Question

Of the following liquids at \(20^{\circ} \mathrm{C}\), which has the smallest viscosity? (a) Dodecane, \(\mathrm{C}_{12} \mathrm{H}_{26} ;\) (b) n-nonane, \(\mathrm{C}_{9} \mathrm{H}_{20} ;\) (c) n-heptane \(\mathrm{C}_{7} \mathrm{H}_{16} ;\) (d) n-pentane \(\mathrm{C}_{5} \mathrm{H}_{12}\)

Short answer

The smallest viscosity is from n-pentane (\(C_{5}H_{12}\)).

Step-by-step solution

Identify molecule size from chemical formulas

The molecule size is relative to the number of carbon (C) atoms in the molecule. Dodecane C12H26 has 12 carbon atoms, n-nonane C9H20 has 9, n-heptane C7H16 has 7, and n-pentane C5H12 has 5.

Relate molecule size to intermolecular forces

Larger molecules have greater intermolecular forces. This means molecules with more carbon atoms will have greater resistance to flow (greater viscosity).

Identify the smallest molecule and therefore the lowest viscosity

The smallest molecule among those given is n-pentane with only 5 carbon atoms, hence it has the smallest intermolecular forces and therefore the smallest viscosity.

Key concepts

Molecule Size

When we talk about molecule size, we’re essentially referring to the dimensions or volume that a single molecule occupies. In organic molecules like hydrocarbons, the size can typically be estimated by the number of carbon atoms they contain. For instance, a molecule with a longer carbon chain will be larger than one with a shorter chain.

Considering our exercise, the molecule sizes vary based on their chemical formulas. Dodecane, for example, with a chemical formula of \texttt{C\(_{12}\) H\(_{26}\)}, has a larger molecular size compared to n-pentane, which has the formula \texttt{C\(_{5}\) H\(_{12}\)}. A larger molecule size commonly translates into greater surface area, which allows more extensive intermolecular interactions. This interplay greatly influences physical properties such as boiling point, melting point, and viscosity.

The exercise hinted that understanding molecule size is crucial for deducing the viscosity of a liquid. By examining the carbon chain length from the chemical formulas provided, we can conclude that n-pentane, the smallest molecule among the given hydrocarbons, will likely exhibit the lowest viscosity.

Intermolecular Forces

Intimately linked to molecule size are the intermolecular forces, the attractions or repulsions that act between neighboring molecules. There are different types of intermolecular forces, including van der Waals forces, dipole-dipole interactions, and hydrogen bonds. For nonpolar molecules like hydrocarbons, van der Waals forces, or dispersion forces, are the primary intermolecular interactions at play.

The strength of these forces generally increases with larger molecule size since there is more area for the forces to take effect. This leads to a higher viscosity, as the molecules will resist flowing past each other more strongly. In the case of our exercise, n-pentane has the weakest van der Waals forces due to its small size, resulting in lower viscosity compared to its larger counterparts such as dodecane, which has stronger intermolecular forces and higher viscosity.

The practical application of understanding these forces comes into play when predicting and comparing the physical properties of different substances, vital for material selection and chemical manufacturing processes.

Chemical Formulas

Chemical formulas provide a concise way to describe the composition of molecules. They tell us the types and quantities of atoms in a molecule. In the context of our exercise, the formulas of dodecane \texttt{(C\(_{12}\) H\(_{26}\))}, n-nonane \texttt{(C\(_{9}\) H\(_{20}\))}, n-heptane \texttt{(C\(_{7}\) H\(_{16}\))}, and n-pentane \texttt{(C\(_{5}\) H\(_{12}\))} provide critical information regarding molecule size and structure.

Interpreting these chemical formulas allows us to determine the number of carbon atoms, which directly ties in with molecule size and therefore the intermolecular forces present. This process is essential for predicting how a substance will behave physically. For students, mastering how to decode chemical formulas is fundamental, as it is not just about the individual atoms but also about how the molecule's structure will influence its properties and interactions with other molecules.