For the solution of the gases $\mathrm{w}, \mathrm{x}, \mathrm{y}$ and z in water at 298 K, the Henrys law constants $\left(\mathrm{K}_{\mathrm{H}}\right)$ are $0.5, 2, 35$ and 40 kbar, respectively. The correct plot for the given data is:

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Solutions

For the solution of the gases

w, x, y

and z in water at 298 K, the Henrys law constants

(K_{H})

are

0.5, 2, 35

and 40 kbar, respectively. The correct plot for the given data is:

Answer: (D)

Henry's law fixes the partial pressure of a dissolved gas as

P_{g a s} = K_{H} X_{g a s}

. With only the gas and water in the liquid,

X_{g a s} = 1 - X_{w a t er}

, so

P_{g a s} = K_{H} (1 - X_{w a t er}) = K_{H} - K_{H} X_{w a t er}

. Plotted against the mole fraction of water, each gas gives a straight line: its intercept on the pressure axis is

K_{H}

(the value when

X_{w a t er} = 0

) and its slope is

- K_{H}

, so every line falls off and all of them reach zero pressure together at

X_{w a t er} = 1

, where no gas is left in the liquid. A larger

K_{H}

means both a higher intercept and a steeper descent, so the four lines order as

w (0.5) < x (2) < y (35) < z (40)

in both intercept and steepness. The correct graph is the one in which these straight lines start from intercepts in that order, with

z

highest and steepest and

w

lowest and gentlest, all converging to zero as the liquid becomes pure water.

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Single correct option