To solve this problem, we use the ideal gas equation which is expressed as PV=nRT. It has been said that the pressure and the temperature for the two gases are equal therefore P/T is a constant value. We can use the two conditions given in order to solve this problem without the pressure and temperature given. Calculation are as follows:
P/RT = n1/V1 = n2/V2
Condition 1 for the carbon dioxide gas and 2 for the nitrogen gas. Let x be the mass of the nitrogen gas.
1.35 g (1mol CO2 / 44.01 g CO2) /1 L = x (1mol N2 / 28.02 g N2) / 1 L
x = 0.86 g N2