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The following data were obtained during the first order thermal decomposition of SO_2 Cl_2 at a constant volume. ( SO_2 Cl_2 g) gives SO_2 (g) plus Cl_2 (g)

4.21   The following data were obtained during the first order thermal decomposition of SO_2 Cl_2 at a constant volume.
            ( SO_2Cl_2 g) \rightarrow SO_2 (g) + Cl_2 (g)

       

           Calculate the rate of the reaction when total pressure is 0.65 atm.

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M manish

The thermal decomposition of SO_{2}Cl_{2} is shown here;

After t time, the total pressure p_{t}p_{0}-p+(p+p) = p_{0}+p

                                               So, p = p_{t}-p_{0}

thus, p_{0}-p = 2p_{0}-p_{t}

for first order reaction,

k= \frac{2.303}{t}\log\frac{p_{0}}{p_{0}-p}
   = \frac{2.303}{360}\log\frac{p_{0}}{2p_{0}-p_{t}}
now putting the values of pressures, when t = 100s
k = \frac{2.303}{100}\log\frac{0.5}{2*0.5-0.6}
   = 2.231 \times 10^{-3}\ s^{-1}

 

when p_{t} = 0.65\ atm

p = p_{t}-p_{0}
    = 0.65 - 0.5
   = 0.15 atm

So, p(_{SO_{2}Cl_{2}}) = p_{0}-p
                            = 0.5 - 0.15
                            = 0.35 atm

Thus, rate of reaction, when the total pressure is 0.65 atm
      rate = k(p(_{SO_{2}Cl_{2}}))
             = 2.31\times 10^{-3}\times 0.35
             = 7.8 \times 10^{-4}\ atm\ s^{-1}

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