Question

$CO_2$ gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of $CO_2$ adsorbed becomes 64 times when the pressure of $CO_2$ is doubled. The value of n in the Freundlich isotherm equation is _________ $\times 10^{-2}$. (Round off to the Nearest Integer)

Hint:

When dealing with ratio problems involving Freundlich or Langmuir isotherms, it is often easiest to write the equation for the two conditions and then divide one by the other. This cancels out the constants (like k) and simplifies the algebra.

Answer 1

Correct Answer: 17

The Freundlich adsorption isotherm is expressed as: x/m = kp^1/n, where x is the mass of adsorbate, m is the mass of adsorbent, p is the pressure, k is a constant, and n is the Freundlich constant. Given that the mass of adsorbed $CO_2$ becomes 64 times when the pressure is doubled, we can set up the equation as follows:

Let x₁/m = kp^1/n represent the original condition, and x₂/m = k(2p)^1/n for the new condition.

According to the problem, x₂ = 64x₁. Therefore:

k(2p)^1/n = 64(kp^1/n)

Dividing both sides by kp^1/n, we get:

(2)^1/n = 64

Rewriting, we have:

2 = 64ⁿ

Taking the logarithm on both sides:

log(2) = n·log(64)

The base of the log is assumed to be 2 (since it simplifies calculations), so:

1 = n·6

Solving for n, we get:

n = 1/6 ≈ 0.1667

To express this in terms of n × 10^-2, multiply by 100:

n = 16.67 ≈ 17

Thus, the value of n is 17, which falls within the expected range of 17—17.