Phosphine (PH3) decomposes at elevated temperatures, yielding gaseous P2 and H2: 2 PH3(g) ⇌ P2(g) + 3 H2(g) Kp = 398 at 873 K If the initial partial pressures are PPH3 = 0.0271 atm, PP2 = 0.863 atm, PH2 = 0.514 atm, calculate Qp. Qp =
Answer (1)
To calculate the reaction quotient Q p for the given reaction at a specific moment, you need to use the formula for Q p which is similar to that of the equilibrium constant K p but at non-equilibrium conditions.
For the reaction:
2 PH 3 ( g ) ⇌ P 2 ( g ) + 3 H 2 ( g )
The expression for Q p is:
Q p = ( P PH 3 ) 2 P P 2 ⋅ ( P H 2 ) 3
Given the initial partial pressures:
P PH 3 = 0.0271 atm
P P 2 = 0.863 atm
P H 2 = 0.514 atm
Substitute these values into the Q p expression:
Q p = ( 0.0271 ) 2 0.863 ⋅ ( 0.514 ) 3
Calculate each part:
( 0.514 ) 3 = 0.514 × 0.514 × 0.514 = 0.1353
0.863 × 0.1353 = 0.1168
( 0.0271 ) 2 = 0.0271 × 0.0271 = 0.000734
Finally, calculate Q p :
Q p = 0.000734 0.1168 = 159.27
Thus, the reaction quotient Q p at the given conditions is approximately 159.27.
