Q.Compare the rms speed of hydrogen molecules at 127 ºC with the rms speed of oxygen molecules at 27 ºC, given that the molecular masses of hydrogen and oxygen are 2 and 32 respectively.

[!TLDR] Form the ratio v_rms(H₂,400K):v_rms(O₂,300K) using v_rms ∝ √(T/M). [! …

Using v_rms = sqrt(3RT/M0), the ratio of rms speeds is v_rms(H2)/v_rms(O2) = sqrt[(T_H2/M_H2)/(T_O2/M_O2)]. Converting temperatures to Kelvin: T_H2 = 127 + 273 = 400 K, T_O2 = 27 + 273 = 300 K. Substituting M_H2 = 2, M_O2 = 32: ratio = sqrt[(400/2)/(300/32)] = sqrt[200/9.375] = sqrt(21.333) ≈ 4.619. Expressing this as an exact ratio: sqrt(200/9.375) = sqrt(200 × 32/300) = sqrt(6 …

Convert both temperatures to Kelvin, then use v_rms ∝ √(T/M) for each gas and sim …

Forgetting to convert 127 ºC and 27 ºC to Kelvin before substituting into the formula -- v_rms depends on ABSOLUTE temperature, and us …