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Ch.10 - Gases
Chapter 10, Problem 45a

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?

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1
Convert the oxygen consumption from mL to liters by dividing by 1000, since 1 L = 1000 mL.
Use the ideal gas law, PV = nRT, to calculate the number of moles of O2 consumed. Rearrange the formula to solve for n (moles): n = PV / RT.
Substitute the given values into the ideal gas law equation: P = 101.33 kPa, V = volume in liters, R = 8.314 L·kPa/(mol·K), and T = 20 °C converted to Kelvin (T = 20 + 273.15).
Calculate the total volume of O2 consumed in 1 day by multiplying the volume consumed in 30 minutes by the number of 30-minute intervals in a day (48 intervals).
Calculate the total moles of O2 consumed in 1 day by multiplying the moles of O2 consumed in 30 minutes by the number of 30-minute intervals in a day.

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Key Concepts

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

Molar Volume of Gases

The molar volume of a gas at standard temperature and pressure (STP) is approximately 22.4 liters per mole. This concept is crucial for converting the volume of oxygen consumed into moles, as it allows us to relate the measured volume of gas to the number of moles using the ideal gas law.
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Ideal Gas Law

The ideal gas law, represented as PV = nRT, relates the pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T) of a gas. Understanding this law is essential for calculating the number of moles of oxygen consumed under specific conditions of pressure and temperature.
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Oxygen Consumption Rate

The oxygen consumption rate indicates how much oxygen is used by an organism over a specific time period, typically expressed in mL O2 per gram of body mass per hour. In this experiment, knowing the rate allows us to calculate the total oxygen consumed by the cockroach over a 24-hour period based on its mass and activity level.
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