CO₂ gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of CO₂ adsorbed becomes 64 times when the pressure of CO₂ is doubled. The value of n in the Freundlich isotherm equation is ____________ × 10⁻². (Round off to the Nearest Integer)

Solution

Chemistry ma’am · 4 steps

Take the ratio of the two Freundlich equations. Then 64 is just a power of 2 and the exponent drops out.

1. Write the isotherm. The Freundlich isotherm is x/m = kP^(1/n). Write it at pressure P and at 2P, with the mass of charcoal m the same both times.

   (x/m)₂/(x/m)₁ = (2P/P)^(1/n) ⇒ 64 = 2^(1/n)

2. Match the powers. k and m cancel in the ratio. Since 64 = 2⁶, the exponents must be equal, so 1/n = 6.
3. Find n. n = 1/6 = 0.1667 = 16.67 × 10⁻².
4. So. Rounded to the nearest integer, the answer is 17.

The common slip: 600. Treating the exponent as n instead of 1/n gives n = 6, which is 600 in units of 10⁻², not 17.

The idea to keep. In Freundlich problems, divide the two equations so k cancels. Then write the ratio as a power of the pressure ratio. Remember that the exponent is 1/n, not n.

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