Question

An ideal gas in a container of volume 500 cc is at a pressure of 2 × 10⁵ N/m². The average kinetic energy of each molecule is 6 × 10⁻²¹ J. The number of gas molecules in the container is ______. 

Options

• 5 × 10²⁵

• 5 × 10²³

• 25 × 10²²

• 2.5 × 10²²

Answer 1

An ideal gas in a container of volume 500 cc is at a pressure of 2 × 10⁵ N/m². The average kinetic energy of each molecule is 6 × 10⁻²¹ J. The number of gas molecules in the container is 2.5 × 10²².

Explanation:

PV = Nk_BT

and (K.E./molecule) = `3/2 "k"_"B""T" = 3/2 "PV"/"N"`

∴ `"N" = 3/2 xx "PV"/("K.E."//"molecule")`

= `3/2 xx (2 xx 10^5 xx 500 xx 10^-6)/(6 xx 10^-21)`

= 2.5 × 10²²