Computing initial reaction speed given reaction constant

**Problem:** $\ce{N2O}$ falls apart in oxygen gas and nitrogen gas according to a first order reaction rate. If you know that the rate constant is $0.38\ \mathrm{s^{-1}}$ at $760\ \mathrm{^\circ C}$, compute then the initial rate for the decomposition of $3.00\ \mathrm{g}$ $\ce{N2O}$ in a barrel of $5.0\ \mathrm{L}$. When the initial concentration doubles, what happens with the rate?


**Attempt at solution:** I set up the reaction as $$\ce{2 N2O -> O2 + 2 N2}$$ The molar mass of $\ce{N2O}$ is $44.019\ \mathrm{mol/g}$, and since we got $3.00\ \mathrm{g}$, this is $132.057\ \mathrm{mol}$. Then I computed $[\ce{N2O}] = 27.01\ \mathrm{M}$ since we had to divide by $5$ because the barrel has a volume of $5.0\ \mathrm{L}$. Then we have $$v = k [\ce{N2O}] = 10.26\ \mathrm{M/s}$$ But I’m not sure if this is the correct approach. Any help please?


