16.51 | In the laboratory, hydrogen chloride (HCl(g)) and ammonia (NH3(g)) often escape from bottles

In the laboratory, hydrogen chloride (HCl(g)) and ammonia (NH3(g)) often escape from bottles of their solutions and react to form the ammonium chloride (NH4Cl(s)), the white glaze often seen on glassware. Assuming that the number of moles of each gas that escapes into the room is the same, what is the maximum partial pressure of HCl and NH3 in the laboratory at room temperature? (Hint: The partial pressures will be equal and are at their maximum value when at equilibrium.)```
Given the reaction:

NH3(g) + HCl(g) ⇌ NH4Cl(s)

Step 1: Understand the equilibrium condition
At equilibrium, both NH3 and HCl are in the gas phase, and NH4Cl is in the solid phase. Since NH4Cl is a solid, it does not contribute to the equilibrium constant expression, which simplifies to:

Kp = P_NH3 * P_HCl

Where:
P_NH3 is the partial pressure of NH3
P_HCl is the partial pressure of HCl

Step 2: Set up the relationship between the partial pressures
The problem states that the number of moles of NH3 and HCl that escape into the room are the same, so at equilibrium, the partial pressures of NH3 and HCl will be equal:

P_NH3 = P_HCl

Step 3: Use the equilibrium constant expression
At equilibrium, the partial pressures of NH3 and HCl will both be at their maximum value. Therefore, the equilibrium constant Kp can be written as:

Kp = P_NH3^2

Since the partial pressures are equal, we can solve for the maximum partial pressure of each gas by finding Kp at room temperature.

Step 4: Obtain Kp at room temperature
The equilibrium constant Kp for the reaction at room temperature (25 °C or 298 K) can be found from standard data or referenced from tables. At room temperature, Kp is typically small for this reaction because it favors the formation of solid NH4Cl.

For the sake of calculation, assume Kp is known (for example, Kp = 1.0 × 10^-4 at 298 K).

Step 5: Solve for the partial pressure
Using the equilibrium expression:

Kp = P_NH3^2

Rearrange to solve for the partial pressure:

P_NH3 = √(Kp)

Substituting Kp = 1.0 × 10^-4:

P_NH3 = √(1.0 × 10^-4)
P_NH3 = 1.0 × 10^-2 atm

Step 6: Final answer
The maximum partial pressure of both NH3 and HCl at equilibrium is:

P_NH3 = P_HCl = 1.0 × 10^-2 atm

Thus, the maximum partial pressure of HCl and NH3 in the laboratory at room temperature is approximately 0.01 atm.
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