A closed vessel contains 10 ~g of an ideal gas X at 300 ~K , which exerts 2 atm pressure. At the same temperature, 80 ~g of another ideal gas Y is added to it and the pressure becomes 6 ~atm . The ratio of root mean square velocities of X a

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A closed vessel contains 10 ~g of an ideal gas X at 300 ~K , which exerts 2 atm pressure. At the same temperature, 80 ~g of another ideal gas Y is added to it and the pressure becomes 6 ~atm . The ratio of root mean square velocities of X and Y at 300 ~K is

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Correct answer: D. 2: 1

For Ideal Gas PV = nRT n P at constant T & ~V . mole = Mass Molar mass For gas X : 10 M _ X 2 ~atm (1) For gas X & Y : 10 M _ X + 80 M _ Y 6 ~atm (2) From (2)-(1) 80 M _ y 4 (3) On dividing (1) by (3) M _ Y 8 M _ X = 1 2 M _ Y M _ X =4 (4) V _ rms = 3 RT M v _ rms 1 M ( V _ ms )_ X ( V _ ms )_ Y = M _ Y M _ x = 4 1 = 2 1

A closed vessel contains 10 ~g of an ideal gas X at 300 ~K , which exerts 2 atm pressure. At the same temperature, 80 ~g of another ideal gas Y is added to it and the pressure becomes 6 ~atm . The ratio of root mean square velocities of X and Y at 300 ~K is

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