Heterogeneous Catalytic Transfer Partial-Hydrogenation with Formic Acid as Hydrogen Source Over the Schiff-Base Modified Gold Nano-Catalyst

Article abstract of DOI:10.1007/s10562-016-1929-9

Abstract: The catalytic hydrogenation transformation with gaseous hydrogen in liquid phase always refers to a harsh condition and over-hydrogenation, and it is highly desired to develop new methods with partial-hydrogenation at mild condition. Herein, a heterogeneous catalytic transfer partial-hydrogenation strategy with formic acid as hydrogen source was developed over the Schiff-base modified gold nano-catalysts. The Au/Schiff-SiO₂catalyst was successfully prepared by one pot aldimine condensation and NaBH₄reduction of a gold precursor. The characterization results indicated that the gold nanoparticles with an average size below 2?nm were highly dispersed over the Schiff-base modified silica support. Such Schiff-based gold nano-catalysts exhibits excellent activity and partial-hydrogenation selectivity, with a high yield (>99%) for phenylacetylene partial-hydrogenation and achieving a 75% chemoselectivity for imines at a relative low temperature and atmospheric pressure. More importantly, the excess of formic acid can be removed by the direct dissociation of formic acid over Au/Schiff-SiO₂catalyst with CO₂emission into atmosphere, which leads to a hydrogen source as clean as hydrogen gaseous, but with a much more high activity and selectivity under mild reaction process. Graphical Abstract: [Figure not available: see fulltext.]

Full text of DOI:10.1007/s10562-016-1929-9

Catal Lett
DOI 10.1007/s10562-016-1929-9
Heterogeneous Catalytic Transfer Partial-Hydrogenation
with Formic Acid as Hydrogen Source Over the Schif-Base
Modiied Gold Nano-Catalyst
Xinkui Wang1 · Zhen Qiu1 · Qinggang Liu1 · Xiao Chen1 · Shengyang Tao1 ·
Chuan Shi1 · Min Pang2 · Changhai Liang1
Received: 10 October 2016 / Accepted: 18 November 2016
© Springer Science+Business Media New York 2016
Abstract The catalytic hydrogenation transformation
with gaseous hydrogen in liquid phase always refers to a
harsh condition and over-hydrogenation, and it is highly
desired to develop new methods with partial-hydrogenation
at mild condition. Herein, a heterogeneous catalytic transfer
partial-hydrogenation strategy with formic acid as hydro-
gen source was developed over the Schif-base modiied
gold nano-catalysts. The Au/Schif-SiO2 catalyst was suc-
cessfully prepared by one pot aldimine condensation and
NaBH4 reduction of a gold precursor. The characterization
results indicated that the gold nanoparticles with an average
size below 2 nm were highly dispersed over the Schif-base
modiied silica support. Such Schif-based gold nano-cat-
alysts exhibits excellent activity and partial-hydrogenation
selectivity, with a high yield (>99%) for phenylacetylene
partial-hydrogenation and achieving a 75% chemoselectiv-
ity for imines at a relative low temperature and atmospheric
pressure. More importantly, the excess of formic acid can
be removed by the direct dissociation of formic acid over
Au/Schif-SiO2 catalyst with CO2 emission into atmos-
phere, which leads to a hydrogen source as clean as hydro-
gen gaseous, but with a much more high activity and selec-
tivity under mild reaction process.
Graphical Abstract
Keywords Gold catalysis · Formic acid · Catalytic
transfer hydrogenation · Phenylacetylene partial-
hydrogenation · Imines
1 Introduction
The hydrogenation transformation is used widely as a basic
process in organic chemistry and ine-chemical synthesis
[1–3]. Admittedly, the hydrogenation with gaseous H2 as
hydrogen source is an efective method, but with a harsh
reaction environment (generally with high pressure and
temperature) due to the hard solubility of H2 into the liq-
uid phase, which not only limits its reactivity in its hydro-
genation, but also leads to a dangerous experiment opera-
tion [4–6]. Therefore, it is highly desired to develop a new
method which could not only be eicient for hydrogenation
transformation but also under mild reaction condition.
Catalytic transfer hydrogenation (CTH) has attracted
much recent interest, which provides an in situ hydrogen
source from hydrogen donors, such as propanol, cyclohexa-
diene, etc., and serves as an attractive alternative to the
* Xinkui Wang
wangxinkui@dlut.edu.cn
* Min Pang
minpang@caep.cn
1
State Key Laboratory of Fine Chemicals, School
of Chemistry, Dalian University of Technology,
Dalian 116024, China
2
Institute of Materials, China Academy of Engineering
Physics, Mianyang 621907, China
Vol.:(0123456789)
1 3

