Question

The adsorption of a gas follows the Langmuir isotherm with $K = 1.25$ kPa$^{-1}$ at 25 $^\circ$C. The pressure (in Pa) at which the surface coverage is 0.2 is ______

Hint:

Langmuir isotherm: $\theta = KP/(1+KP)$ – solve for $P$ algebraically.

Answer 1

Correct Answer: 200

Step 1: Write Langmuir equation.
\[ \theta = \frac{KP}{1 + KP} \] Step 2: Substitute $\theta = 0.2$, $K = 1.25$ kPa$^{-1$.}
Let $P$ be pressure in kPa.
\[ 0.2 = \frac{1.25P}{1 + 1.25P} \] Step 3: Rearranging.
\[ 0.2(1 + 1.25P) = 1.25P \] \[ 0.2 + 0.25P = 1.25P \] \[ 0.2 = 1.00P \] \[ P = 0.20 \, \text{kPa} \] Step 4: Convert to Pa.
\[ 0.20 \, \text{kPa} = 200 \, \text{Pa} \] Step 5: Conclusion.
The required pressure is 200 Pa.