At STP, the ratio of the root- mean- square speed of CO₂to that of SO₂is _ . A) 1.000 B) 1.207 C) 1.456 D) 2.001 E) 2.119

Question

Quizplus · Accepted Answer

The root-mean-square speed of a gas is given by the formula v(rms) = sqrt(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas. At STP (Standard Temperature and Pressure), the temperature is 273K and the pressure is 1 atm. Since both COS and SO2 have the same temperature and pressure, we can cancel these factors out in the ratio. The molar mass of COS is 60 g/mol and the molar mass of SO2 is 64 g/mol. Plugging in these values, we get:
v(rms)COS / v(rms)SO2 = sqrt(3RT/MCOS) / sqrt(3RT/MSO2)
v(rms)COS / v(rms)SO2 = sqrt(MSO2/MCOS)
v(rms)COS / v(rms)SO2 = sqrt(64/60) ≈ 1.207
Therefore, the ratio of the root-mean-square speed of COS to SO2 is 1.207. The answer is B.

At STP, the Ratio of the Root- Mean- Square Speed