If the pressure of N2 and H2 mixture in a closed apparatus is 1000 atm and 20% of the mixture reacts then the pressure at the same tempature would be.

To solve this problem, we need to apply some fundamental principles of gas behavior and the concept of partial pressures. Let's break it down step by step. We start with a mixture of nitrogen (N2) and hydrogen (H2) at a total pressure of 1000 atm, and we know that 20% of this mixture reacts.

Understanding the Mixture

Initially, we can represent the total pressure of the gas mixture using Dalton's Law of Partial Pressures. This law states that in a mixture of non-reacting gases, the total pressure is equal to the sum of the partial pressures of the individual gases.

Calculating Initial Partial Pressures

Assuming our mixture consists of 1000 atm of total pressure, let's denote the partial pressures of N2 and H2. If we do not know their exact proportions, we can denote them as P(N2) and P(H2). For simplicity, let's assume they were initially in equal proportions, meaning:

• P(N2) = 500 atm
• P(H2) = 500 atm

This assumption will help us understand the changes during the reaction.

Reaction Dynamics

The mixture of nitrogen and hydrogen can react to form ammonia (NH3) according to the equation:N2 + 3H2 ⇌ 2NH3From this equation, we observe that one mole of nitrogen reacts with three moles of hydrogen. If 20% of the mixture reacts, we need to determine how much of each gas is consumed.

Calculating the Reaction

If 20% of the total pressure of the gas mixture reacts, we can calculate the pressure of the gases that react. Since the total pressure is 1000 atm, the pressure that reacts is:Pressure Reacted = 1000 atm × 0.20 = 200 atmThis pressure corresponds to the consumption of nitrogen and hydrogen in the stoichiometric ratio from the reaction equation.

Distributing the Reacted Pressure

In our assumption that nitrogen and hydrogen started equally, we will consider the partial pressures consumed during the reaction. For our reaction, for every 1 atm of N2 that reacts, 3 atm of H2 react. Therefore, if we let x be the pressure of N2 consumed, then:

• Pressure of N2 consumed = x
• Pressure of H2 consumed = 3x

From our earlier calculation, we know that the total reacted pressure is 200 atm:x + 3x = 200 atm This simplifies to:4x = 200 atmThus, we find:x = 50 atmSo, 50 atm of nitrogen and 150 atm of hydrogen react.

Final Pressure Calculation

Now, we can determine the new partial pressures after the reaction takes place:

• Remaining P(N2) = 500 atm - 50 atm = 450 atm
• Remaining P(H2) = 500 atm - 150 atm = 350 atm

To find the total pressure after the reaction, we need to account for the pressure of ammonia produced. According to the reaction stoichiometry, 50 atm of N2 produces 100 atm of NH3 (since 1 N2 produces 2 NH3):P(NH3) = 2 × 50 atm = 100 atmNow, we can sum the final pressures:Total Pressure = P(N2) + P(H2) + P(NH3)Substituting the values:Total Pressure = 450 atm + 350 atm + 100 atm = 900 atmThus, the final pressure in the system, after 20% of the gas mixture reacts, will be 900 atm.