Question

An athlete is given 100 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) \(319 \mathrm{~g}\)

Short answer

The mass of water he needs to perspire is approximately 319 g, so the correct answer is (d).

Step-by-step solution

Calculate Utilized Energy

The athlete utilizes 50% of the given energy. Hence, the utilized energy is calculated as follows:\[ \text{Utilized Energy} = 0.5 \times 1560 \, \text{kJ} = 780 \, \text{kJ} \]

Determine Moles of Water Evaporated

Given the enthalpy of evaporation of water as \(44 \, \text{kJ/mol}\), we calculate the moles of water required to evaporate using the utilized energy:\[ \text{Moles of } \mathrm{H}_2 \mathrm{O} = \frac{780 \, \text{kJ}}{44 \, \text{kJ/mol}} \approx 17.727 \, \text{mol} \]

Calculate Mass of Water

The molar mass of water (\(\mathrm{H}_2\mathrm{O}\)) is \(18 \, \text{g/mol}\). Calculate the total mass of water that needs to be evaporated:\[ \text{Mass of Water} = 17.727 \, \text{mol} \times 18 \, \text{g/mol} = 319.086 \, \text{g} \]

Select the Closest Answer

The calculated mass of approximately \(319.086 \, \text{g}\) is closest to option (d) \(319 \, \text{g}\). Therefore, the correct answer is (d).

Key concepts

Enthalpy of evaporation

Enthalpy of evaporation is a key concept in thermodynamics. It refers to the amount of energy required to convert a liquid into a vapor without changing its temperature. For water, this enthalpy is significant because water is commonly found on Earth and is vital for many processes. The enthalpy of evaporation is given as a specific energy value per mole of substance. For water (H_2O), the enthalpy of evaporation is 44 kJ/mol. This means that for every mole of water to transition from liquid to gas, 44 kJ of energy must be provided. Understanding this concept is crucial as it helps in calculating how much water would evaporate using a specific amount of energy, like in the case of the athlete sweating to regulate body temperature.

Energy conversion

Energy conversion involves changing one form of energy into another. In the context of the given exercise, the focus is on how the energy from glucose, a simple sugar, is converted into different forms within the body. When an athlete consumes glucose, it is metabolized and converted into energy. In this problem, 1560 kJ of energy is initially available. However, the athlete only uses 50% of this energy, which is 780 kJ. The body uses this energy primarily to function during activities, and some of it is lost as heat. Any excess energy can potentially convert into fat or be dissipated through processes like evaporation of sweat.

Molar mass calculation

Molar mass calculation is essential to determine the mass of a substance from its amount in moles. To do this, we need the molar mass of the substance, which is the mass of one mole of that substance, typically measured in grams per mole. For water (H_2O), the molar mass is 18 g/mol. This means that one mole of water weighs 18 grams. In the exercise, we calculate how much water needs to be evaporated to use up the athlete's utilized energy. By knowing the number of moles of water that need evaporating (17.727 mol), we compute the total mass by multiplying the number of moles by the molar mass: \[ \text{Mass of Water} = 17.727 \, \text{mol} \times 18 \, \text{g/mol} = 319.086 \, \text{g} \] This gives us the mass of water needed to avoid extra energy storage.

Exercise physiology

Exercise physiology explores how the body responds to physical activity. Particularly, it looks at how energy from food is used and managed during exercise. When engaging in strenuous activities, the body requires a significant amount of energy. The exercise here provides insight into how energy management is critical for athletes. When glucose is consumed, it is broken down to provide energy for muscle contractions and other metabolic activities. Furthermore, exercise physiology considers how byproducts like heat are managed. Sweating is a mechanism the body uses to cool down, and in this scenario, the athlete uses 50% of their energy to perspire and evaporate water, effectively releasing excess heat and preventing energy from being stored as fat. Understanding these physiological processes can help optimize an athlete's performance and recovery.