I think I might have read the question wrong.
I calculated the partial volume of CO2 at 0.819 atm. Even though a gas volume = its container (assuming rigid container).
I also assumed that in the flask there is a mixture of CO2 and air.
I think you are to calculate the new volume of CO2 if the temperature and pressure are changed to STP.
For that change, you are correct to use P1V1/T1 = P2V2/T2
After all that I get 9.68 mL