# Video: Using First-Order Reaction Law to Calculate the Reaction Rate of the Dinitrogen Pentoxide Decomposition

Dinitrogen pentoxide decomposes in chloroform to form nitrogen dioxide and oxygen, as shown. 2N₂O₅ → 4NO₂ + O₂ The decomposition is a first-order reaction with a rate constant of 6.20 × 10⁻⁴ min⁻¹ at 45°C. Calculate the rate of reaction in molars per second when [N₂O₅] = 0.400 M.

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### Video Transcript

Dinitrogen pentoxide decomposes in chloroform to form nitrogen dioxide and oxygen, as shown. 2N₂O₅ react to form 4NO₂ plus O₂. The decomposition is a first-order reaction with a rate constant of 6.20 times 10 to the minus four per minute at 45 degrees Celsius. Calculate the rate of reaction in molars per second when the concentration of N₂O₅ is equal to 0.400 molars.

First, let’s recap what a first-order reaction is. Let’s imagine we have a rate equation where the rate is equal to the rate constant multiplied by various concentrations raised to various powers. A first-order reaction is one where the sum of the powers in the rate equation is one. In this case, our only reactant is dinitrogen pentoxide. So, our rate equation must be rate equals 𝑘 times the concentration of dinitrogen pentoxide. This is the only equation where the sum of the powers is one, and we contain our reactant.

Now what we need to do is substitute in our rate constant and the concentration of dinitrogen pentoxide to find the rate. So our rate is equal to the rate constant, 6.20 times 10 to the minus four per minute, multiplied by the concentration of dinitrogen pentoxide, 0.400 molars. Which is equal to 2.48 times 10 to the minus four molars per minute. However, we’re not quite done.

The question asks for the rate of reaction in molars per second. There are 60 seconds in a minute, so there is one minute per 60 seconds. If we multiply our answer in molars per minute by one minute per 60 seconds, we get 4.13 recurring times 10 to the minus six molars per second. You can get from the numerical value of one to the numerical value of the other by simply dividing by 60. It makes sense that if we consume 2.48 times 10 to the minus four molars in a minute, we will consume 60 times less in a second.

But we aren’t quite done because all the values in our calculation are given to three significant figures. So, we should give our answer to the same precision. So the rate of reaction in molars per second, when the concentration of dinitrogen pentoxide is 0.400 molars, is 4.13 times 10 to the minus six molars per second.