Sulfuryl chloride, SO2Cl2, decomposes to SO2 and Cl2 according to the reaction
SO2Cl2(g) -> SO2(g) + Cl2(g)
The reaction is first order in SO2Cl2, and the value of the rate constant, k, is 2.20*10-5 /s at 300K.
(a) Calculate the intial rate of reaction when a reactor is charged with SO2Cl2 at a concentration of 0.22 mol/L.
Enter the numerical value in mol/L s:
b) Calculate how long it will take for the conctration of SO2Cl2 in the reactor in part (a) to fall to 1/4 of its initial value.
Enter the numerical value in s:
b.
ln*(No/N) = kt
No = 100
N = 25
k is given
Solve for t.
6.3e4
THEN HOW DO YOU DO A)?
For a) dc/dt=-KC=2.2*10*-5*0.22=4.84*10^-6
b) 6.34*10^4
To calculate the initial rate of reaction, we can use the rate law equation:
rate = k [SO2Cl2]
Given that the reaction is first order with respect to SO2Cl2, the rate law equation becomes:
rate = k [SO2Cl2]^1
We are given the concentration of SO2Cl2 as 0.22 mol/L and the rate constant (k) as 2.20 * 10^-5 /s.
Substituting the given values into the rate law equation:
rate = (2.20 * 10^-5 /s) * (0.22 mol/L)
Simplifying the expression:
rate = 4.84 * 10^-6 mol/L s
Therefore, the initial rate of reaction when the reactor is charged with SO2Cl2 at a concentration of 0.22 mol/L is 4.84 * 10^-6 mol/L s.
To calculate the time it will take for the concentration of SO2Cl2 to fall to 1/4 of its initial value, we can use the first-order reaction decay equation:
[SO2Cl2]t = [SO2Cl2]0 * e^(-kt)
Where:
[SO2Cl2]t is the concentration of SO2Cl2 at time t,
[SO2Cl2]0 is the initial concentration of SO2Cl2,
k is the rate constant,
t is the time.
In this case, we want to find the time it takes for [SO2Cl2]t to be 1/4 of [SO2Cl2]0.
Let's assume that [SO2Cl2]t/ [SO2Cl2]0 = 1/4.
Substituting the given values into the decay equation:
(1/4) = (0.22 mol/L) * e^(-kt)
Rearranging the equation to isolate t:
e^(-kt) = (1/4) / (0.22 mol/L)
Taking the natural logarithm (ln) of both sides:
-ln(4) = -kt
Simplifying the expression:
t = -ln(4) / k
Substituting the given value of k:
t = -ln(4) / (2.20 * 10^-5 /s)
Calculating the value using a calculator:
t ≈ 9.23 x 10^4 seconds
Therefore, it will take approximately 9.23 x 10^4 seconds for the concentration of SO2Cl2 in the reactor to fall to 1/4 of its initial value.