For a reaction of 2HI=H2+I2,one mole of HI is introduced into vessel at constant temperature.Calculate no of moles of I2,when equilibrium is reached(kc=0.0156)
To calculate the number of moles of I2 when equilibrium is reached for the reaction 2HI <=> H2 + I2, we need to use the equilibrium constant (Kc) and the initial moles of HI introduced.
Let's assume that x moles of HI react to form x moles of H2 and x moles of I2 at equilibrium.
The balanced equation tells us that 2 moles of HI react to form 1 mole of I2. Therefore, the moles of I2 at equilibrium will be equal to half the moles of HI that reacted.
Given that the initial moles of HI introduced into the vessel is 1 mole, and only a fraction of it reacts, we can assume that the moles of HI that react is also x.
So, using the equation: 2HI <=> H2 + I2
The initial moles of HI (before the reaction starts) = 1 mole
The moles of HI that react at equilibrium = x (assuming the reaction goes to completion)
The moles of I2 that are produced = 1/2 * x (since 2 moles of HI produces 1 mole of I2)
Now, we need to apply the equilibrium constant (Kc) to find the value of x.
The expression for Kc for this reaction is given as:
Kc = [H2][I2] / [HI]^2
Given that Kc = 0.0156 and the initial moles of HI = 1 mole, we can substitute these values into the equation as follows:
0.0156 = (x/2) / (1 - x)^2
Simplifying the equation:
0.0156 = (x/2) / (1 - 2x + x^2)
0.0156 = x / (2 - 4x + 2x^2)
0.0156(2 - 4x + 2x^2) = x
0.0312 - 0.0624x + 0.0312x^2 = x
0.0312x^2 - 1.0624x + 0.0312 = 0
Now, we can solve this quadratic equation to find the value of x. We can use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 0.0312, b = -1.0624, and c = 0.0312.
After solving the quadratic equation, you will obtain two values for x. One will be positive and the other will be negative. We discard the negative value since we are looking for the number of moles of I2 at equilibrium, which cannot be negative.
Therefore, the positive value of x will be the moles of HI that reacted, and the moles of I2 produced will be half of that positive value.
Let me know if you would like me to solve the quadratic equation and find the exact value of x and the number of moles of I2.