances. One important property of sea water is its density, which is a measure of how much mass a certain volume of it contains. For sea water, the typical density is approximately 1.0 g/cm^3. This means that one cubic centimeter of sea water has a mass of about 1 gram.

Understanding the density of sea water is crucial for various calculations, such as converting volumes of oceans into mass, as density acts as the bridge between these two measurements.

• Water density varies slightly due to temperature and salinity, but typical sea water is around 1.0 g/cm³.
• To convert volume to mass, multiply the volume by the density.

For large bodies of water like oceans, knowing the overall volume and density helps estimate the total mass, which is integral to understanding the distribution of substances within sea water, like chloride ions.

Chloride Ion Concentration

The concentration of chloride ions in sea water is a measure of how much chloride is dissolved in a specific amount of sea water. Chloride ions, denoted as \(\mathrm{Cl}^{-}\), primarily originate from dissolved salts, such as sodium chloride. In sea water, the concentration is approximately 19 g of \(\mathrm{Cl}^{-}\) per kilogram of sea water.

This concentration information is essential to determine the total amount of chloride ions in the oceans. By converting kilograms of sea water to grams, we find there are 0.019 grams of chloride per gram of sea water. This value is used to calculate the mass of chloride in vast volumes like the Earth's oceans.

• Chloride concentration reflects the abundance of chlorine, an essential element.
• The concentration is used to scale up calculations to massive ocean volumes.

Such calculations help scientists estimate the reservoirs of chlorine and other elements in global water bodies.

Molecular Weight of Chlorine

Atomic and molecular weights are fundamental concepts in chemistry, as they allow for the translation of mass into the number of moles. For chlorine atoms, which are part of the chloride ions \(\mathrm{Cl}^{-}\), the atomic weight is given as 35.5 g/mole.

The molecular weight serves as a conversion factor when moving between the mass of a substance to the amount in moles. Since chemical reactions occur at the atomic and molecular levels, counting molecules by measuring their mass involves using this atomic weight.

• One mole of chlorine has a mass of 35.5 grams.
• Molecular weights allow chemists to determine how many molecules or ions are in a given mass.

In the case of sea water, after determining the mass of chloride ions using volume and concentration, the number of moles is calculated by dividing the total mass of \(\mathrm{Cl}^{-}\) by its molecular weight. This approach enables a better understanding of elemental distributions in large contexts, such as Earth's oceans.