The equilibrium pressure of H2 is 0.96 atm and the impossible solution of the quadratic equation is -1.379.
The equilibrium pressure of H2 is calculated by creating ICE table as follows;
2 N H3 ( g ) ⟷ N2( g ) + 3H2
I: 1 1 1
C: -2x x 3x
E: 1 - 2x 1 + x 1 + 3x
[tex]KP = \frac{(N_2)(H_2)^3}{(NH_3)^2} \\\\0.83 = \frac{(1 + x)(1 + 3x)^3}{(1 - 2x)^2}[/tex]
0.83(1 - 2x)² = (1 + x)(1 + 3x)³
0.83(1 - 4x + 4x²) = (1 + x)((1 + 3x)³)
0.83 - 3.32x + 3.32x² = (1 + x)((1 + 3x)³)
0.83 - 3.32x + 3.32x² = 1 + 10x + 36x² + 54x³ + 27x⁴
27x⁴ + 54x³ + 32.68x² + 13.32x + 0.17 = 0
x = -1.379 or - 0.013
H2 = 1 + 3(-1.379)
H2 = -3.13 atm
H2 = 1 + 3(-0.013)
H2 = 0.96 atm
Thus, the equilibrium pressure of H2 is 0.96 atm and the impossible solution of the quadratic equation is -1.379.
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