I tried working out this problem but am unsure of a few steps. Please help me if you can.
Consider O3 --->1.5O2
At 210degrees Celsius and an initial gas pressure of 0.23atm, it is found that the rate of reaction is 1.8E-2 mol/(Lxs).
a) What is the change in the total gas pressure in 1.79E-2s?
b)If the reaction has an order of 1.5, what is the rate constant?
a) This is how I thought the approach to this problem should be:
Using the formula Rate = V/(uVRT) x (dP/dt) where u is stoichiometric coefficient, the two V's are the volume of the gas and the volume of the container, R is the universal gas constant and T is temperature. Dp/dt refers to the change in pressure of the gas versus the change in time.
Since both Oxygen and ozone are gases we need to use this equation twice, find the change in pressure for each and then add them together. THat's what i think anyway.
Do people out there agree with me that dPressure (change in pressure) would be written as final-initial (where final is what we are solving for)?
Solving for O3 I got: Given that the two Volume's are the same, I cancelled those out. We have Rate, u, R and T as well as dt so I put all those numbers in and wrote dP as (final-.23atm) and solved for the final, which I got 0.217atm. Would the stoichiometric coefficient be +1 or -1?
Using the similar technique, I got 0.249atm for 02, using +1.5 as the stoichiometric coefficient. I then took the (0.217atm-0.23atm) and added it to (0.249atm-0.23atm) and got 0.006 atm and said this was the total change in gas pressure.
Do people agree?
for b) using Rate = k[O3]^1.5, and solving for [O3] using Pressure of O3 x Volume = molesO3xRxT and isolated moles/V since that is concentration. I used the Pressure of O3 as 0.23atm, or should i use the change in pressure? I then solved for the [O3] and plugged in the reaction rate from before and got 40.74 for k, the rate constant. To me, this just seems to be big of an answer? Anyone have any suggestions?
Thanks a lot.
Let's go step by step to analyze your approach and see if we agree with your calculations.
a) To find the change in total gas pressure, you correctly use the formula Rate = V/(uVRT) x (dP/dt), where V is the volume of the gas, R is the universal gas constant, T is the temperature, u is the stoichiometric coefficient, and dP/dt represents the change in pressure with respect to time.
To determine the change in pressure for each gas, you have to consider the stoichiometric coefficients. In this case, the stoichiometric coefficient for O3 is -1 (since it is consumed) and for O2, it is +1.5 (since it is produced). So, your approach is correct.
However, to find the change in pressure, you need to use the initial and final pressures of each gas. The final pressure of O3 should be the one you are solving for. So the equation would be: final pressure of O3 - initial pressure of O3 = -1 x rate x V / (u x R x T) x dt. Similarly, for O2, it would be: final pressure of O2 - initial pressure of O2 = +1.5 x rate x V / (u x R x T) x dt.
Now, let's focus on solving for the final pressures of O3 and O2.
For O3, you correctly plugged in the given values in the equation, but you should subtract the initial pressure of O3 from the final pressure instead of the other way around. So it would be: final pressure of O3 - 0.23 atm = -1 x 1.8E-2 mol/(Lxs) x V / (-1 x R x T) x dt.
Similarly, for O2, it would be: final pressure of O2 - 0.23 atm = +1.5 x 1.8E-2 mol/(Lxs) x V / (1.5 x R x T) x dt.
After solving these equations, you should obtain the final pressures of both gases. Then, you can calculate the change in total gas pressure by subtracting the initial total pressure (0.23 atm) from the final total pressure (the sum of the final pressures of O3 and O2).
b) To determine the rate constant (k), you need to use the given rate equation: Rate = k[O3]^1.5.
First, calculate the concentration of O3 using its pressure and volume, assuming ideal gas behavior (Pressure x Volume = moles x R x T) to get the number of moles per liter of O3.
Next, substitute this concentration value ([O3]) and the given rate (1.8E-2 mol/(Lxs)) into the rate equation to solve for k. It's essential to use the initial pressure of O3 to calculate its concentration because the rate is given at that initial pressure.
Upon solving, you should obtain a value for k, which represents the rate constant for the reaction.
Make sure to use the correct signs and units in your calculations and equations. Double-check your arithmetic and calculations to ensure accuracy.
I hope this helps you understand the steps involved, and please feel free to ask any further questions!