The decomposition of HI(g) is represented by the equation:
2HI(g) <-> H2(g) + I2(g)
Kc= 64 at 25°C.
If the equilibrium concentrations of H2 and I2 at 400°C are found to be [H2] = 5.4x10-4 M and [I2] = 8.8x10-3 M, what is the equilibrium concentration of HI?
Set up an ICE chart, substitute into Kc, and solve for HI.
Post your work if you get stuck.
To find the equilibrium concentration of HI, we can use the equilibrium expression and the values given.
The equation for the decomposition reaction is:
2HI(g) ↔ H2(g) + I2(g)
The equilibrium constant expression (Kc) is given by:
Kc = [H2][I2] / [HI]^2
Given:
[H2] = 5.4x10^-4 M
[I2] = 8.8x10^-3 M
Kc = 64
Plugging in the given values into the equilibrium constant expression, we have:
64 = (5.4x10^-4)(8.8x10^-3) / [HI]^2
To find [HI], we can rearrange the equation:
[HI]^2 = (5.4x10^-4)(8.8x10^-3) / 64
Now, solve for [HI]:
[HI]^2 = (4.752x10^-6) / 64
[HI]^2 = 7.425x10^-8
Taking the square root of both sides, we get:
[HI] = √(7.425x10^-8)
[HI] ≈ 8.617x10^-5 M
Therefore, the equilibrium concentration of HI is approximately 8.617x10^-5 M.
To find the equilibrium concentration of HI, you need to use the equilibrium constant expression and the given equilibrium concentrations of H2 and I2. Here's how you can solve the problem step-by-step:
Step 1: Write down the balanced equation for the decomposition of HI:
2HI(g) ↔ H2(g) + I2(g)
Step 2: Write the expression for the equilibrium constant, Kc. The expression is derived from the law of mass action, which states:
Kc = [H2][I2] / [HI]^2
Step 3: Substitute the given equilibrium concentrations into the equilibrium constant expression:
Kc = (5.4x10-4)(8.8x10-3) / [HI]^2
Step 4: Rearrange the equation to solve for [HI]^2:
[HI]^2 = (5.4x10-4)(8.8x10-3) / Kc
Step 5: Calculate [HI] by taking the square root of both sides:
[HI] = √[(5.4x10-4)(8.8x10-3) / Kc]
Step 6: Plug in the given value of Kc (64) and evaluate:
[HI] = √[(5.4x10-4)(8.8x10-3) / 64]
Step 7: Calculate the equilibrium concentration of HI using a calculator:
[HI] ≈ 2.6x10-3 M
Therefore, the equilibrium concentration of HI is approximately 2.6x10-3 M.