# Answer to Question #37856 in Physical Chemistry for chamalis

Question #37856

the decomposition reaction SO2Cl2 -SO2 + Cl2 is the first order reaction with rate constant (k)=2.2times ten exponent negative five at temperature of 320.What percent of SO2Cl2 is decomposed at temperature 320 after 90 minutes.

Expert's answer

Write the equation for the first order kinetics:

kt = ln(c0/c)

where k is the reaction rate constant, t - time, c0 - the initial amount of reactant, c - the amount of reactant at the moment of time t. The percent of the remaining in system sulfuryl chloride is the ratio c/c0. So the percent of decomposed SO2Cl2 is 1 - c/c0, and this value can be obtained from the equation:

c0/c = exp(kt); c/c0 = exp(-kt); %(reaction) = 1 - c/c0 = 1 - exp(-kt)

%(reaction) = 0.00198 = 0.2%

kt = ln(c0/c)

where k is the reaction rate constant, t - time, c0 - the initial amount of reactant, c - the amount of reactant at the moment of time t. The percent of the remaining in system sulfuryl chloride is the ratio c/c0. So the percent of decomposed SO2Cl2 is 1 - c/c0, and this value can be obtained from the equation:

c0/c = exp(kt); c/c0 = exp(-kt); %(reaction) = 1 - c/c0 = 1 - exp(-kt)

%(reaction) = 0.00198 = 0.2%

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