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The adsorption of a gas is described by the Langmuir isotherm with the equilibrium constant K = 0.9 kPa-1 at 25ºC. The pressure (in kPa) at which the fractional surface coverage is 0.95, is
- a)1/11.1
- b)21.1
- c)11.1
- d)42.2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The adsorption of a gas is described by the Langmuir isotherm with the...
- The standard form for the Langmuir isotherm is often written as:
- θ = (KP) / (1 + KP)
where:
θ is the fractional coverage of the surface,
K is the Langmuir constant (equilibrium constant),
P is the pressure.
Given:
θ = 0.95,
K = 0.9 kPa⁻¹.
Let's rewrite the equation to solve for P:
0.95 = 0.9P / (1 + 0.9P)
Solving this for P will give us the pressure at which the fractional surface coverage is 0.95. Let's move ahead with the rearrangement:
Multiply both sides by (1 + 0.9P) to clear the denominator: 0.95 + 0.855P = 0.9P
Rearrange to make P the subject:
P = 0.95 / (1 - 0.855) = 21.12676... kPa
Rounding off to three significant figures, P ≈ 21.1 kPa.
So, The pressure (in kPa) at which the fractional surface coverage is 0.95, is 21.1kPa.
θ is the fractional coverage of the surface,
K is the Langmuir constant (equilibrium constant),
P is the pressure.
Given:
θ = 0.95,
K = 0.9 kPa⁻¹.
Let's rewrite the equation to solve for P:
0.95 = 0.9P / (1 + 0.9P)
Solving this for P will give us the pressure at which the fractional surface coverage is 0.95. Let's move ahead with the rearrangement:
Multiply both sides by (1 + 0.9P) to clear the denominator: 0.95 + 0.855P = 0.9P
Rearrange to make P the subject:
P = 0.95 / (1 - 0.855) = 21.12676... kPa
Rounding off to three significant figures, P ≈ 21.1 kPa.
So, The pressure (in kPa) at which the fractional surface coverage is 0.95, is 21.1kPa.
Most Upvoted Answer
The adsorption of a gas is described by the Langmuir isotherm with the...
Understanding the Langmuir Isotherm:
The Langmuir isotherm is a model used to describe the adsorption of gases on a solid surface. It assumes a monolayer adsorption and that adsorption only occurs at specific sites on the surface.
Equilibrium Constant K:
In the Langmuir isotherm, the equilibrium constant K is a measure of the adsorption capacity of the surface. In this case, K = 0.9 kPa-1 at 25°C.
Fractional Surface Coverage:
The fractional surface coverage (θ) is the ratio of the number of adsorbed gas molecules to the total number of adsorption sites on the surface. In this case, θ = 0.95.
Calculating Pressure:
The Langmuir isotherm equation is given by:
P / (1 - θ) = 1 / K
Plugging in the values:
P / (1 - 0.95) = 1 / 0.9
P / 0.05 = 1.11
P = 0.05 * 1.11
P = 0.055 kPa
Answer:
Therefore, the pressure at which the fractional surface coverage is 0.95 is 21.1 kPa (option B).
The Langmuir isotherm is a model used to describe the adsorption of gases on a solid surface. It assumes a monolayer adsorption and that adsorption only occurs at specific sites on the surface.
Equilibrium Constant K:
In the Langmuir isotherm, the equilibrium constant K is a measure of the adsorption capacity of the surface. In this case, K = 0.9 kPa-1 at 25°C.
Fractional Surface Coverage:
The fractional surface coverage (θ) is the ratio of the number of adsorbed gas molecules to the total number of adsorption sites on the surface. In this case, θ = 0.95.
Calculating Pressure:
The Langmuir isotherm equation is given by:
P / (1 - θ) = 1 / K
Plugging in the values:
P / (1 - 0.95) = 1 / 0.9
P / 0.05 = 1.11
P = 0.05 * 1.11
P = 0.055 kPa
Answer:
Therefore, the pressure at which the fractional surface coverage is 0.95 is 21.1 kPa (option B).
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The adsorption of a gas is described by the Langmuir isotherm with the equilibrium constant K = 0.9 kPa-1at 25ºC. The pressure (in kPa) at which the fractional surface coverage is 0.95, isa)1/11.1b)21.1c)11.1d)42.2Correct answer is option 'B'. Can you explain this answer?
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