QUESTION #2: The following results were reported by Langmuir for the adsorption of N2(g) on (mica) a surface at 20 °C. Pressure (atm) | 2.8 | 4.0 | 6.0 | 9.4 | 17.1 | 33.5 Amount of gas adsorbed (mm³) at 20 °C and 1atm | 12.0 | 15.1 | 19.0 | 23.9 | 28.2 | 33 a) Make a linear plot of these values in order to test Langmuir isotherm. If it applies, evaluate the constant ‘K’. b) A maximum of about 10¹? molecules usually covers 1 cm² of a surface. Make an estimate of the effective surface area in Langmuir experiment.
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First, we need to write down the Langmuir isotherm equation: $$\frac{x}{m} = \frac{KP}{1 + KP}$$ where $x$ is the amount of gas adsorbed, $m$ is the mass of the adsorbent, $K$ is the Langmuir constant, and $P$ is the pressure. Show more…
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Use the following data to determine the Langmuir adsorption parameters for nitrogen on mica: $$\begin{array}{cc} V_{\text {ds}}\left(\mathrm{cm}^{3} \mathrm{g}^{-1}\right) & P(\text { Torr }) \\ \hline 0.494 & 2.1 \times 10^{-3} \\ 0.782 & 4.60 \times 10^{-3} \\ 1.16 & 1.30 \times 10^{-2} \end{array}$$
The adsorption of CO gas on charcoal at 273 K fit to the Langmuir isotherm, θ = Kp / (1 + Kp) = V / Vm. Its linear plot of p/V vs. p of the CO gas variation introduced the following least square linear equation p/V (kPa/cm³) = 1.2 kPa/cm³ + 0.0100 cm⁻³ p. Based on these results and given the surface area of a CO molecule 818 nm², the adsorption isotherm equilibrium constant (K) and the surface area of 1 g charcoal at 273 K and 1 atm, respectively, should be A) 1.2e2 kPa⁻¹ and 1.1 km² B) 1.2e-2 kPa⁻¹ and 2.2 km² C) 1.2e-2 kPa⁻¹ and 1.1 km² D) 8.3e-3 kPa⁻¹ and 1.1 km² E) 8.3e-3 kPa⁻¹ and 2.2 km²
Adi S.
Langmuir's adsorption equation which describes the amount of gas adsorbed on a solid surface is written as: $$ \frac{\mathrm{p}}{\mathrm{x} / \mathrm{m}}=\frac{1}{\mathrm{ab}}+\frac{\mathrm{p}}{\mathrm{b}} $$ Here $\mathrm{x} / \mathrm{m}$ is the extent of adsorption, $\mathrm{a}$ and $\mathrm{b}$ are constants, and $\mathrm{p}$ is the gas pressure. On the basis of the above equation indicate which of the following statements is correct:
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