Question

Two gases X and Y are found in the atmosphere only trace amounts because they decompose quickly. When exposed to ultraviolet light the half-life of Xis 0.50 h, while that of Y is 90. min. Suppose an atmospheric scientist studying these decompositions fills a transparent 5.0 L flask with Xand Y and exposes the flask to UV light. Initially, the partial pressure of X is 3.0 times greater than the partial pressure of Y. dlo yes As both gases decompose, will the partial pressure of X ever fall below the partial pressure of Y? no X If you said yes, calculate the time it takes the partial pressure of X to fall below the partial pressure of Y. Round your answer to 2 significant digits.

Answer 1

(a Yes (b) Suppose at ime t minutes ; the partial pressuru of X and Y ane laual 3P. So; ihitial pressuru of Yi P Supp Initial pressu re of X is Jhe decompositan follews first orden kinethcs larbal pressure of 2, X at tme t is: O 693 xt 36 Pr = 3Px e Fanhal pressuna of Y at time t is- 0.693 Py= fxe .: Pe-Py 3f x e O-693xt - Pxe 0693xt 30 90 11 bo th sides Jaking In on O69 3rt 90 6-693xt 3 0 g0 30 t = 71minutes 71.3 minutes parhal pressure of X us So after partial pressure of Y 713 minutes Chour 6o minutes) 2 hours. (ho sighifiant dig Answer is Finnl ansuer is 12 hours