For the thermal decomposition of nitrous oxide, 2 N2O1g2S 2 N21g2 + O21g2, values of the parameters in the Arrhenius equation are A = 4.2 * 109 s-1 and Ea = 222 kJ>mol. If a stream of N2O is passed through a tube 25 mm in diameter and 20 cm long at a flow rate of 0.75 L/min at what temperature should the tube be maintained to have a partial pressure of 1.0 mm of O2 in the exit gas? Assume that the total pressure of the gas in the tube is 1.50 atm.

Verified step by step guidance

1. Identify the reaction: The decomposition of nitrous oxide (N2O) into nitrogen (N2) and oxygen (O2) is given by the equation: 2 N2O(g) -> 2 N2(g) + O2(g).
2. Use the Arrhenius equation: The rate constant k can be determined using the Arrhenius equation: k = A * e^(-Ea/(RT)), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
3. Calculate the rate of formation of O2: Since the reaction produces 1 mole of O2 for every 2 moles of N2O decomposed, use the flow rate and the volume of the tube to determine the rate of formation of O2.
4. Relate the rate of formation to partial pressure: Use the ideal gas law to relate the rate of formation of O2 to its partial pressure in the exit gas. The partial pressure of O2 is given as 1.0 mm Hg.
5. Solve for temperature: Rearrange the Arrhenius equation to solve for the temperature T that will result in the desired partial pressure of O2, considering the total pressure and flow conditions.

Key Concepts

Arrhenius Equation

The Arrhenius equation describes the temperature dependence of reaction rates. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature in Kelvin. Understanding this equation is crucial for determining how temperature affects the rate of the thermal decomposition of nitrous oxide.

Partial Pressure

Partial pressure refers to the pressure exerted by a single component of a gas mixture. According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of its individual components. In this question, knowing how to calculate and manipulate partial pressures is essential for determining the conditions under which the desired amount of O2 is produced in the exit gas.

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature, pressure, and volume. Key laws include Boyle's Law, Charles's Law, and the Ideal Gas Law (PV = nRT). These principles are necessary for understanding how the flow rate, volume, and pressure of gases interact in the tube, which is critical for solving the problem regarding the thermal decomposition of nitrous oxide.