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The following data were obtained during ...

The following data were obtained during the first order thermal decomposition of `SO_(2) CI_(2)` at a constant volume:
`SO_(2) CI_(2) (g) to SO_(2) (g) + CI_(2) (g)`

Calculate the rate constant.
(Given, `log 4 = 0.6021, log 2 = 0.3010`)

Text Solution

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`SO_(2) CI_(2) (g) to SO_(2) (g) + CI_(2) (g)`
Initial pressure `P i " "0" "0`
After time,t `P i-P" "P" "P`
Total pressure after time `t`,
i.e. `P_(t) = P i - P + P + P = P i + P`
`rArr P = P_(t) - P_i `
Thus, `a = P i and a-x = P i - P = P = P i - (P_t - P i)`
`= P i - P_(t) + P i = 2P i - P t`
Substituting the values of a and `(a - x)` in equation,
`k = (2.303)/( t) log"" (a)/( a-x)`
`k = (2.303)/( t) log"" (P i)/ (2_(p_i - p_t) )`
Calculation of rate constant `(k)`, when `t= 100" s"`
Given, `p_i = 0.4" atm" and p_(t) = 0.7" atm"`
Then, ` = (2.303)/( 100) log"" (P_i)/( (2_(P_i - P_t) ) )`
`= (2.303)/( 100) log"" (0.4)/( (2 xx 0.4 - 0.7))`
`= (2.303)/( 100) log"" (0.4)/(0.1) = (2.303)/( 100 )log 4`
`= (2.303)/( 100) xx 0.6021 = 0.01387 = 1.387 xx 10^(-2)" s"^(-1)`
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