Hello, I am stuck on problem number 5.97 from the textbook: Chemistry, TheMolecu

Question

Hello,
I am stuck on problem number 5.97 from the textbook: Chemistry, TheMolecular Nature of Matter and Change 4th Ed. by Martin Silberberg(2006).

The problem states:
An atmospheric chemist studying the reactions of the pollutantSO2 places a mixture of SO2 and O2in a 2.00 L container at 900K and an initial pressure of 1.95 atm.When the reaction occurs, gaseous SO3 forms, and thepressure eventually falls to 1.65 atm. How many moles ofSO3 form?

The answer in the back of the book is given as:1.62x10-2 moles, but I don't understand how it isarrived at. Can anyone help?

Thank you,
Sabzi

Explanation / Answer

             SO2 + ½ O2 -> SO3

The total number of gas particles before reaction is

PV = nRT

             (1.95)(2) = n(0.0821)(900)

       0.0528 moles = n

Every mole of SO3 which forms consumes 1½moles of reactants, meaning that 1½ moles of particles(reactants) would be reduced to 1 mole (products), ie., by thefactor 1/1½ or 66.7%. Stated another way, when 1mole of SO3 forms, 1½ moles of reactantsdisappear:

(remaining moles) = (original moles)– (1.5 - 1.0) (per mole SO3 formed).

The term (1.5 – 1.0) is the difference between theaggregate coefficients of the products and that of thereactants. If you’d used the equation

             2SO2 + O2 -> 2SO3

you’d have

(remaining moles) = (original moles) – (3 - 2) (per 2moles SO3 formed)

which would give you the same ratio of moles formed to molesreduced.

Given that the pressure is reduced from 1.95 atm to 1.65 atm(assuming constant temperature and volume), the reduction inpressure comes from the reduction in the number of gaseousparticles.

(remaining moles) / (original moles) = 1.65 / 1.95

That’s the chemistry. The solution is pure algebra.

Let x=number of moles of SO3 formed

0.0528 =number of moles of reactants (total) beforereaction starts

   initial moles / finalmoles            = 1.95 / 1.65

          0.0528 / (0.0528 – ½ x ) = 1.1818

          0.0528 = (0.0528 – 0.5 x ) ( 1.1818 )

          0.0528 = .0624 – x 0.591

          0.0162 moles =   x

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