Dinitrogen pentoxide (N2O5) decomposes in chloroform as a solvent to yield NO2 and O2. The decomposition is first order with a rate constant at 45 _x001E_C of 1.0 * 10^-5 s^-1. Calculate the partial pressure of O2 produced from 1.00 L of 0.600 M N2O5 solution at 45 _x001E_C over a period of 20.0 h if the gas is collected in a 10.0-L container. (Assume that the products do not dissolve in chloroform.)

Verified step by step guidance

Step 1: Determine the initial moles of N2O5 using the concentration and volume of the solution. Use the formula: moles = concentration (M) * volume (L).

Step 2: Use the first-order kinetics equation to find the remaining concentration of N2O5 after 20.0 hours. The equation is: [A] = [A]0 * e^(-kt), where [A]0 is the initial concentration, k is the rate constant, and t is the time in seconds.

Step 3: Calculate the change in moles of N2O5, which is the initial moles minus the moles remaining after 20.0 hours. This change represents the moles of N2O5 that have decomposed.

Step 4: Use the stoichiometry of the reaction to determine the moles of O2 produced. The balanced equation for the decomposition is: 2 N2O5 -> 4 NO2 + O2. From this, determine the moles of O2 produced from the decomposed N2O5.

Step 5: Calculate the partial pressure of O2 using the ideal gas law: PV = nRT. Use the moles of O2, the volume of the container (10.0 L), and the appropriate value for R (0.0821 L atm/mol K) to find the pressure, assuming the temperature is constant at 45°C (convert to Kelvin).

Key Concepts

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

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. In this case, the decomposition of dinitrogen pentoxide (N2O5) follows first-order kinetics, meaning that as N2O5 decomposes, the rate of reaction depends solely on its concentration. The rate constant (k) quantifies this relationship, allowing for the calculation of concentration changes over time.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T) of a gas. In this problem, after calculating the moles of O2 produced from the decomposition of N2O5, the Ideal Gas Law can be used to determine the partial pressure of O2 in a specified volume (10.0 L) at a given temperature. This law is fundamental for understanding gas behavior under varying conditions.

Concentration and Molarity

Concentration, often expressed in molarity (M), is a measure of the amount of solute in a given volume of solution. In this scenario, the initial concentration of N2O5 is given as 0.600 M, which indicates that there are 0.600 moles of N2O5 per liter of solution. Understanding how to convert between concentration and moles is essential for calculating the amount of O2 produced during the reaction and subsequently applying the Ideal Gas Law.

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E + S ⇌ ES (fast)

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where E = enzyme, S = substrate, ES = enzyme9substrate complex, and P = product.

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