At 627^(@)C and 1 atm pressure, SO_(3) undergoes partial dissociation into SO_(2) and O_(2) SO_(3) hArr SO_(2) + (1)/(2)O_(2) if the observed density of the equilibrium mixture is 0.925 g/L, calculate degree of dissociation of SO_(3).

At 627^(@)C and 1 atm pressure, SO_(3) undergoes partial dissociation

1.	At 627^(@)C and 1 atm pressure, SO_(3) undergoes partial dissociation into SO_(2) and O_(2) SO_(3) hArr SO_(2) + (1)/(2)O_(2) if the observed density of the equilibrium mixture is 0.925 g/L, calculate degree of dissociation of SO_(3).
Answer» Solution :Let the initial no. of moles of `SO_(3)` be 1and its degree of DISSOCIATION x. `{:(1,,0,,0,"Initial no. of moles"),(SO_(3),+,SO_(2),+,(1)/(2)O_(2),),(1-x,,x,,x//2,"Moles at equilibrium"):}` `therefore` total no. of moles at eqb. `= 1- x + x + (x)/(2) = 1 + (x)/(2)` Thus applying PV = nRT `1 xx V = (1+(x)/(2)) xx 0.0821 xx (627 + 273)` `V = (1+(x)/(2)) xx 73.89` litres. Now w.t of 1 mole of `SO_(3) = 80g` and therefore, from the law of conservation of mass, we have, wt. of gases at eqb. = 80 g. `therefore "DENSITY" = ("wt. in g")/("vol. in LITRE") = (80)/((1+(x)/(2)) xx 73.89) = 0.925` (given) or x = 0.34.