A mixture of Nitrogen and Hydrogen (1:3 mole ratio) is at an initial pressure of 200atm. If 20% of the mixture reacts by the time equilibrium is reached, the equilibrium pressure of the mixture is

Options

A. Data insufficient
B. 180 atm
C. 170 atm
D. 160 atm

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Initial Moles of Nitrogen and Hydrogen
Given the mole ratio of Nitrogen (N₂) to Hydrogen (H₂) is 1:3, we can express the moles as follows:
- Let the moles of N₂ = x
- Then the moles of H₂ = 3x

### Step 2: Calculate the Total Moles in the Mixture
The total moles in the mixture can be calculated as:
\[ \text{Total moles} = x + 3x = 4x \]

### Step 3: Calculate the Initial Pressure Contribution of Each Gas
The initial pressure of the mixture is given as 200 atm. The partial pressure of each gas can be calculated using the mole fraction:
- The mole fraction of N₂ = \( \frac{x}{4x} = \frac{1}{4} \)
- The mole fraction of H₂ = \( \frac{3x}{4x} = \frac{3}{4} \)

Using Dalton's Law of Partial Pressures:
- Initial pressure of N₂ = \( 200 \times \frac{1}{4} = 50 \, \text{atm} \)
- Initial pressure of H₂ = \( 200 \times \frac{3}{4} = 150 \, \text{atm} \)

### Step 4: Calculate the Total Initial Pressure
The total initial pressure is already given as 200 atm.

### Step 5: Calculate the Amount of Reactants that React
It is given that 20% of the mixture reacts. Therefore, the pressure of the mixture that reacts is:
\[ \text{Pressure reacted} = 200 \times \frac{20}{100} = 40 \, \text{atm} \]

### Step 6: Determine the Change in Pressure Due to Reaction
From the balanced chemical reaction:
\[ N_2 + 3H_2 \rightarrow 2NH_3 \]
1 mole of N₂ reacts with 3 moles of H₂ to produce 2 moles of NH₃. Thus, the change in pressure can be calculated:
- For every 4 moles of reactants (1 N₂ + 3 H₂), we produce 2 moles of NH₃.
- The pressure decrease due to the reaction is 40 atm (reactants) which produces 20 atm of NH₃.

### Step 7: Calculate the Equilibrium Pressure
The equilibrium pressure can be calculated by subtracting the pressure that reacted from the initial pressure:
\[ \text{Equilibrium Pressure} = \text{Initial Pressure} - \text{Pressure reacted} \]
\[ \text{Equilibrium Pressure} = 200 \, \text{atm} - 20 \, \text{atm} = 180 \, \text{atm} \]

### Final Answer
The equilibrium pressure of the mixture is **180 atm**.

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