The decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 10-2 s-1.
(a) If we begin with an initial SO2Cl2 pressure of 425 torr, what is the pressure of this substance after 74 s?
what is the equation to solve this?
ln(Po/P) = kt
Po = initial P
P = final P. Solve for this.
k = given
t = given
i got 11873 which seems kinda high..?
is k negative because of the s-1?
without making it negative i got 15.21 which seemed more reasonable but when i plugged it in it was wrong
k is not negative.
I obtained 15.23. How is the problem stated? If k = 4.50E-2 then you are allowed three significant figures and you should report 15.2 and the data base is counting it wrong because you are using too many places. If k = 4.5E-2 you are allowed only two significant figures and you should report 15.
i just tried that and it is wrong.
does the temperature it gives have anything to do with the problem?
The correct answer is 15 torr.
Does the problem as for P in torr or some other unit?
torr
To solve this problem, we can use the first-order reaction rate equation, which is given by:
ln([A]t/[A]0) = -kt
Where:
[A]t represents the concentration of the reactant at time t,
[A]0 represents the initial concentration of the reactant,
k is the rate constant, and
t is the time.
In this case, we are given the initial pressure of SO2Cl2, so we need to convert it to concentration. The ideal gas law can be used to convert pressure to concentration:
PV = nRT
Where:
P is the pressure,
V is the volume,
n is the number of moles,
R is the ideal gas constant (0.08206 L·atm/(mol·K)), and
T is the temperature in Kelvin.
First, we need to convert the pressure from torr to atm since the ideal gas constant is given in atm units.
1 atm = 760 torr
So, to convert the pressure to atm:
P (atm) = 425 torr / 760 torr/atm
P (atm) ≈ 0.559 atm
Next, we need to convert the pressure to concentration using the ideal gas law equation. Let's assume a volume of 1 L for simplicity:
n/V = P/RT
Where:
n/V is the concentration,
P is the pressure,
R is the ideal gas constant (0.08206 L·atm/(mol·K)), and
T is the temperature in Kelvin.
Concentration (C) = (0.559 atm) / (0.08206 L·atm/(mol·K) * 660 K)
C ≈ 0.0108 mol/L
Now we have the initial concentration ([A]0).
We are given the rate constant (k) as 4.5 * 10^-2 s^-1, and the time (t) as 74 s.
We can now substitute the values into the first-order rate equation:
ln([A]t/[A]0) = -kt
ln([A]t / 0.0108) = (-4.5 * 10^-2 s^-1) * (74 s)
Now solve for [A]t by isolating it:
[A]t = 0.0108 * e^(-4.5 * 10^-2 s^-1 * 74 s)
Calculating this expression will give you the pressure or concentration of SO2Cl2 after 74 seconds.