Which of the following graph correctly represents the plots of K_H at 1 bar for gases in water versus temperature?

Solution

Chemistry ma’am · 4 steps

Bigger K_H means a less soluble gas, so helium goes on top, and each curve rises first, then falls.

1. Read K_H. Henry's law is p = K_H x. At the same pressure of 1 bar, a larger K_H gives a smaller mole fraction x in water, so a larger K_H means a less soluble gas.
2. Order of gases. He is the least soluble gas in water, and CH₄ dissolves far better than He or N₂. At 298 K, K_H is about 145 kbar for He, 76.5 kbar for N₂, 34.9 kbar for O₂ and 0.41 kbar for CH₄. So the order is He > N₂ > O₂ > CH₄.
3. Shape with temperature. Gases become less soluble as cold water warms, so K_H rises at first. For gases in water, K_H then passes through a maximum and falls at higher temperatures. It also has a definite non-zero value at 0 °C.

   Option	Order of gases (top to bottom)	Shape of curves	Verdict
   (a)	O₂ > N₂ > He, reversed	rise, then fall	wrong order
   (b)	He > N₂ > CH₄, correct	rise, then fall, correct	correct
   (c)	He > N₂ > O₂	fall, then rise	wrong shape
   (d)	O₂ > N₂ > He, reversed	straight lines from zero	wrong order and shape

4. So. Only (b) puts the least soluble gas, He, on top and the most soluble gas, CH₄, at the bottom, with each curve rising to a maximum and then falling. The answer is (b).

The idea to keep. In p = K_H x, a big K_H means a gas that barely dissolves. Rank the gases by solubility, flip that order for K_H, and remember that K_H rises with temperature at first.

Answer from the NTA final answer key. Solution by PrepWiser.