The first-order decomposition of SO₂Cl₂ to sulfur dioxide gas and chlorine gas at 320^$\circ$C has a half-life of 8.75 hr. If 600. mmHg of pure SO₂Cl₂ is placed in a 5.00-L flask at 320^$\circ$C, how long does it take for the total pressure in the flask to rise to 1.000 atm

Question

Quizplus · Accepted Answer

First, we need to find the rate constant, k, using the half-life of the reaction:

t1/2 = 8.75 hr
k = ln(2) / t1/2 = ln(2) / 8.75 hr = 0.0792 hr^-1

Next, we can use the following integrated rate law to find the time it takes for the total pressure in the flask to reach 1.000 atm:

ln(P/P0) = -kt

where P is the final pressure (1.000 atm), P0 is the initial pressure (600. mmHg), and t is the time we're trying to find.

First, we need to convert the initial pressure to atm:

P0 = 600. mmHg * (1 atm / 760 mmHg) = 0.7894 atm

Now we can plug in the known values and solve for t:

ln(1.000 atm / 0.7894 atm) = (-0.0792 hr^-1) * t
t = 3.91 hr

Therefore, the answer is choice C.

The First-Order Decomposition of SO2Cl2 to Sulfur Dioxide Gas and Chlorine

The First-Order Decomposition of SO₂Cl₂ to Sulfur Dioxide Gas and Chlorine