Question

Question #3a8f6

Answer 1

You would need the number of moles of dinitrogen pentoxide present in the container, or at least a mass of the compound, in order to solve for its initial concentration.

Since no such information was given, I assume you have to express the rate law for this reaction in a more general way.

So, you know that dinitrogen pentoxide decomposes by a first-order reaction

`N_2O_5 -> "products"`

This means that its rate law can be expressed like this

`"rate" = k * [N_2O_5]`, where

`k` - the rate constant - in your case `5.2 * 10^(-3)"s"^(-1)`
`[N_2O_5]` - the concentration of dinitrogen pentoxide.

Let's say you have a mass of x grams of dinitrogen pentoxide given. Determine the number of moles present by using the compound's molar mass

`"x grams" * ("1 mole "N_2O_5)/"108.01 g" = "x/108.01 moles"` `N_2O_5`

This means that its initial concentration will be

`C = n/V = "x/108.01 moles"/("0.750 L") = x/"81.0" M"`

The initial rate of decomposition will then be

`"rate" = 5.2 * 10^(-3)"s"^(-1) * x/81.0"M" = 6.42 * x * 10^(-5)"M" * "s"^(-1)`