Sketch shows the plot of Z vs P for 1 mol of a hypothetical gas at three distinct temperature.

Boyle’s temperature is the temperature at which a gas shows ideal behaviour over a pressure range in the low pressure region. Boyle’s temperature `(T_(b)) = (a)/(Rb)`. If a plot is obtained at temperatures well below Boyle’s temperature then the curve will show negative deviation, in low pressure region and positive deviation in the high pressure region. Near critical temperature the curve is more like `CO_(2)` and the temperature well above critical temperature curve is more like `H_(2)` as shown above. At high pressure suppose all the constant temperature curve varies linearly with pressure according to the following equation: `Z =1 + (Pb)/(RT) (R = 2 cal mol^(-1) K^(-1))`
For 500 K plot the value of Z changes from 2 to 2.2 if pressure is varied from 1000 atm to 1200 atm (high pressure) then the value of `(b)/(RT)` will be :

Options

A. `10^(-3) atm^(-1)`
B. `2 xx 10^(-3) atm^(-1)`
C. `5 xx 10^(-4) atm^(-1)`
D. `10^(-4) atm^(-1)`

Answer

A

Explanation

Slope in high P region `=(b)/(RT) = (2.2 -2)/(1200 - 1000) = (0.2)/(200) = 10^(-3) atm^(-1)`