The decomposition of hydrogen iodide if the equation: 2HI (g)--> H2 (g) + I2 (g) The reaction is second order and has a constant rate equal to 1, 6X10^-3 L/mol * s at 700 degrees. If the initial HI concentration in a vessel is 3.4X10 ^-2m. How many minutes will it take for the concentration to be reduced to 8,0X10^-2 M ?
Is that 1/A - 1/Ao = kt ?
To solve this problem, we can use the rate equation for a second-order reaction:
1/[HI]t - 1/[HI]0 = kt
Where [HI]t is the concentration of HI at time t, [HI]0 is the initial concentration of HI, k is the rate constant, and t is the time.
Given that the rate constant (k) is equal to 1.6x10^-3 L/mol*s, we can rearrange the equation to solve for t:
1/[HI]t - 1/[HI]0 = kt
1/8.0x10^-2 M - 1/3.4x10^-2 M = (1.6x10^-3 L/mol*s) * t
To simplify the equations, we can take the reciprocal of both concentrations:
1/[HI]t = 125 M^-1
1/[HI]0 = 29.4 M^-1
Substituting these values into the equation, we get:
(125 M^-1) - (29.4 M^-1) = (1.6x10^-3 L/mol*s) * t
95.6 M^-1 = (1.6x10^-3 L/mol*s) * t
Now, solve for t:
t = (95.6 M^-1) / (1.6x10^-3 L/mol*s)
t ≈ 59,750 seconds
To convert the time to minutes, divide by 60:
t ≈ 59,750 seconds / 60 seconds/minute
t ≈ 995.83 minutes
Therefore, it will take approximately 995.83 minutes for the concentration of HI to be reduced to 8.0x10^-2 M.
To determine the time it takes for the concentration to be reduced to a certain value, we can use the integrated rate law for a second-order reaction:
1/[HI]t - 1/[HI]0 = kt
Where [HI]t is the concentration at time t, [HI]0 is the initial concentration, k is the rate constant, and t is the time it takes for the concentration to change.
Given:
Initial concentration ([HI]0) = 3.4X10^-2 M
Final concentration ([HI]t) = 8.0X10^-2 M
Rate constant (k) = 1.6X10^-3 L/mol * s
Rearranging the equation gives:
1/[HI]t = kt + 1/[HI]0
Substituting the values:
1/(8.0X10^-2) = (1.6X10^-3)(t) + 1/(3.4X10^-2)
Simplifying, we get:
12.5 = (1.6X10^-3)(t) + 29.4
Subtracting 29.4 from both sides:
-16.9 = (1.6X10^-3)(t)
Dividing both sides by 1.6X10^-3:
t = -16.9 / (1.6X10^-3)
t ≈ -10562.5 s
Since time cannot be negative, we take the absolute value:
t ≈ 10562.5 s
To convert seconds to minutes, divide by 60:
t ≈ 176 min
Therefore, it will take approximately 176 minutes for the concentration of HI to be reduced to 8.0X10^-2 M.