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A nitrogen-hydrogen mixture initially in...

A nitrogen-hydrogen mixture initially in the moler ratio of `1:3` reached equilibrium to from ammonia when 25% of the `N_(2)and N_(2)` had reacterd .If the pressure of the system was 21 atm , the partial pressure of ammonia at the equilibrium was :

A

`4.5 atm`

B

`3.0`atm

C

`2.0`atm`

D

`1.5atm`

Text Solution

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To solve the problem step by step, we will follow the process of determining the equilibrium conditions and calculating the partial pressure of ammonia. ### Step 1: Write the balanced chemical equation. The reaction for the formation of ammonia from nitrogen and hydrogen is given by: \[ N_2 + 3H_2 \rightleftharpoons 2NH_3 \] ### Step 2: Define initial moles based on the molar ratio. Given the initial molar ratio of nitrogen to hydrogen is 1:3, we can assume: - Let the number of moles of \( N_2 \) be \( a \). - Therefore, the number of moles of \( H_2 \) will be \( 3a \). - The initial moles of ammonia \( NH_3 \) is \( 0 \). ### Step 3: Determine the change in moles at equilibrium. It is given that 25% of nitrogen has reacted. Therefore: - The amount of nitrogen that reacted is \( 0.25a \). - According to the stoichiometry of the reaction, for every 1 mole of \( N_2 \) that reacts, 3 moles of \( H_2 \) react and 2 moles of \( NH_3 \) are formed. Thus: - Moles of \( N_2 \) at equilibrium: \[ a - 0.25a = 0.75a \] - Moles of \( H_2 \) that reacted: \[ 3 \times 0.25a = 0.75a \] - Moles of \( H_2 \) at equilibrium: \[ 3a - 0.75a = 2.25a \] - Moles of \( NH_3 \) formed: \[ 2 \times 0.25a = 0.5a \] ### Step 4: Calculate the total moles at equilibrium. Now, we can calculate the total number of moles at equilibrium: \[ \text{Total moles} = \text{moles of } N_2 + \text{moles of } H_2 + \text{moles of } NH_3 \] \[ = 0.75a + 2.25a + 0.5a = 3.5a \] ### Step 5: Calculate the mole fraction of ammonia. The mole fraction of ammonia (\( X_{NH_3} \)) is given by: \[ X_{NH_3} = \frac{\text{moles of } NH_3}{\text{total moles at equilibrium}} = \frac{0.5a}{3.5a} = \frac{0.5}{3.5} = \frac{1}{7} \] ### Step 6: Calculate the partial pressure of ammonia. The partial pressure of ammonia (\( P_{NH_3} \)) can be calculated using the total pressure of the system: \[ P_{NH_3} = X_{NH_3} \times P_{\text{total}} \] Given that the total pressure \( P_{\text{total}} \) is 21 atm: \[ P_{NH_3} = \frac{1}{7} \times 21 \text{ atm} = 3 \text{ atm} \] ### Conclusion The partial pressure of ammonia at equilibrium is **3 atm**. ---
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