The r.m.s. speed of oxygen molecules at $47 ° C$ is equal to that of the hydrogen molecules kept at ______ $° C.$

(Mass of oxygen molecule / mass of hydrogen molecule = 32/2) [2026]

Question

The r.m.s. speed of oxygen molecules at $47 ° C$ is equal to that of the hydrogen molecules kept at ______ $° C.$

(Mass of oxygen molecule / mass of hydrogen molecule = 32/2) [2026]

Smart Achievers · Accepted Answer

(2)

$V_{rms} = \sqrt{\frac{3 R T}{M}}$

$V_{{rms}_{O_{2}}} = V_{{rms}_{H_{2}}}$

$T_{O_{2}} = 273 + 47 = 320 K$

$\sqrt{\frac{3 R T_{O_{2}}}{M_{O_{2}}}} = \sqrt{\frac{3 R T_{H_{2}}}{M_{H_{2}}}}$

$\frac{T_{O_{2}}}{M_{O_{2}}} = \frac{T_{H_{2}}}{M_{H_{2}}}$

$\frac{320}{32} = \frac{T_{H_{2}}}{2}$

$T_{H_{2}} = 20 K$

$T_{H_{2}} = - 253 ° C$

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