Problem 46 - Chemistry The Central Science

Question

The physical fitness of athletes is measured by " \(V_{\mathrm{O}_{2}}\) max," which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill). An average male has a \(V_{\mathrm{O}_{2}}\) max of \(45 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}\) body mass \(/ \mathrm{min}\), but a world-class male athlete can have a \(V_{\mathrm{O}_{2}}\) max reading of \(88.0 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}\) body mass \(/ \mathrm{min.}\) (a) Calculate the volume of oxygen, in mL, consumed in 1 hr by an average man who weighs 185 lbs and has a \(V_{\mathrm{O}_{2}}\) max reading of 47.5 \(\mathrm{mL} \mathrm{O}_{2} / \mathrm{kg}\) body mass \(/ \mathrm{min}\) (b) If this man lost \(20 \mathrm{lb}\), exercised, and increased his \(V_{\mathrm{O}_{2}}\) max to \(65.0 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}\) body mass \(/ \mathrm{min}\), how many mL of oxygen would he consume in \(1 \mathrm{hr}\) ?

Step-by-Step Solution

Answer

For scenario (a), the individual consumes \(239,036.325\,\text{mL}\) of oxygen in 1 hour, and for scenario (b), after losing 20 lbs and increasing the VO2 max, the individual consumes \(291,886.92\,\text{mL}\) of oxygen in 1 hour.

Step 1: Convert weight from lbs to kg

To convert the weight from lbs to kg, use the conversion factor (1 kg = 2.20462 lbs). Weight in kg = Weight in lbs / 2.20462

Step 2: Calculate the volume of oxygen consumed per minute using given VO2 max

Volume of oxygen consumed per minute = VO2 max (in mL/kg/min) * Weight (in kg)

Step 3: Calculate the volume of oxygen consumed in 1 hour

Since there are 60 minutes in one hour, we need to multiply the volume of oxygen consumed per minute by 60. Volume of oxygen consumed in 1 hour = Volume of oxygen consumed per minute * 60 Now, we will perform the calculations for both scenario (a) and scenario (b). (a) Weight in lbs: 185 VO2 max: 47.5 mL O2/kg/min

Step 1a: Convert weight to kg

Weight in kg = 185 lbs / 2.20462 = 83.9145 kg

Step 2a: Calculate the volume of oxygen consumed per minute

Volume of oxygen consumed per minute = 47.5 mL/kg/min * 83.9145 kg = 3983.93875 mL/min

Step 3a: Calculate the volume of oxygen consumed in 1 hour

Volume of oxygen consumed in 1 hour = 3983.93875 mL/min * 60 = 239036.325 mL (b) Weight after losing 20 lbs: 185 - 20 = 165 lbs VO2 max: 65.0 mL O2/kg/min

Step 1b: Convert new weight to kg

New weight in kg = 165 lbs / 2.20462 = 74.8428 kg

Step 2b: Calculate the volume of oxygen consumed per minute with the new VO2 max

Volume of oxygen consumed per minute = 65.0 mL/kg/min * 74.8428 kg = 4864.782 mL/min

Step 3b: Calculate the volume of oxygen consumed in 1 hour

Volume of oxygen consumed in 1 hour = 4864.782 mL/min * 60 = 291886.92 mL So, for scenario (a), the individual consumes 239036.325 mL of oxygen in 1 hour, and for scenario (b), after losing 20 lbs and increasing the VO2 max, the individual consumes 291886.92 mL of oxygen in 1 hour.

Key Concepts

Oxygen Consumption

Understanding oxygen consumption is essential in the field of exercise physiology, particularly when evaluating an athlete's aerobic capacity. Oxygen consumption refers to the amount of oxygen that a person's body uses during physical activity. The more intense the activity, the higher the oxygen consumption, as the muscles require more energy to sustain the effort.

The measurement of oxygen consumed is typically expressed in milliliters of oxygen per kilogram of body weight per minute (mL O₂/kg/min). This unit allows for comparison across individuals of different sizes and fitness levels. The term V̇O₂ max is used to denote the maximum volume of oxygen that an individual can use in one minute and is a key indicator of their cardiovascular fitness.

To improve a student's understanding of this concept, it's important to emphasize the relationship between oxygen uptake and energy expenditure. During aerobic exercises like running or cycling, the body's demand for energy increases, and so does the need for oxygen to produce that energy.

In our example, we calculated the total volume of oxygen consumption over one hour based on the athlete's V̇O₂ max. Providing visuals or analogies, such as likening the amount of oxygen consumed to the number of balloons filled in an hour, can make this abstract concept more tangible for students.

Exercise Physiology

The study of exercise physiology involves understanding the acute responses and chronic adaptations of the body to physical activity. One of the central components of exercise physiology is aerobic fitness, assessed by measuring V̇O₂ max. Aerobic fitness levels are crucial for endurance sports but also have a significant impact on overall health.

When explaining the concept of V̇O₂ max to students, it's beneficial to connect it to real-life activities. For example, a higher V̇O₂ max means that an athlete can perform activities like running, swimming, or cycling at a higher intensity for a longer period before fatigue sets in.

Improving Athletic Performance

Illustrating how athletes work to improve their V̇O₂ max with training can offer students practical insight into the adaptability of the human body. For instance, detailing various training methods, such as interval training or resistance exercises, can show how different strategies are used to increase aerobic capacity. By providing such context, students can better appreciate the physiological changes discussed in the textbook solutions.

Unit Conversion

Unit conversion is a fundamental skill in science and is especially pertinent when dealing with measurement units in physiology and medicine. In the example calculations, we needed to convert weight from pounds to kilograms since the V̇O₂ max is given in terms of kilograms.

To make unit conversion more approachable for students, presenting it as a simple process of multiplication or division using conversion factors is effective. In our case, we describe the conversion of weight from pounds (lbs) to kilograms (kg), using the conversion factor of 1 kg being equal to 2.20462 lbs. Showing step-by-step conversions helps demystify the process and gives students a methodical way to approach similar problems.

Practical Tips for Conversion

Using tools such as conversion charts or even smartphone apps that assist with unit conversion can also be highlighted as helpful resources. Drawing connections to everyday references, such as relating pounds to common weights like a bag of flour, can make this mathematical process more relatable and less intimidating.