# Finding the P of a reactant after t seconds

1. Sep 12, 2006

### future_vet

Hello,

I need to find the pressure of a substance after 65 s. I have the initial pressure, the order of the reaction, the Temp., and the rate k for the decomposition.
I know that if it was about concentrations, I would use
ln [A]t = k x t x ln [A]o

If it's about pressure, do I use the same formula? Or is there a separate one? (if there is one, I can't find it...)

Thank you,

Joanna.

2. Sep 12, 2006

### Gokul43201

Staff Emeritus
1. The equation you've written down works only for a particular order of the reaction. I hope you know which one.

2. How is the pressure related to the concentration, if the volume is fixed? Can you write down the relation and check whether the arte equation changes?

3. With any homework/textbook problem, please post the entire question, exactly as given to you. It leaves less room for ambiguity and confusion. Right now, I don't know if you're assuming 1st order kinetics because that is stated in the problem, or because of a concenptual error.

3. Sep 12, 2006

### future_vet

Hello,

I am sorry, yes the fact that it is a first order reaction was given to us.
It's the decomposition of sulfuryl chloride.

SO2CL2 (g) -> SO2 (g) + Cl2 (g)

We have time and pressure data:
Time (S) Pressure SO2CL2 (atm)
0 ---------------- 1.000
2500 ------------- 0.947
5000 ------------- 0.895
7500-------------- 0.848
10000 -------------0.803

We need to know the magnitude of the first order rate constant. It may be that the teacher skipped this concept. It was not given as homework, but I am doing all the exercises in the book to be ready for the exam.

~J.

4. Sep 12, 2006

### Gokul43201

Staff Emeritus
Solving problems in science isn't about finding the right equation in the chapter you are covering at the moment. Just because an equation doesn't exist for the problem you have, does not mean there isn't a solution that is accessible to you. You may have to dig back into conpcepts learned in the past. For instance, how is the partial pressure related to the number of moles? Let's start right there. Let's see if we can write down the relationship between partial pressure of So2Cl2 and the concentration of SO2Cl2.

There's a piece of information that's missing here, that requires an assumption be made. Nothing is said about the conditions of the reaction (isobaric, isochoric, etc.) Assume that the total volume of the reaction vessel and the temperature are constant.

Hint: recall mole fraction.

5. Sep 12, 2006

### future_vet

Well, the partial pressure is the mole fraction (the number of moles in the first experiment divided by the # of moles in the 2nd) times the total pressure. Is this correct?

I have to say, I had to make a little research to find the info. I had never seen this in my life. I took the previous class at another college, so I may be lacking some things.

~J.

6. Sep 12, 2006

### Gokul43201

Staff Emeritus
Yes, that's right, and that's the first step.

Let's write that down:

$$p(SO_2Cl_2) = \chi (SO_2Cl_2) \cdot P_{tot}$$

The mole fraction, $\chi$ of a thing is simply the number of moles of that thing divided by the total number of moles. In this case, there will be, in addition to the SO2Cl2, some number of moles of each of the products that are formed.

$$\chi(SO_2Cl_2) = \frac {n(SO_2Cl_2)}{n_{tot}}$$

$$\implies p(SO_2Cl_2) = \frac {n(SO_2Cl_2)}{n_{tot}} \cdot P_{tot}$$

Also, keep in mind that all these species that are present at any point of time are gaseous, and will all contribute to the total pressure. The total pressure can be related to the total number of moles through the Ideal Gas Law:

$$P_{tot} = \frac{n_{tot}RT}{V}$$

Substituting for the total pressure in the above equation, you have:

$$\implies p(SO_2Cl_2) = \frac {n(SO_2Cl_2)}{n_{tot}} \cdot \frac{n_{tot}RT}{V} = \frac {n(SO_2Cl_2)}{V} \cdot RT$$

With that we have an equation that relates the partial pressure (p) to the concentration (n/V).

Substitute this relation into the first order rate equation that you wrote down in the OP. What do you get?

Last edited: Sep 12, 2006
7. Sep 13, 2006

### future_vet

I should get that program to write nice understandable equations...

Back to the topic:

With so many unknowns, do we have to find a way to "combine" that last equation, and the one I talked about in the first post? Do we find similarities, to get rid of the unknowns and replace them with values we already have, and get a precise answer?
Or is the answer going to have unknowns in it that cannot be removed?

~J.

8. Sep 13, 2006

### Gokul43201

Staff Emeritus
1. There is an error in your original equation - find it and fix it.

2. [A] represents the concentration of A, or the number of moles of A per unit volume. So simply replace [A]o with n(A,0)/V and [A]_t with n(A,t)/V. Next, substitute n(A,0)/V = p(A,0)/RT and n(A,t)/V = p(A,t)/RT into the equation. Make this substitution and write it down, and see if anything cancels off. You're not going to know what the outcome will be unless you do the math - there's no avoiding that.