$\pu{2.0 L}$ of $\ce{O2 (g)}$ and $\pu{8.0 L}$ of $\ce{N2}$, each at $\pu{0.00^\circ C}$ and $\pu{1.00 atm}$, are mixed together. The nonreactive gaseous mixture is compressed to occupy $\pu{2.0 L}$ at $\pu{298 K}$. What is the pressure exerted by this mixture?
I tried to solve this problem by first using
$$P_\mathrm{tot}=\frac{n_\mathrm{tot}RT}{V}\quad(T=\text{constant}; V=\text{constant})$$
then using
$$V_\mathrm{tot}=\frac{n_\mathrm{tot}RT}{P}\quad(T=\text{constant}; P=\text{constant})$$
Plugging in the numbers for the second equation
$$10=\frac{n_\mathrm{tot}\cdot 8.314\cdot 273}{101325}$$ $$n_\mathrm{tot}=\pu{0.45 mol}$$
Then plugging in the numbers for the first equation
$$P_\mathrm{tot}=\frac{0.45\cdot 8.314\cdot 298}{2}=\pu{6.76 atm}$$
Whereas the answer is $\pu{5.5 atm}$. What am I doing wrong here?