A flask contains argon and chlorine gases in a mass ratio of 2:1 at 27°C. Given molar masses M(Ar) = 40 u and M(Cl₂) = 70 u, find v(RMS)(Ar)/v(RMS)(Cl₂).
Options

Question

A flask contains argon and chlorine gases in a mass ratio of 2:1 at 27°C. Given molar masses M(Ar) = 40 u and M(Cl₂) = 70 u, find v(RMS)(Ar)/v(RMS)(Cl₂).

G1 Physics · Accepted Answer

Step 1: For any ideal gas, v(RMS) = √(3RT/M), where M is the molar mass. Step 2: Both gases are at the same temperature, so their rms-speed ratio depends only on molar masses, not the mass ratio in the flask. Step 3: v(RMS)(Ar)/v(RMS)(Cl₂) = √(M(Cl₂)/M(Ar)) = √(70/40). Step 4: Simplify √(7/4) = √7/2. Final answer: √7/2 (Option C).