For the reaction H2+I2 give 2HI the equilibrium constant =62.5 at 800K and ∆H=-10.4KJ calculate the Equilibrium constant at 1000K

To find the equilibrium constant at a different temperature, we can use the van 't Hoff equation, which relates the change in the equilibrium constant with temperature to the change in enthalpy. The equation is given by:

van 't Hoff Equation

The van 't Hoff equation is expressed as:

ln(K2/K1) = -ΔH/R * (1/T2 - 1/T1)

Where:

• K1 = equilibrium constant at the initial temperature (800 K)
• K2 = equilibrium constant at the final temperature (1000 K)
• ΔH = change in enthalpy (in Joules per mole)
• R = universal gas constant (8.314 J/(mol·K))
• T1 = initial temperature (800 K)
• T2 = final temperature (1000 K)

Given Values

From the problem, we have:

• K1 = 62.5
• ΔH = -10.4 kJ = -10,400 J (since we need to convert kJ to J)
• T1 = 800 K
• T2 = 1000 K

Calculating K2

Now, we can plug these values into the van 't Hoff equation:

First, calculate the term (1/T2 - 1/T1):

• 1/T1 = 1/800 = 0.00125 K^-1
• 1/T2 = 1/1000 = 0.001 K^-1
• 1/T2 - 1/T1 = 0.001 - 0.00125 = -0.00025 K^-1

Now substitute these values into the van 't Hoff equation:

ln(K2/62.5) = -(-10,400 J / 8.314 J/(mol·K)) * (-0.00025 K^-1)

Calculating the Right Side

First, calculate the left side:

• -ΔH/R = -(-10,400 J) / 8.314 J/(mol·K) = 1256.6 K

Now, multiply this by the temperature difference:

ln(K2/62.5) = 1256.6 K * (-0.00025 K^-1) = -0.31415

Finding K2

Now, we can solve for K2:

K2/62.5 = e^-0.31415

Calculating the exponential:

K2/62.5 = 0.7305

Finally, multiply both sides by 62.5:

K2 = 62.5 * 0.7305 = 45.6

Final Result

The equilibrium constant at 1000 K is approximately 45.6.