X. Wang et al.
reactions with gaseous molecular hydrogen [7–11]. With
the merit of hydrogen source in liquid phase, the hydro-
genation transformation can occur at a reaction condition-
friendly and with a promoted catalytic reactivity. However,
the import of sacriicial hydrogen donors which will be
oxided as a residual in the reaction system, which will lead
to the contamination of products and increase the separat-
ing cost for product puriication. As a practical application
view, it is highly to conduct catalytic transfer hydrogena-
tion at a heterogeneous condition with a hydrogen source as
clean as gaseous hydrogen.
water under vigorous stirring for 2 h, then put appropri-
ate NaBH4 into the above solutions, continue to stir for 2 h
before iltered and washed thoroughly with deionized water.
The mixture was transferred into Telon lined autoclave and
maintained at 105°C overnight, and then the precipitate
was iltered, washed thoroughly with deionized water and
dried in vacuum at 120°C for 12 h. The Pd/Schif-SiO2, Pt/
Schif-SiO2 and Ag/Schif-SiO2 were prepared in the same
manner.
2.1.2 Au/TiO2
Among diferent hydrogen sources, formic acid was
considered as the most promising candidate, which can not
only provide high throughput of hydrogen atoms, but also
avoid the contamination of products by releasing the CO2
into gas phase [12–18]. However, the production of hydro-
gen from formic acid always needs basic additives, such as
triethylamine or formic salts. Fortunately, in our previous
research, we have found that the Schif-base modiied gold
nanocatalysts showed excellent catalytic performances for
H2 production in catalytic dehydrogenation of high-con-
centration FA without any additive [19]. More importantly,
the gold nanocatalyst is generally considered as an efec-
tive catalyst for the partial hydrogenation in various organic
functional synthesis. Therefore, inspired by our previous
work on the dehydrogenation of formic acid as well as the
partial chemo selectivity properties of gold nano-catalysts,
we reported here a formic acid-mediated CTH of phenyla-
cetylene (PA) to Styrene (ST) and the synthesis of imines
compound from the reduction-coupling of nitroarenes and
carbonyl using the Schif-base modiied gold as catalyst,
which provides a new route for the partial-hydrogenation in
ine-chemical synthesis.
The Au/TiO2 catalyst was prepared according to the lit-
erature [12]. Briely, the aqueous solutions of HAuCl4 was
heated to 80°C under vigorous stirring. Using the dropwise
addition of NaOH (0.2 M) to tune the pH of 7.0, then put
1 g TiO2 (P25) into the solution, meanwhile, keeping the
pH at 7.0. Before the suspension cooled to room tempera-
ture (25°C), the mixture was stirred for another 2 h at the
same temperature. The precipitate was washed with deion-
ized water until the free of chloride ions. The samples were
dried under vacuum at room temperature for 12 h and then
calcined in air at 350°C for 2 h.
2.1.3 Au/SBA-15-Amine
The Au/SBA-15-Amine catalyst was prepared according to
the literature [19]. Briely, 1.0 g of SBA-15 and 2.1 mmol
of APTES were mixed and stirred thoroughly in 150 mL of
anhydrous ethanol for 12 h at 80°C, aim to graft the surface
of SBA-15 with primary amine moieties. After iltration
and washed with ethanol, “SBA-15-Amine” was obtained
by drying in vacuum at 120°C for 12 h. Au nanoparticles
(NPs) supported on the surface of SBA-15-Amine were
prepared by the same synthetic procedure as that for Au/
Schif-SiO2 catalyst, and the obtained catalyst was denoted
as Au/SBA-15-Amine.
2 Experimental
2.1 Catalyst Synthesis
2.1.1 Au/Schif-SiO2
2.2 Characterizations
The actual gold loading of the catalysts was determined by
inductively coupled plasma atomic emission spectroscopy
(ICP-AES). High-angle annual dark-iled scanning trans-
mission electron microscopy (HAADF-STEM) images
were recorded on a FEI Tecnai G2 F30 S-Twin micro-
scope that was operated at 300 kV. The samples for elec-
tron microscopy were prepared by grinding and subsequent
dispersing the powder in ethanol and drops of the suspen-
sion were deposited onto a clean carbon-enhanced copper
grid and then dried in air. Power X-ray difraction (XRD)
analysis was carried out on a PW3040/60 X’Pert PRO
(PANalytical) difract meter (CuKa X-ray source, oper-
ated at 40 kV and 50 mA). The Fourier transform infrared
The Au/Schif-SiO2 catalyst was successfully prepared by
one pot aldimine condensation and NaBH4 reduction of
a gold precursor according to our previous reported pro-
cedure [19]. Briely, 10 mL HCHO solution (37%) and
4.5 g APTES (3-aminopropyltriethoxysilane) was added
into 150 mL deionized water with stirring for 2 h at room
temperature, and then the slurry was iltered, washed thor-
oughly with deionized water and dried in oven overnight
to obtain the Schif base modiied SiO2 powders (denoted
as Schif-SiO2). For obtaining the Au/Schif-SiO2 cata-
lyst, 1.0 g Schif-SiO2 powders and 3.1 mL HAuCl4·4H2O
(0.01 g/mL) solutions were added into 150 mL deionized
1 3

