For same mass of two different ideal gases of molecular weights `M_(1) and M_(2)` plots of log V vs log P at a given constant temperature are shown. Identify the correct option.

Options

A. `M_(1)gtM_(2)`
B. `M_(1)=M_(2)`
C. `M_(1)ltM_(2)`
D. Can be predicted only if temperature is known

Answer

A

Explanation

For ideal gases,
`pV=nRT=(w)/(M)RT" "(because n=(w)/(M))`
For same mass of gases at constant
temperature, w RT is constant (say K)
`pV=(K)/(M)`
Taking log on both sides,
`logp+logV=log""(K)/(M)`
`"or "logV=-logP+log""(K)/(M)`
Comnparing with eqaution of straight line
`(y=mx+c)`
`"For ideal gas (1), Intercept (1)"=log""(K)/(M_(1))`
`"For ideal gas (2), Intercept (2)"=log""(K)/(M_(2))`
From graph,
`log""(K)/(M_(2)) gt log""(K)/(M_(1))`
`"or "(K)/(M_(2)) gt (K)/(M_(1)) therefore M_(1) gt M_(2)`