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The partial pressure of carbon dioxide in the flask is 0,69 atm and the total pressure in the flask is 1,62 atm

Explanation:

Let think the Ideal gas equation

Pressure . volume = n.R.T

where R = 0,082 L.atm/ mol.K

T is temperature in K (T in °C + 273)

n = moles

In a mixture you have to think P as Total Pressure and n, the total moles (mol from any gas in the mixture)

You have mass, so let's get the moles

H2 = 0,545g/ 2,016 g/m = 0,270 moles

CO2 = 8,89 g/44 g/m = 0,202 moles

Total moles = 0,270 + 0,202 = 0,472 moles

Pressure = (0,472 moles . 0,082L.atm/mol.K . 347K) / 8,30L

Pressure = 1,62 atm

Pressure of CO2 must be calculated by the same rule, just take account moles from CO2

Pressure = (0,202 moles . 0,082L.atm/mol.K . 347K) / 8,30L

Pressure = 0,692 atm

There is another way to solve the partial pressure which involves the molar fraction.

Pressure in one gas / Total pressure = n moles in one gas / Total moles

Pressure CO2 / Total pressure = n moles CO2 / Total moles

Pressure CO2 = (n moles CO2/Total moles). Total pressure

Pressure CO2 = (0,202 moles / 0,472 moles). 1,62 atm

Pressure CO2 =  0,69 atm