Heterogeneous Catalytic Transfer Partial-Hydrogenation with Formic Acid as Hydrogen Source…
(FT-IR) spectroscopy were acquired with a spectrometer
(Bruker tensor 27) equipped with a DLATGS detector and
operated at a resolution of 4 cm−1. The UV–Vis absorp-
tion spectra in solution state and in ilm state were taken on
Agilent Cary 5000 spectrophotometer. The product result
was analysed by GC-FID Shanghai Tianmei, GC7890II
equipped with an HP-5 column (30 m×0.32×0.25 mm)
using anisole as internal standard. The injection-port tem-
perature was 270°C, the detector temperature was 250°C,
and the initial oven temperature was held at 100°C and
hold for 3 min, then with the heating rate 20°C min−1 to
inal 250°C, keeping 4 min.
2.3 Catalytic Test
2.3.1 The CTH of Phenylacetylene to Styrene
Fig. 1 XRD patterns of a Schif-SiO2 support; b fresh Au/Schif-
SiO2
A solvent (10 mL) solution of PA (1 mmol), formic acid
(0.5 mL), anisole (1 mmol, the internal standard) and cat-
alyst (1.5 mol% metal) was put into a three-necked lask
(50 mL) with a relux condenser. The resulting mixture
was vigorously stirred in a thermostatic oil bath at set
temperature.
resonance (SPR) of the Au NPs with size >2 nm cannot
be well distinguished. In order to clarify the surface moie-
ties of our catalysts, we have performed FT-IR spectra of
the fresh 2.57 wt% Au/Schif-SiO2 (as seen in Fig. 4). The
absorption bands at 2935 and 2872 cm−1 are assigned to
asymmetric and symmetric vibrations of the –CH2 groups
in the propyl chain of the APTES, respectively, while the
band at 917 cm−1 can be assigned to (–NH) moiety. In addi-
tion, a remark peak at 1659 cm−1, ascribed to the stretching
vibration of Schif base (–N=C) is observed, which means
that the Schif base is successfully grafted on the surface of
support. Therefore, the gold nano-catalyst with an average
size below 2 nm over the Schif-base modiied silica sup-
port is successful synthesised.
2.3.2 The CTH of Nitrobenzene and Benzaldehyde
to Imines
A mixture of nitrobenzene (1 mmol), benzaldehyde
(1 mmol), formic acid (10 mmol), catalyst (1.5 mol %
metal), solvents (10 mL) and anisole (1 mmol, the internal
standard) were charged into a 50 mL three-necked lask
with a relux condenser. The resulting mixture was vigor-
ously stirred in a thermostatic oil bath at set temperature.
The unique catalytic transfer hydrogenation perfor-
mances of such Schif-base modiied gold nano-catalysts
have been tested in the partial-hydrogenation of PA and the
synthesis of imines from nitroarenes and carbonyl, using
formic acid as hydrogen source. Styrene is an important
monomer in the production of polystyrene, which serves as
a widely used class of thermoplastic [20–23]. Commercial
ST produced from the direct dehydrogenation of ethylben-
zene generally contains a trace of PA, which has negative
impact on the polymerization of ST monomers, and will
also induce undesired cross-liking polymer chains [24,
25]. Therefore, it is required to reduce the level of PA to
<10 ppm before polymerization via a partial hydrogena-
tion process [26–28]. As seen in Table 1, we have tested
the catalytic performance of Au/Schif-SiO2 catalysts at dif-
ferent reaction temperatures and compared with other dif-
ferent catalysts in the CTH of PA without additives. It can
be seen that Au/Schif-SiO2 shows excellent performances
(entry 4, Table 1), which achieves a nearly 100% yield to
3 Results and Discussion
Figure 1 shows the XRD pattern of fresh Au/Schif-SiO2
with a metal loading of 2.57 wt% (determined from ICP-
AES). No peak of Au was detected and only the difraction
peak of amorphous silica was observed, implying that the
gold particles are highly dispersed on the support. In order
to clearly examine the metal particle size and size distribu-
tion of the gold catalysts on the support, HAADF-STEM
technique was employed. From the HAADF-STEM images
of 2.57 wt% Au/Schif-SiO2 (Fig. 2), the gold NPs were
homogeneously dispersed on the support with an average
size below 2 nm (1.75 0.3 nm), which is in well agree-
ment with the XRD results. It is worth mentioning that the
gold NPs do not change a lot after ive times of recycles
(1.82 0.3 nm) in the acid environment. Correspondingly,
from the UV–vis spectrum (Fig. 3), the characteristic peak
maximum at 530 nm derived from the surface plasmon
1 3

