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 o

Question

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

TestHub · Accepted Answer

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

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