Problem 19 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

(a) List the non-covalent interactions present in liquid water. Which is responsible for the strongest interactions between the molecules? (b) Explain why the value of \(\Delta_{\mathrm{vap}} H^{\mathrm{O}}\left(\mathrm{H}_{2} \mathrm{O}\right)\) is unusually high for a molecule of its size. (c) \(\ln\) a storm, \(3 \mathrm{cm}\) of rain falls on the city of Leeds, which has an area of approximately \(500 \mathrm{km}^{2}\). Estimate the energy released as heat when this quantity of water condenses from vapour to form rain. (Density of water is \(1.00 \mathrm{gcm}^{-3}\) \(\Delta_{\mathrm{vap}} H^{\mathrm{e}}\left(\mathrm{H}_{2} \mathrm{O}\right)=+40.7 \mathrm{kJmol}^{-1}\) at \(298 \mathrm{K}\) (d) The output from a large 2000 MW power station is \(2000 \mathrm{MJs}^{-1}\). How long would it take the power station to deliver the same quantity of energy as was released by the condensation of the rain in (c)? (Sections 1.7 and 1.8 )

Step-by-Step Solution

Answer

(a) Hydrogen bonds; strongest in water. (b) Strong hydrogen bonds increase \( \Delta_{\mathrm{vap}} H^{\mathrm{O}} \). (c) Energy released: \(3.39 \times 10^{13} \mathrm{kJ} \). (d) Takes \( 538 \) years for the power station.

Step 1: Identify Non-Covalent Interactions in Liquid Water

The non-covalent interactions present in liquid water include hydrogen bonds, dipole-dipole interactions, and London dispersion forces. Among these, hydrogen bonds are the strongest and most significant interaction due to the polarity of water molecules and its ability to form hydrogen bonds with adjacent molecules.

Step 2: Explain High Enthalpy of Vaporization

The high value of \( \Delta_{\mathrm{vap}} H^{\mathrm{O}}(\mathrm{H}_{2} \mathrm{O}) \) is due to strong hydrogen bonding in liquid water. Breaking these intermolecular hydrogen bonds requires a significant amount of energy, making the enthalpy of vaporization unusually high for a molecule of water's size.

Step 3: Calculate the Volume and Mass of Rainwater

Calculate the volume of rainwater by multiplying the area of Leeds by the rain depth: \( 500 \mathrm{km}^2 \times 3 \mathrm{cm} = 500,000,000 \mathrm{m}^2 \times 0.03 \mathrm{m} = 15,000,000 \mathrm{m}^3 \). The mass of water, using its density, is \( 15,000,000 \mathrm{m}^3 \times 1,000 \mathrm{kg/m}^3 = 15,000,000,000 \mathrm{kg} \).

Step 4: Calculate Energy Released as Heat

First, convert the mass of water to moles: \( \frac{15,000,000,000 \mathrm{kg}}{0.018 \mathrm{kg/mol}} = 8.33 \times 10^{11} \mathrm{mol} \). Then, calculate the energy released using the enthalpy change for condensation: \( 8.33 \times 10^{11} \mathrm{mol} \times 40.7 \mathrm{kJ/mol} = 3.39 \times 10^{13} \mathrm{kJ} \).

Step 5: Determine Time Required to Deliver Energy

Convert the energy released to megajoules: \( 3.39 \times 10^{13} \mathrm{kJ} = 3.39 \times 10^{13} \mathrm{MJ} \). Given the power station's output of \( 2000 \mathrm{MJ/s} \), the time required is \( \frac{3.39 \times 10^{13} \mathrm{MJ}}{2000 \mathrm{MJ/s}} = 1.695 \times 10^{10} \mathrm{s} \). Convert to years for practicality: \( \frac{1.695 \times 10^{10} \mathrm{s}}{3.154 \times 10^{7} \mathrm{s/year}} \approx 538.1 \mathrm{years} \).

