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Ch.10 - Gases
Chapter 10, Problem 45

In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In 30 minutes, the average cockroach (running at 0.08 km/h) consumed 1.0 mL of O2 at 101.33 kPa pressure and 20 °C per gram of insect mass. (b) This same cockroach is caught by a child and placed in a 2.0-L fruit jar with a tight lid. Assuming the same level of continuous activity as in the research, how much of the available O2 will the cockroach consume in 1 day? (Air is 21 mol % O2.)

Verified step by step guidance
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First, calculate the total volume of oxygen available in the 2.0-L jar. Since air is 21% oxygen by mole, multiply the total volume of the jar by 0.21 to find the volume of oxygen.
Next, convert the volume of oxygen from liters to milliliters, as the oxygen consumption rate is given in milliliters.
Determine the total oxygen consumption of the cockroach in 1 day. Since the cockroach consumes 1.0 mL of O2 per gram of insect mass in 30 minutes, calculate the total consumption over 24 hours (1 day) by multiplying the 30-minute consumption by the number of 30-minute intervals in a day.
Assume the mass of the cockroach remains constant and use the calculated daily oxygen consumption to determine how much of the available oxygen in the jar will be consumed.
Finally, compare the total available oxygen in the jar to the total oxygen consumption over 1 day to determine how much of the available oxygen will be consumed by the cockroach.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Oxygen Consumption and Metabolism

Oxygen consumption is a measure of metabolic activity, reflecting how organisms utilize oxygen for energy production. In this context, the cockroach's oxygen consumption rate indicates its metabolic rate while running. Understanding how metabolic rates vary with activity levels is crucial for predicting oxygen needs in different scenarios.
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Gas Laws and Partial Pressure

Gas laws, particularly Dalton's Law of Partial Pressures, explain how gases behave in mixtures. In this case, the total pressure in the jar affects the amount of oxygen available for the cockroach. Knowing that air is composed of 21% oxygen allows us to calculate the partial pressure of oxygen, which is essential for determining how much oxygen the cockroach can consume.
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Volume and Molar Relationships

Understanding the relationship between volume, moles, and gas behavior is key to solving this problem. The ideal gas law (PV=nRT) can be used to relate the volume of the jar to the number of moles of oxygen present. This relationship helps in calculating how much oxygen the cockroach will consume over a specified time, given its metabolic rate.
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Related Practice
Textbook Question

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (b) What volume would the gas occupy at STP?

Textbook Question

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (c) At what temperature would the pressure in the tank equal 15.2 MPa?

Textbook Question

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (d) What would be the pressure of the gas, in kPa, if it were transferred to a container at 24 °C whose volume is 55.0 L?

Textbook Question

In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In 30 minutes the average cockroach (running at 0.08 km/h) consumed 1.0 mL of O2 at 101.33 kPa pressure and 20 °C per gram of insect mass. (a) How many moles of O2 would be consumed in 1 day by a 6.3-g cockroach moving at this speed?

Textbook Question

The physical fitness of athletes is measured by 'VO2 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 VO2 max of 45 mL O2/kg body mass/min, but a world-class male athlete can have a VO2 max reading of 88.0 mL O2/kg body mass/min. (a) Calculate the volume of oxygen, in mL, consumed in 1 hr by an average man who weighs 85 kg and has a VO2 max reading of 47.5 mL O2/kg body mass/min. (b) If this man lost 10 kg, exercised, and increased his VO2 max to 65.0 mL O2/kg body mass/min, how many mL of oxygen would he consume in 1 hr?

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Textbook Question
Rank the following gases from least dense to most dense at101.33 kPa and 298 K: O2, Ar, NH3, HCl.