A vessel contains 1.6g of dioxygen at STP(273.15k,1atm pressure). The gas is now trasnferred to another vessel at constnat temperature. Whre pressure becomes half of the original pressure. Calculate
( a) Volume of the new vessel.
(b) number of molecuels of dioxygen.

Explanation

(i) `"1.6 g O"_(2)=1.6//32 mol="1.05 mol, 1 mol of O"_(2)" at STP has volume of = 22.4 L"`
`therefore" 0.05 mol of O"_(2)" at STP has volume "=22.4xx0.05=1.12 L`
(Remember. 1 mol of gas = 22.4 L if STP conditions are 273.15 K and atm
`" = 22.7 L if STP conditions are 273.15 K and 1 bar")`
`"Now, "V_(1)=1.12L," "P_(1)="1 atm , "V_(2)=?," "P_(2)=(1)/(2)" atm = 0.5 atm"`
As temperature remains constant, applying Boyle's law, `P_(1)V_(1)=P_(2)V_(2) or V_(2)=(P_(1)V_(1))/(P_(2))=("1 atm"xx1.12L)/("0.5 atm")=2.24 L`
(ii) Number of molecules in 1.6 g `O_(2)`, i.e., 0.05 mol `O_(2)=0.05xx6.022xx10^(23)=3.011xx10^(22)`.