X. Wang et al.
Fig. 2 HAADF-STEM image of Au/Schif-SiO2 a fresh; b used
ST at 60°C without basic additives. As far as we know, this
is the irst report to the formic acid mediated CTH of PA
to ST without any additives, comparing with the previous
researches [29–34]. When gold NPs supported on other
supports, such as TiO2 (P25) or amine-functionalized SBA-
15, the conversion of PA is neglectable at the same reaction
condition (entry 7 and 8, Table 1). Even for the commer-
cial Pd/C hydrogenation catalyst (from Alfa Aesar), there is
almost no conversion of PA at the same reaction condition
(entry 9, Table 1). However, the as-prepared Pd/Schif-SiO2
(<10% conversion of PA) shows higher activity than the
commercial Pd/C catalyst, suggesting that the Schif base
on the support promotes CTH of PA (entry 10, Table 1).
In fact, in our previous report [19], we have found that the
Schif base on the support plays an important role on the
hydrogenation production from formic acid. The catalytic
performance with H2 gaseous as hydrogen source, as shown
in Table 1 entry 11 and 12 indicated that when at the same
reaction condition with formic acid as hydrogen source, no
conversion of PA occurs; until only raising up to 120°C,
the conversion of PA can be achieved at 91% with 99%
ST selectivity. Therefore, the hydrogen atom is directly
transferred from formic acid to the PA substrate over Au/
Schif-SiO2 catalyst rather than using the formation of H2
as hydrogen source. Meanwhile, both the rate and volume
of hydrogen production were suppressed due to the in-situ
hydrogenation of PA during formic acid decomposition (as
seen in Fig. 5).
We have also analysed the evolution of conversion/selec-
tivity with reaction time for CTH of PA with FA over Au/
1 3

Heterogeneous Catalytic Transfer Partial-Hydrogenation with Formic Acid as Hydrogen Source…
Table 1 Catalytic performance of various catalysts in PA hydrogena-
tion
Entry Catalyst
T (°C) Solvent
Con.b (%) Sel.b (%)
1
2
3
4
5
6
7
Au/Schif-SiO2
25
40
50
60
70
60
60
n-Hexane
n-Hexane
n-Hexane
n-Hexane
n-Hexane
n-Hexane
n-Hexane
8
>99
>99
>99
>99
91
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Schif-SiO2
16
61
>99
88
–
–
Au/SBA-15-
amine
Trace
82
8
9
Au/TiO2
60
60
n-Hexane
n-Hexane
–
–
Pd/C (alfa
aesar)
Trace
59
10
Pd/Schif-SiO2
Au/Schif-SiO2
60
60
n-Hexane
n-Hexane
n-Hexane
Ethanol
8
60
11a
12a
13
–
–
Fig. 3 UV–Vis spectra of a Schif-SiO2 support; b fresh Au/Schif-
SiO2
Au/Schif-SiO2 120
90
90
92
>99
95
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
60
60
60
14
Toluene
>99
>99
15
Cycloheaxne 87
Reaction condition: 1 mmol PA, 0.5 mL HCOOH, 10 mL n-hexane,
metal (1.5 mol%), 1 h
aReaction condition: 1 mmol PA, 10 mL n-hexane, metal (1.5 mol%),
1 MPa H2, 1.5 h
bThe conversion and selectivity were determined by GC using anisole
as the internal standard
Fig. 4 FT-IR spectra of a Schif-SiO2 support; b fresh Au/Schif-
SiO2
Schif-SiO2 catalyst. As depicted in Fig. 6, the formation of
ST keep its excellent selectivity (>99%) even the complete
conversion of PA. The hydrogenation rate decreases with
increasing the reaction time. The conversion rate in the irst
30 min is clearly faster than the next 30 min, which might
be explained by the prior adsorption of HCOOH to the cat-
alyst so that the adsorption/activation of PA happens at the
cost of the decomposition of HCOOH. We have also per-
foremed catalytic testing with other solvent, including eth-
anol, toluene, and cyclohexane, as seen in entry 13–15 in
Table 1. It was found that such Au/Schif-base catalysts can
always achieve an extra high chemoselectivity toward ST,
irrespective of solvent used. As a result, such gold nano-
catalyst is intrinsic preference toward the chemoselectiv-
ity hydorgenation of PA to ST, which might be caused by
Fig. 5 The decomposition of formic acid over the Au/Schif-SiO2
without PA (illed square); with PA existing (illed circle). Reaction
condition: 0.5 mL HCOOH, 10 mL n-hexane, metal (1.5 mol%),
60°C, 1 h
its precedence toward PA activation and its inert bebavior
toward ST chemosorption.
Finally, in order to evaluate the industrial applicability
of such Au/Schif-SiO2 catalysts in the purify process of
1 3

