The compressibility factor of a gas can be written to first order as Z = 1 + (P)/(RT)(b - (a)/(RT)). For nitrogen (a = 1.39 L^2 atm mol^-2, b = 0.0391 L mol^-1, R = 0.0821 L atm K^-1 mol^-1) which statements are correct?

At 300 K the bracket b - a/RT is negative

At 600 K the bracket b - a/RT is positive

At 300 K and 10 atm, Z is approximately 0.993

The bracket vanishes at about 433 K

At 300 K the bracket b - a/RT is negative

At 600 K the bracket b - a/RT is positive

At 300 K and 10 atm, Z is approximately 0.993

The bracket vanishes at about 433 K

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3rg066

The compressibility factor of a gas can be written to first order as $Z = 1 + \frac{P}{RT} (b - \frac{a}{RT})$ . For nitrogen ( $a = 1.39 L^{2} atm mo l^{- 2}$ , $b = 0.0391 L mo l^{- 1}$ , $R = 0.0821 L atm K^{- 1} mo l^{- 1}$ ) which statements are correct?

300 K

a / RT = 1.39/24.63 = 0.0564

, larger than

b = 0.0391

, so the bracket is

- 0.0173

(A true). At

600 K

a / RT = 0.0282

, smaller than

b

(B true).

Z = 1 + \frac{10}{24.63} \times (- 0.0173) = 0.9930 \approx 0.993

(C true). The bracket is zero at

T = a / R b = 433 K

(D true).