O2 rms 4.28×10^4 cm/s CO2 rms

O2 rms 4.28×10^4 cm/s CO2 rms

 

 

If the rms speed of an O2 molecule is 4.28×10^4 cm/s at 25℃,

what is the rms speed of a CO2 molecule at the same temperature?

 

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u_rms = root(3RT/M)

( 참고 https://ywpop.tistory.com/45 )

 

---> CO2의 rms 속도는 O2보다 느리다.

 

 

 

O2의 rms 속도

4.28×10^4 cm/s = [3RT / (32/1000)]^(1/2) ...(1)

 

 

 

CO2의 rms 속도

x = [3RT / (44/1000)]^(1/2) ... (2)

 

 

 

(1)식 / (2)식

 

(4.28×10^4) / x = [3RT / (32/1000)]^(1/2) / [3RT / (44/1000)]^(1/2)

 

(4.28×10^4) / x = [(44/1000) / (32/1000)]^(1/2)

 

x = (4.28×10^4) / [(44/1000) / (32/1000)]^(1/2)

= 3.65×10^4

 

 

 

답: 3.65×10^4 cm/s

 

 

 

 

[참고]

R = 8.314 인데, 이 값을 모른다고 가정하고,

R을 계산하면,

u_rms = root(3RT/M)

 

u_rms^2 = 3RT / M

 

R = u_rms^2 × M / 3T

= (4.28×10^4)^2 × (32/1000) / (3 × (273.15+25))

= 65536

 

 

 

65536 값으로 CO2의 rms 속도를 계산하면,

u_rms = [3 × 65536 × (273.15+25) / (44/1000)]^(1/2)

= 3.65×10^4

 

 

 

 

[키워드] CO2 rms 기준문서, If the rms speed of an O2 molecule at a particular temperature is 4.28×10^4 cm/s, what is the rms speed of a CO2 molecule at the same temperature?