Key Concepts

Hydrogen Bonding

In liquid water, molecules are connected through different types of non-covalent interactions, but hydrogen bonding stands out as the most significant one. A hydrogen bond occurs when a hydrogen atom is attracted to an electronegative atom, such as oxygen, in a nearby molecule. This forms a bridge, bonding the molecules closely together.

Water is a polar molecule; its oxygen has a slight negative charge, while the hydrogens have a slight positive charge. This difference in charge, or polarity, causes water molecules to align in specific ways, creating pathways for hydrogen bonds.

• This kind of interaction contributes to water's high boiling point compared to other molecules of similar size.
• Hydrogen bonds play a vital role in defining the water's structure and properties, generating a cohesive nature and surface tension.
• They also facilitate many biological processes and reactions within living organisms.

Constantly forming and breaking, hydrogen bonds are crucial in maintaining the liquid state of water under standard conditions.

Enthalpy of Vaporization

The enthalpy of vaporization ( \( \Delta_{\mathrm{vap}} H^{\mathrm{O}}\left(\mathrm{H}_{2} \mathrm{O}\right) \) ) is the heat required to convert a liquid into a gas at constant pressure. For water, this value is unusually high, making it an intriguing study area. The main reason for this is hydrogen bonding.

When water transitions from liquid to gas, each molecule must break free from the surrounding network of hydrogen bonds. This process demands a considerable energy input.

• Breaking these bonds absorbs a large amount of energy, which substantially raises the enthalpy of vaporization.
• As a result, water has a temperature-stabilizing effect, with climates in its vicinity less prone to extreme temperature changes.
• This property is crucial for bodily temperature regulation in living organisms and maintaining ecological balance.

Water's enthalpy of vaporization helps us understand its role in thermal regulation in nature and technology.

Energy Calculations

To understand how much energy is released when water changes state, such as from vapor to liquid, we perform energy calculations. In our scenario, rainfall over Leeds can release substantial heat energy due to condensation. Here's how you can calculate it:

First, compute the mass of the raining water. Calculate the area of impact and multiply by the depth of the rain. Then, using the density of water (1 g/cm³), convert this volume into mass.

• Volume = Area x Depth = 500 km² x 3 cm = 15 million m³ (15 billion liters).
• Mass = Volume x Density = 15 billion kg (since 1 liter of water weighs about 1 kg).

Next, convert the mass of water to moles using water's molar mass. Once you have the number of moles, calculate the total energy released using the enthalpy of vaporization. The result offers insight into the energy dynamics associated with water's phase changes.

Rainfall Condensation

When water vapor condenses to form rain, a significant amount of energy, in the form of heat, is released. This process is crucial for understanding climatic and weather patterns. Rainfall condensation is an exothermic reaction, meaning it releases heat into the environment.

The condensed vapor turns back into liquid water, liberating energy equivalent to the energy needed for vaporization. Meteorologically, this process can moderate temperatures by releasing heat into the atmosphere, affecting storm systems and thermal currents.

• Condensation is vital for cloud formation, influencing precipitation cycles.
• The energy released can drive winds and contribute to weather phenomena.
• This self-regulating cycle plays an essential role in maintaining ecological and climate stability.

Understanding rainfall condensation helps us predict and interpret weather patterns and its impact on global weather dynamics.

Power Station Energy Output

Power stations play a critical role in converting energy from various sources into electricity. Their output can be equated to other energy processes for comparison. In the context of our rainfall scenario, understanding the time a power station would need to deliver the same energy as rain condensation is intriguing.

A large power station might produce energy at a continuous rate, such as 2000 MW, which translates to 2000 MJ per second. Converting the total energy released by the rain into megajoules offers a way to equate these two vastly different energy scenarios.

• Calculate the total energy from the rain and express it in MJ.
• Compare this with the station's output to find the equivalent time for energy production.
• This comparison provides a tangible sense of the vast energy dynamics occurring in natural processes.

Such calculations enlighten our understanding of how human-engineered systems relate to natural energy transformations on Earth.