Problem 91 - Chemistry and Chemical Reactivity

Question

A paper published in the research journal Science in 2007 (S. Vallina and R. Simo, Science, Vol. \(315,\) p. \(506,\) January 26,2007 ) reported studies of dimethylsulfide (DMS), an important greenhouse gas that is released by marine phytoplankton. This gas "represents the largest natural source of atmospheric sulfur and a major precursor of hygroscopic (i.e., cloud-forming) particles in clean air over the remote oceans, thereby acting to reduce the amount of solar radiation that crosses the atmosphere and is absorbed by the ocean." (a) Sketch the Lewis structure of dimethylsulfide, \(\mathrm{CH}_{3} \mathrm{SCH}_{3},\) and list the bond angles in the molecule. (b) Use electronegativities to decide where the positive and negative charges lie in the molecule. Is the molecule polar? (c) The mean seawater concentration of DMS in the ocean in the region between \(15^{\circ}\) north latitude and \(15^{\circ}\) south latitude is \(2.7 \mathrm{nM}\) (nanomolar). How many molecules of DMS are present in \(1.0 \mathrm{m}^{3}\) of seawater?

Step-by-Step Solution

Answer

DMS has a bent polar structure with bond angles about 104.5°, and there are approximately 1.63 × 10^15 molecules in 1 m³ of seawater.

Step 1: Draw the Lewis Structure

Dimethylsulfide (DMS), \(\mathrm{CH}_{3}\mathrm{SCH}_{3},\) consists of a sulfur (S) atom bonded to two methyl groups (\(-\mathrm{CH}_{3}\) groups). Each carbon (C) atom in the methyl group forms bonds with three hydrogen (H) atoms and one bond with the sulfur atom. The sulfur atom forms two single bonds, one to each carbon atom. The Lewis structure of DMS is:\[\begin{align*}H & - C - S - C - H \ & | & | \H & H & H \ & | \ & H \\end{align*}\]

Step 2: Determine Bond Angles

In the DMS molecular structure, the central sulfur atom is bonded to two carbon atoms in a tetrahedral arrangement. Due to the two lone pairs on sulfur, the ideal tetrahedral bond angle of \(109.5^{\circ}\) is slightly reduced. So, we expect bond angles close to \(104.5^{\circ}\) near the sulfur due to lone pair-bond pair repulsion.

Step 3: Evaluate Molecular Polarity

The electronegativity of sulfur is higher than that of carbon, creating a polarization towards the sulfur atom in each C-S bond. Electrons are drawn closer to the sulfur, making it slightly negative (\(\delta^{-}\)), forcing the carbons to be slightly positive (\(\delta^{+}\)). Since DMS has an asymmetrical structure and a net molecular dipole, it is polar.

Step 4: Calculate Number of DMS Molecules in Seawater

The concentration of DMS in seawater is given as \(2.7 \,\mathrm{nM}\) or \(2.7 \times 10^{-9} \,\mathrm{mol/m}^3\). According to Avogadro's number, one mole contains \( 6.022 \times 10^{23}\) molecules.To find the total number of molecules in \1.0 \,\mathrm{m}^3\ of seawater:\[\begin{align*}\text{Number of molecules} &= 2.7 \times 10^{-9} \,\text{mol/m}^3 \times 6.022 \times 10^{23} \,\text{molecules/mol} \&= 1.6259 \times 10^{15} \,\text{molecules}.\end{align*}\]

Key Concepts

Lewis structure

Dimethylsulfide, often abbreviated as DMS, is an interesting molecule that can be represented using the Lewis structure. To start, it consists of a sulfur atom bonded to two methyl groups, each of which is denoted as \(-\text{CH}_3\). Each carbon (C) atom in these methyl groups is connected to three hydrogen (H) atoms and one sulfur atom. When sketching out the Lewis structure for DMS, recall:

• Each hydrogen forms a single bond to the carbon.
• Each carbon forms a single bond to sulfur.

Visualizing the connections, the sulfur forms the central atom, flanked by carbons on either side. By placing these bonds on paper, you'll see how the electrons are distributed. The typical representation is:\[\begin{align*}H & - C - S - C - H \ & | | \H & H H \ & | \ & H \\end{align*}\]This structure helps us understand where electrons might be shared or lone pairs might be present.

molecular polarity

Understanding molecular polarity involves examining how electrons are distributed within the molecule. In DMS, the polarity comes from differences in electronegativity between the atoms. Here's what happens:

• Sulfur is more electronegative than carbon, so it pulls shared electrons towards itself in the C-S bonds.
• This electron movement induces partial charges: sulfur becomes slightly negative \((\delta^-)\), while the carbon attached becomes slightly positive \((\delta^+)\).

DMS does not have a symmetrical structure, as both methyl groups ( \(-\text{CH}_3\) ) push down on one side (due to lone pair repulsions as well). This causes an overall molecular dipole across the molecule, making it polar. Polarity affects many properties, like how DMS interacts with other molecules, particularly in solutions.

tetrahedral bond angle

The tetrahedral bond angle is a key concept when studying molecular shapes. Typically, when atoms form a tetrahedral geometry, the bond angle is approximately \(109.5^\circ\). However, DMS has certain peculiarities:

• The sulfur atom has two lone pairs of electrons.
• Lone pairs repel bonding pairs more strongly than bonding pairs repel one another.

These lone pairs cause a deviation from the ideal tetrahedral angle. Therefore, in DMS, the bond angle gets reduced to around \(104.5^\circ\). This reduction affects how the molecule appears in space and is crucial in determining molecular interactions and the overall geometry.

electronegativity

Electronegativity is a term used to describe how strongly an atom attracts electrons towards itself. In examining DMS, we focus on the atoms involved:

• Sulfur is relatively more electronegative than carbon and hydrogen.
• This results in a net dipole moment in the bonds, particularly the C-S bonds.

In simpler terms, electrons in DMS are unevenly distributed, creating spots where electrons are more concentrated. Electronegativity differences explain why sulfur in DMS holds a slightly negative charge, affecting how it interacts with light and other compounds. In many reactions involving S-C-H groups, electronegativity dictates behavior and molecule orientation.

Avogadro's number

To understand how many molecules are in a given sample, we use Avogadro's number, which is \(6.022 \times 10^{23}\) molecules per mole. This number bridges the microscopic world of atoms and molecules with the macroscopic world we observe. In the context of DMS dissolved in seawater:

• A concentration of \(2.7 \times 10^{-9} \text{ mol/m}^3\) is provided.
• Multiplying this by Avogadro's number gives the number of molecules in 1 cubic meter.

So, the calculation goes like this:\[\text{Number of molecules} = 2.7 \times 10^{-9} \text{ mol/m}^3 \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.6259 \times 10^{15} \text{ molecules}\]Through this calculation, we can appreciate just how numerous molecules are, even in tiny concentrations—a testament to the scale at which chemical processes operate.