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Q.

SO3 gas is entering the environment at a constant rate of 6.93×106gm/L/ day  due to the emission of polluting gases from thermal power plant, but at the same time it is decomposing and following first order kinetics with half life of 100 days. Based on above information, select the true statement(s).

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a

Concentration of SO3 in Kota is 1.25×105M (Assume SO3  present in Kota with constant concentration means rate of formation and dissociation of SO3 are equal).

b

An industry is manufacturing H2SO4 at the rate of 980 kg per day with the use of SO3 in air it should use 8×105 Litre air/day.

c

If SO3 emission is stopped then after 1000 days its concentrations will reduce to 1.2×108M

d

If103L of air is passed through 1 L pure water (assuming all SO3 to dissolved in it) and resulting solution is titrated against 1 N, NaOH solution of which 15 ml is consumed.

answer is A, B, C, D.

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Detailed Solution

Assuming SO3 conc. to be x M

 (a) dxdt=6.93×10680kx

When SO3  concentration will reach steady state or constant concentration

dxdt=0x=6.93×10680=6.93×10680×0.693×102=1.25×105M

(b) Total time  =10t1/2=10×100=1000 days 

k=1tlnSO30SO3t;SO3t=1.25×108M

(c) Eq. of  SO3=Eq. of NaOH 

103×1.25×105×2=1×VV=2.5×103 litre 

(d) Mol of SO3=Mol of  H2SO4

V×1.25×105=980×10398V=8×108 litre 

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