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 1 h the average cockroach running at 0.08 km/h consumed 0.8 mL of O2 at 1 atm pressure and 24°C per gram of insect mass. a. How many moles of O2 would be consumed in 1 h by a 5.2-g cockroach moving at this speed?

Verified step by step guidance

1. 1. First, we need to understand that the given oxygen consumption is per gram of insect mass. So, for a 5.2-g cockroach, the total oxygen consumption would be 5.2 times the given rate. That is, 5.2 * 0.8 mL = 4.16 mL of O2.
2. 2. Now, we need to convert this volume of O2 at the given conditions to moles. We can use the ideal gas law for this. The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
3. 3. We know that at STP (Standard Temperature and Pressure, which is 0°C and 1 atm), 1 mole of any gas occupies 22.4 L. However, our conditions are not at STP. The temperature is 24°C, not 0°C. So, we need to adjust for this. We can convert the temperature to Kelvin by adding 273 to the Celsius temperature. So, 24°C = 297 K.
4. 4. Now, we can rearrange the ideal gas law to solve for n (number of moles). The rearranged formula is n = PV/RT. We know that P = 1 atm, V = 4.16 mL (which we need to convert to L by dividing by 1000, so V = 0.00416 L), R = 0.0821 L.atm/K.mol (the value of R in these units), and T = 297 K.
5. 5. Substitute these values into the formula to find the number of moles of O2 consumed by the cockroach in 1 hour.

Key Concepts

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 essential for converting the volume of gas consumed (in mL) into moles. In this case, knowing the volume of O2 consumed allows us to apply the ideal gas law or molar volume relationships to find the number of moles.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. In this context, it helps determine how the amount of oxygen consumed relates to the mass of the cockroach. By using the oxygen consumption rate per gram of insect mass, we can calculate the total oxygen consumed by the specific mass of the cockroach.

Gas Laws

Gas laws describe the behavior of gases under various conditions of pressure, volume, and temperature. In this scenario, the ideal gas law (PV=nRT) can be applied to relate the pressure, volume, and temperature of the oxygen consumed. Understanding these relationships is crucial for accurately calculating the moles of O2 based on the experimental conditions provided.