At what temperature, the root-mean-square velocity of SO2 will be the same as that of CH4 at 27°C ?

Question

At what temperature, the root-mean-square velocity of SO2 will be the same as that of CH4 at 27°C ? (A) 3000 K (B) 1345 K (C) 1200 K (D) 1700 K

Tardigrade Admin · Accepted Answer

Root-mean-square velocity =√(3RT/M) The value for CH4 at 27°C or 300 K =√(3R×300/16) Now for SO2 Root-mean-square velocity =√(3RT/64) or, √(3R×300/16) =√(3R× T/64) or T=1200 K

Q. At what temperature, the root-mean-square velocity of $S O_{2}$ will be the same as that of $C H_{4}$ at $2 7^{\circ} C$ ?

$3000 K$

$1345 K$

$1200 K$

$1700 K$

Root-mean-square velocity $= \frac{3 RT}{M}$
The value for $C H_{4}$ at $2 7^{\circ} C$ or $300 K = \frac{3 R \times 300}{16}$
Now for $S O_{2}$
Root-mean-square velocity $= \frac{3 RT}{64}$
or, $\frac{3 R \times 300}{16}$
$= \frac{3 R \times T}{64}$
or $T = 1200 K$

Q. At what temperature, the root-mean-square velocity of SO2​ will be the same as that of CH4​ at 27∘C ?

3000K

1345K

1200K

1700K