# Question #3a8f6

Mar 15, 2015

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

${N}_{2} {O}_{5} \to \text{products}$

This means that its rate law can be expressed like this

$\text{rate} = k \cdot \left[{N}_{2} {O}_{5}\right]$, where

$k$ - the rate constant - in your case $5.2 \cdot {10}^{- 3} {\text{s}}^{- 1}$
$\left[{N}_{2} {O}_{5}\right]$ - 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

$\text{x grams" * ("1 mole "N_2O_5)/"108.01 g" = "x/108.01 moles}$ ${N}_{2} {O}_{5}$

This means that its initial concentration will be

$C = \frac{n}{V} = \text{x/108.01 moles"/("0.750 L") = x/"81.0" M}$

The initial rate of decomposition will then be

${\text{rate" = 5.2 * 10^(-3)"s"^(-1) * x/81.0"M" = 6.42 * x * 10^(-5)"M" * "s}}^{- 1}$