The decomposition of NH4Cl can be accomplished by heating it in an evacuated cylinder. The products are NH3 and HCl gas. If the total pressure after heating is 4.4 atm, determine Kp.
Please help me with the steps on how to do solve this.
........NH4Cl(s) ==> NH3(g) + HCl(g)
I......solid.........0.........0
C......solid.........p.........p
E......solid.........p.........p
Kp = pNH3*pHCl
The problems tell you that pNH3 + pHCl = 4.4 atm and since pNH3 = pHCl that makes 2p = 4.4 and p = 2.2 atm
Substitute into Kp expression and solve for Kp.
Thank you!!
To solve this problem, you will need to use the ideal gas law, the equation for Kp, and the stoichiometry of the reaction. Here are the steps to solve it:
Step 1: Write the balanced equation for the decomposition reaction of NH4Cl:
NH4Cl(g) → NH3(g) + HCl(g)
Step 2: Use the ideal gas law to relate the total pressure after heating to the partial pressures of the gases. The ideal gas law equation is:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in kelvin.
Step 3: Assume the volume is constant, so the ideal gas law equation becomes:
Ptotal = PNH3 + PHCl
Where Ptotal is the total pressure and PNH3, PHCl are the partial pressures of NH3 and HCl respectively.
Step 4: Use the stoichiometry of the reaction to determine the ratio of moles of NH3 and HCl produced. The balanced equation in Step 1 tells us that for every NH4Cl molecule decomposed, one NH3 and one HCl molecule are produced.
Step 5: Let's assume that x moles of NH4Cl decompose. Therefore, x moles of NH3 and x moles of HCl are formed. Since the ratio of NH3 and HCl produced is 1:1, the partial pressure of NH3 and HCl will be the same.
Step 6: Express the partial pressure of NH3 (PNH3) and HCl (PHCl) in terms of x:
PNH3 = PHCl = x / V
Where V is the volume (assumed constant).
Step 7: From Step 3, we know that the total pressure is equal to the sum of the partial pressures:
Ptotal = PNH3 + PHCl
Ptotal = (x / V) + (x / V)
Ptotal = (2x / V)
Step 8: Finally, use the expression for Ptotal from Step 7 to calculate Kp. The equation for Kp is:
Kp = (PNH3 * PHCl) / (PNH4Cl)
Kp = ((x / V) * (x / V)) / (PNH4Cl)
Kp = ((x / V)^2) / PNH4Cl
Step 9: Substitute the given total pressure (Ptotal) into the expression for Kp and solve for x:
Kp = ((x / V)^2) / PNH4Cl = (2x / V) / PNH4Cl
Kp = (2x / V) / PNH4Cl = 4.4 / PNH4Cl
Step 10: Rearrange the equation to solve for x:
2x = 4.4 * (V / PNH4Cl)
x = 2.2 * (V / PNH4Cl)
Step 11: Substitute the value of x obtained in Step 10 into the expression for Kp:
Kp = ((x / V)^2) / PNH4Cl
Kp = ((2.2 * (V / PNH4Cl)) / V)^2 / PNH4Cl
Kp = (2.2 / PNH4Cl)^2
Step 12: Simplify the expression for Kp:
Kp = 2.2^2 / PNH4Cl^2
Therefore, the value of Kp is 4.84 / PNH4Cl^2, where PNH4Cl is the partial pressure of NH4Cl.