# Determining the reaction time of water synthesis by use of differential equations

How do I determine the reaction speed?

I know you need a value, k, and order, which is only gained through experimentation, but how do the differential equations play in? How do I plot the result?

Assuming it's the first order ...

How do I proceed? I now have this function but I am not sure what to do with it. I do not have the means to observe the reaction and figure out its k-value or order. Is this reaction a known one, though? Is the order and k-value something you can find on the Internet?:

$$\ce{2H2 + O2 -> 2H2O}$$

• You either guess at the elementary steps and derive the rate law from that, or you perform the measurements and determine an experimental rate law. There is no other way. You can find pretty much anything on the internet. – Zhe Dec 8 '17 at 18:21
• Unfortunately, I have been unable to find the order/value on the internet – javanewbie Dec 8 '17 at 18:32
• Because there's no "order/value"? Mechanism of this reaction is quite complicated, assuming it could be first order was overoptimistic as there's no order, only in specific situation it may seem there is. – Mithoron Dec 8 '17 at 23:14
• Assuming you somehow can get the air resistance and other stuff out of the way, you would, in effect, be measuring the thrust (force provided by the reaction) vs time. This would depend on the exiting reaction mixture. In this case, it is hot steam. (Also, if you react gases in an otherwise uncontrolled manner, you'll get an explosion, no sustained thrust as such). You can calculate how much of the reaction must have taken place to deliver that thrust. So, I'd say it is possible, but only if the errors in measurement are low enough... – Eashaan Godbole Dec 9 '17 at 15:02

How do I determine the reaction speed?

The rate of reaction can be determined experimentally or theoretically, the latter case requiring that a reaction mechanism be known. Proposing a reaction mechanism requires knowledge of the reaction at multiple regimes and some guesswork. Evidence for a certain reaction mechanism is usually indirect.

Theoretically speaking, once the reaction mechanism and rate constants are known, we can write down a coupled system of kinetic rate equations and solve them simultaneously to find the rate of reaction.

I know you need a value, k, and order, which is only gained through experimentation, but how do the differential equations play in? How do I plot the result?

The differential equations govern the reacting system, and their solution completely specifies the system, enabling you to find the rate of reaction. You would then simply plot, say, the rate of reaction vs. time.

How do I proceed? I now have this function but I am not sure what to do with it. I do not have the means to observe the reaction and figure out its k-value or order.

I don't believe you can proceed, because your initial assumption was wrong. The combustion of hydrogen is far more complicated than a first-order reaction, which you have assumed; you should not, therefore, expect that your first-order analysis should describe your system well.

Is this reaction a known one, though? Is the order and k-value something you can find on the Internet?

It has certainly been studied. I will refer you to Reaction mechanism of combustion of H2 and the links therein.

• Thank you. What about the combustion of solid sulphur to form sulphurdioxide? I found out that giving a rate constant to the combustion of hydrogen is incredibly complex. Is it the same for sulphur? – javanewbie Dec 17 '17 at 12:38
• @javanewbie, essentially all combustion reactions will have very complicated mechanisms. – a-cyclohexane-molecule Dec 17 '17 at 17:42