Problem 101 - A Complete Resource Book in Chemistry for JEE Main

Question

An athlete is given \(100 \mathrm{~g}\) of glucose of energy equivalent to \(1560 \mathrm{~kJ}\). He utilizes \(50 \%\) of this gained energy in the event. In order to avoid storage of energy in the body, calculate the mass of water he would need to perspire. Enthalpy of \(\mathrm{H}_{2} \mathrm{O}\) for evaporation is \(44 \mathrm{~kJ} \mathrm{~mol}^{-1}\). (a) \(346 \mathrm{~g}\) (b) \(316 \mathrm{~g}\) (c) \(323 \mathrm{~g}\) (d) \(319 \mathrm{~g}\)

Step-by-Step Solution

Answer

The mass of water the athlete needs to perspire is approximately 319 g (option d).

Step 1: Calculate energy utilized

The athlete uses 50% of the energy gained from glucose. If the total energy is 1560 kJ, the utilized energy is:\[\text{Utilized Energy} = 0.5 \times 1560 \, \text{kJ} = 780 \, \text{kJ} \]

Step 2: Determine moles of water evaporated

Use the enthalpy of evaporation of water to find out how many moles of water are required to dissipate 780 kJ of energy:\[\text{Moles of } \mathrm{H}_2\mathrm{O} = \frac{780 \, \text{kJ}}{44 \, \text{kJ/mol}} = 17.727 \, \text{mol} \]

Step 3: Calculate mass of water evaporated

Convert moles of water evaporated to grams using the molar mass of water (18 g/mol):\[ \text{Mass of } \mathrm{H}_2\mathrm{O} = 17.727 \, \text{mol} \times 18 \, \text{g/mol} = 319.086 \, \text{g} \]

Step 4: Choose the closest answer

Round the calculated mass to the closest value among the given options: The closest value to 319.086 g is 319 g, which corresponds to option (d).

Key Concepts

Energy Conversion

Energy conversion is a fundamental concept in the study of thermodynamics and chemistry. It involves the transformation of energy from one form to another. In biological systems, like our bodies, the conversion of energy is a continuous process.

For example, when an athlete consumes glucose, a type of sugar, the chemical energy stored in glucose is released and used to power various bodily functions. This process can be thought of as converting chemical energy into kinetic energy that the body can use.

• The energy from glucose is measured in kilojoules (kJ), which is a unit of energy in the metric system.
• In our exercise, the athlete has taken energy equivalent to 1560 kJ from glucose.
• Half of this energy is utilized during physical activity.

This conversion of energy is crucial as it allows the body to perform tasks such as movement and maintaining body temperature, showing how energy conversion sustains life.

Enthalpy of Evaporation

The enthalpy of evaporation, also known as the heat of vaporization, is the energy required to convert a given quantity of a liquid into a gas at a constant temperature and pressure.

In our exercise, the enthalpy of evaporation for water is given as 44 kJ/mol. This means that for 1 mole of water to evaporate, 44 kJ of energy is needed. This energy exchange is crucial for understanding how perspiration helps regulate body temperature.

• The enthalpy of evaporation is important in cooling processes because when a liquid evaporates, it absorbs energy from the surroundings, effectively cooling the surface.
• In the context of the athlete's exercise, knowing the enthalpy allows us to calculate how much water needs to be evaporated to dissipate the utilized body heat.

This knowledge helps explain how sweating cools us down naturally and how the body maintains thermal balance, especially during physical exertion.

Calculation of Molar Mass

Molar mass is a measure of the mass of a substance's molecules in grams per mole, a standard unit in chemistry.

Understanding how to calculate molar mass allows us to convert between the number of particles (molecules, atoms, etc.) and the mass of a substance.

• The molar mass of water is calculated by adding up the atomic masses of two hydrogen atoms and one oxygen atom, which comes to approximately 18 g/mol.
• In our context, this value helps determine the mass of water that evaporates when the athlete perspires.
• With 17.727 moles of evaporated water calculated previously, multiplying by the molar mass gives us the total mass in grams.

Grasping how to calculate and use molar mass is key in translating between the molecular scale and the weight we can measure, important in both academic studies and practical applications.

Glucose Metabolism

Glucose metabolism is the biochemical pathway by which glucose, a simple sugar, is used by the body to produce energy.

This process is vital for athletes as it provides the quick burst of energy needed during physical exertion. It involves several steps where glucose is broken down in cells, releasing energy stored in its chemical bonds.

• The main purpose is to convert glucose into ATP (adenosine triphosphate), the energy currency of the cell.
• For the athlete, glucose metabolism allows the conversion of stored chemical energy in glucose into kinetic energy and heat, fueling muscles and maintaining bodily functions.

Overall, understanding how glucose is metabolized gives insight into how our bodies function under stress and how energy from food is utilized, impacting both health and athletic performance.