At which temperature nitrogen under 1.00 atm pressure has the same root mean square speed as that of CO 2 at STP

Question

At which temperature nitrogen under 1.00 atm pressure has the same root mean square speed as that of CO 2 at STP (A) 0° C (B) 27° C (C) -99° C (D) -200° C

Tardigrade Admin · Accepted Answer

Let RMS speed of nitrogen at T K be u and is equal to that of CO 2 at STP u=√(3 R T/28)=√(3 R × 273/44) T=(273 × 28/44) =173.73 K =-99.27° C

Q. At which temperature nitrogen under $1.00$ atm pressure has the same root mean square speed as that of $C O_{2}$ at STP

$0^{\circ} C$

$2 7^{\circ} C$

$- 9 9^{\circ} C$

$- 20 0^{\circ} C$

Let RMS speed of nitrogen at $T K$ be $u$ and is equal to that of $C O_{2}$ at STP
$u = \frac{3 RT}{28} = \frac{3 R \times 273}{44}$
$T = \frac{273 \times 28}{44}$
$= 173.73 K = - 99.2 7^{\circ} C$

Q. At which temperature nitrogen under 1.00 atm pressure has the same root mean square speed as that of CO2​ at STP

0∘C

27∘C

−99∘C

−200∘C