where a = K/kT. Equation 7.13 is the Langmuir adsorption equation. A
plot of 1/q versus 1/[A] or 1/P yields a straight line with a slope equal to
the reciprocal of the equilibrium constant (or kT/K).
The fraction q can be related to the following ratio:
q =
V
V m
(7.14)
In this equation, V is the volume of the gas adsorbed to the surface and
V m represents the volume of gas corresponding to monolayer coverage.
Complete monolayer coverage corresponds to q = 1, and V = V m . Equation 7.14 can be substituted into Equation 7.13, giving Equation 7.15:
1
V
=
1
aPV m
+
1
V m
(7.15)
Example 7.2 The Adsorption of Nitrogen onto a Mica
Surface follows the Langmuir Adsorption Model
The following data were collected at 273.15 K. Determine the value
of a, V m , and the total number of surface sites. What would the
concentration of surface sites be if the mica substrate was a square
with 2-cm sides?
P/10
−12 torr
2.50
1.32
0.48
0.30
0.20
V/10
−8 m
3
3.40
2.92
2.00
1.54
1.25
Solution According to Equation 7.15, a plot of 1/V versus 1/P will
have a slope of 1/aV m and an intercept of 1/V m . Figure 7.11 shows
this plot. A linear fit to the data yields the equation y = 1 × 10
–5 x +
3 × 10
7
.
The intercept on the y-axis is equal to 3 × 10
7 = 1/V m , and so V m =
3.3 × 10
–8 m
3
.
From the slope 1 × 10
–5 = 1/aV m , and so a = 3.0 × 10
12 torr
−1
.
To determine the total number of sites on the mica surface, we first
need to determine the number of molecules corresponding to V m .
First, we know that under these conditions, 1 mol of gas occupies
2.24 × 10
–2 m
3
.
CHAPTER 7: Fundamentals of Surface Nanoscience
238
plot of 1/q versus 1/[A] or 1/P yields a straight line with a slope equal to
the reciprocal of the equilibrium constant (or kT/K).
The fraction q can be related to the following ratio:
q =
V
V m
(7.14)
In this equation, V is the volume of the gas adsorbed to the surface and
V m represents the volume of gas corresponding to monolayer coverage.
Complete monolayer coverage corresponds to q = 1, and V = V m . Equation 7.14 can be substituted into Equation 7.13, giving Equation 7.15:
1
V
=
1
aPV m
+
1
V m
(7.15)
Example 7.2 The Adsorption of Nitrogen onto a Mica
Surface follows the Langmuir Adsorption Model
The following data were collected at 273.15 K. Determine the value
of a, V m , and the total number of surface sites. What would the
concentration of surface sites be if the mica substrate was a square
with 2-cm sides?
P/10
−12 torr
2.50
1.32
0.48
0.30
0.20
V/10
−8 m
3
3.40
2.92
2.00
1.54
1.25
Solution According to Equation 7.15, a plot of 1/V versus 1/P will
have a slope of 1/aV m and an intercept of 1/V m . Figure 7.11 shows
this plot. A linear fit to the data yields the equation y = 1 × 10
–5 x +
3 × 10
7
.
The intercept on the y-axis is equal to 3 × 10
7 = 1/V m , and so V m =
3.3 × 10
–8 m
3
.
From the slope 1 × 10
–5 = 1/aV m , and so a = 3.0 × 10
12 torr
−1
.
To determine the total number of sites on the mica surface, we first
need to determine the number of molecules corresponding to V m .
First, we know that under these conditions, 1 mol of gas occupies
2.24 × 10
–2 m
3
.
CHAPTER 7: Fundamentals of Surface Nanoscience
238