Answer:
The quantity of hydrazine formed is 3.16 mmoles
Explanation:
This is a typical equilibrium problem.
Initially we have 10 moles of ammonia, so I don't have any hydrazine or hydrogen. During the reaction, an X amount of moles of ammonia reacts to give half moles of hydrazine and hydrogen. The ratio of reagent to product is 2 to 1.
In equilibrium I will have the 10 moles of ammonia - X and X/2 moles of hydrazine and hydrogen.
2 NH₃ → H₄N₂ + H₂
Initial 10m - -
React x x/2 x/2
Eq 10-x x/2 x/2
Since the volume is 1L the concentration is molar. REMEMBER THAT IN EQUILIBRIUM WE WORK WITH MOLAR CONCENTRATIONS
The expression of Kc is [H₄N₂]. [H2] / [NH3]²
1x10⁻⁷ = [x/2] . [x/2] / (10-x)²
1x10⁻⁷ = 1/4x² / 100-20x+x²
1x10⁻⁷ (100-20x+x²) = 1/4x²
1/4x² - 1x10⁻⁵ + 2x10⁻⁶x = 0 This is a quadratic equation
1/4 = a ; 2x10⁻⁶ = b ; -1x10⁻⁵ = c
(-b +- √(b²-4ac))/2a
x1 = 6.32x10⁻³
x2 = -6.32x10⁻³
Concentrations can not be negative, so we take x1
[H₄N₂] = x/2
[H₄N₂] = 6.32x10⁻³/2 = 3.16x10⁻³ moles
1mmol = 1000 moles
3.16x10⁻³ moles . 1000 = 3.16 mmoles
