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5. Calculate
(a) the rms speed of an oxygen molecule at `0°C`
(b) determine how many times per second it would move back and forth across a `7.0`-`m`-long room on the average, assuming it made very few collisions with other molecules.
5. Calculate
(a) the rms speed of an oxygen molecule at 0°C
(b) determine how many times per second it would move back and forth across a 7.0-m-long room on the average, assuming it made very few collisions with other molecules. `v_(rms) = sqrt((3kT)/m)`
`overline(v^2) = overline(v_x^2)+overline(v_y^2)+overline(v_z^2) = 3 overline(v_x^2)`
a) `v_(rms) =461\ m//s`
b) times/sec ` = 19 ` times/sec
Given:
`T = 0°C = 273\ K`
`L = 7.0\ m`
Known:
`m_O_2 = 32\ u = 32 times 1.66 times 01^(-27)\ kg`
`k = 1.38 times 10^(-23)\ J//K`
Equations:
`v_(rms) = sqrt((3kT)/m)`
`overline(v^2) = overline(v_x^2)+overline(v_y^2)+overline(v_z^2) = 3 overline(v_x^2)`
a)
`v_(rms) = sqrt((3kT)/m_o_2)`
`v_(rms) = sqrt((3(1.38 times 10^(-23)\ J//K)(273\ K))/(32 times 1.66 times 01^(-27)\ kg))`
`v_(rms) =461\ m//s`
b)
Let's only consider the `x` component
`overline(v^2) = overline(v_x^2)+overline(v_y^2)+overline(v_z^2) = 3 overline(v_x^2)`
`overline(v_x^2) = overline(v_x^2)/3`
`overline(v_x) = v_(rms)/sqrt(3)`
The distance a molecule move back and forth equals `2L`
`t = d/overline(v_x) = (2L)/(v_(rms)/sqrt(3))`
`t = (2sqrt(3)L)/v_(rms)`
times/sec `= 1/t = v_(rms)/(2sqrt(3)L)`
times/sec ` = (461\ m//s)/(2sqrt(3)( 7.0\ m))`
times/sec ` = 19 ` times/sec |