An equimolar mixture of an alkane and an alkene is thermally decomposed into elements. The temperature is constant and the pressure increase is of 3.5. How many atoms of carbon contain the hidrocarbures?

C_nH_{2n+2} + C_nH_{2n} \rightarrow 2nC + 2n+1H_2

P_2= 3.5P_1

How to use the pressure so that to find the number of atoms?

3

How did you get this?

Look at the answer to a very similar problem submitted by endlesslove230 on December 19.
I think these are very odd problems - it is not easy to decoompose a hydrocarbon to its elements.
Try the problem using the hints given in the earlier answer. See how far you can go and we will give more help as you need it.

How are you doing? You have the correct formula to solve the problem, but it should be written CnH2n+2 + CnH2n ==> 2nC + (2n +1)H2. If you start with 1 mole of each gas, how many moles of H2 are generated? Solve for n.

If there is 1 mole of each gas, there should result 1 mole of C and 1 mole of H2. Isn't it?

NO. As your equation shows, it depends on the formula of the hydrocarbon. With n carbons, 1 mole of alkane will give n moles of carbon atoms and 2n + 2 moles of hydrogen atoms or n + 1 moles of H2 molecules. Of course the carbon is a solid and does not contribute to the pressure of the system; that is due solely to the moles of H2. Likewise, a mole of alkene will give n moles of C and 2n moles of H (or n moles of H2). This is the key to your answer. Keep working, you're on your way.

Ok. I got it: there are n moles of carbon and 2n+1 moles of H2. Now, in order to find n I need to work with the moles of H2 and the pressure. I tried using the equation of state, but I didn't get anything. I think there must be something else.

OK. Let's say you start with two moles of HCs (hydrocarbon) with a total pressure of two atm. What is the final pressure? Since each mole of gas gives one atm of partial pressure, you now know the total moles of H2 produced in the reaction. You have shown that there are 2n+1 moles of H2 so you can solve for n, the number of C atoms in each HC molecule. Keep going.

So P1=2 atm and P2=7 atm. If I solve 2n+1=7 I get n=3, but I don't think this is correct because 7 is the pressure of H2 and 2n+1 the number of moles.

No, you solved it! Every mole of H2 generates one atm of pressure, so there are seven moles of H2. Therefore, as you say, 2n+1 = 7 and n=1. That's the answer! N is the number of carbon atoms in the alkane and alkene. So the alkane and alkene are propane and propene respectively.
Good work!

n = 3. My mistake.

Ok, thank you for help. It wasn't as difficult as I thought, though it was a little bit strange to use pressure and moles in the same equation.

Referring to endlesslove230's problem (since you suggested it to me):
If in the beginning are 100L of C4H6 and it is decomposed at 70%, it means that only 70L react. The reaction is C4H6 => 4C + 3H2, so there should be 30L of H2. What to do next?

If 70% react, 70L of C4H6 will decompose.

From the equation, 1 L of C4H6 (completely reacted) gives 3 L of H2
70 L of C4H6 (completely reacted) will give 210 L of H2 and not 30 L.

So, decomposing 100 L of C4H6 at 70% will give 210 L of H2