A gas is at temperature `80^(@)C` and pressure `5xx10^(-10)Nm^(-2)`. What is the number of molecules per `m^(3)` if Boltzmann's constant is `1.38xx10^(-23)JK^(-1)`

Explanation

Temperature T = 80 + 273 = 353K
Pressure `P = 5 xx10^(-10) N//m^2`
`K_B=R/N:. R = K_BN`
`P=nRT=nK_BNT`
Number of molecules,
`nN=P/(K_BT)`
`(5xx10^(-10))/(353xx1.38xx10^(-23))`
`=(5xx10^(-10+23))/(353xx1.38)`
`=(5xx10^(13))/487 = 0.102xx10^(12)`
`:.` Number of molecules `=1.02xx10^(11)`