An open vessel at 27^(@)C is heated until 3//5^(th) of the air in its has been expelled. Assuming that the volume of the vessel remains constant find (a) the temperature at which vessel was heated ? (b) the air escaped out if vessel is heated to 900 K? (c ) temperature at which half of the air escapes out ?

An open vessel at 27^(@)C is heated until 3//5^(th) of the air in its

1.	An open vessel at 27^(@)C is heated until 3//5^(th) of the air in its has been expelled. Assuming that the volume of the vessel remains constant find (a) the temperature at which vessel was heated ? (b) the air escaped out if vessel is heated to 900 K? (c ) temperature at which half of the air escapes out ?
Answer» Solution :ONE should clearly note the FACT that on heating a gas in a vessel there are the number of moles of gas which go out, the volume of vessel remains CONSTANT. Let initial moles of gas at 300 K be .n.. On heating 3//5 moles of air are escaped out at temperature T. `therefore` Moles of air left at temperature `T=(n-(3)/(5)n)=(2n)/(5)` (a) Under similar conditions of P and V `n_(1)T_(1)=n_(2)T_(2)` `nxx300=(2n)/(5)xxT` `T=750 K` (B) On heating vessel to 900 K, let `n_(1)` moles be left again `n_(1) T_(1)=n_(2)T_(2)` `n_(1)xx900=300xxn` `RARR n_(1)=(1)/(3)n` `therefore ` Moles escaped out `=n-(n)/(3)=(2)/(3) n` moles (c ) Let n/2 moles are escaped out at temperature T then `n_(1)T_(1)=n_(2)T_(2)` `(n)/(2)xxT =nxx300` `T=600 K`