X. Wang et al.
since imines and their derivatives are important chemical
intermediates for variegated applications on pharmacy,
ine chemistry and agro chemistry [35–39]. Up to now,
however, there are only a few reports for the formation of
imines from nitroarenes and carbonyl compounds with
molecular H2 as hydrogen source [40, 41]. Aim to acquire
a reaction condition-friendly environment, the aqueous-
methanol or CO/H2O as the hydrogen source to replace
molecule H2 have been reported [42, 43].
Here, we try to use formic acid as the hydrogen source
for imines synthesis over the Au/Schif-SiO2 catalysts
(Scheme 2). As seen in Table 2, we have tested the cata-
lytic performance of Au/Schif-SiO2 catalysts compared
with other diferent catalysts. It can be seen that the Au/
Schif-SiO2 catalyst achieved 75% selectivity to imines
with 91% conversion of nitrobenzene (entry 6, Table 2).
While Ag/Schif-SiO2 and Pt/Schif-SiO2 have no activ-
ity in the synthesis of imines (entry 1 and 3, Table 2). Pd/
Schif-SiO2 showed a low activity and it was easily to over-
hydrogenation to get N-phenylbenzylamine (4a) (entry 2,
Table 2). The efect of temperature was investigated over
Au/Schif-SiO2 catalysts (entry 4–7, Table 2). The results
showed that 70°C was the preferable temperature for this
reaction, The main by-product nitrones (5a) was emerged at
lower temperature (50°C), which needs to continue hydro-
deoxygenation to get the imines. While at higher tempera-
ture (90°C), dehydrogenation of formic acid become very
fast and nitrobenzene (1a) was reduced to aniline (6a) eas-
ily. As we know, the kinds of solvent may inluence on the
catalytic performance. Several common organic solvents
Fig. 6 Time-conversion/selectivity plot for the CTH of PA over Au/
Schif-SiO2. Reaction condition: 1 mmol phenylacetylene, 13 mmol
HCOOH, 10 mL n-hexane, metal (1.5 mol%), 60°C
ST monomers, we have also performed the CTH of PA in
a non-solvent system with 1 mmol PA in a large amount of
ST (10 mL) (Scheme1). The loss of ST was <2.8%, indi-
cating that this Au/Schif-SiO2 can be a good choice in the
removal of the tiny amount of PA in the ST feedstock. In
addition, the excess FA can be further decomposed thor-
oughly and the produced water can also be easily separate
from the target products, serving as a green process for ST
puriication.
The catalytic transformation of nitroarenes and car-
bonyl compounds to imines is wildly used in industry
Scheme 1 CTH of phenylacet-
ylene in the presence of styrene
with large excess
Scheme 2 CTH of nitrobenzene and benzaldehyde for the synthesis of imines
1 3

Heterogeneous Catalytic Transfer Partial-Hydrogenation with Formic Acid as Hydrogen Source…
Table 2 Experimental results
Entry
Catalyst
T (°C)
Solvent
Con.b (%)
Selectivity
of the synthesis of imines
from nitrobenzene (1a) and
benzaldehyde (2a)
3a
4a
5a
6a
1
Ag/Schif-SiO2
Pd/Schif-SiO2
Pt/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Au/Schif-SiO2
Pd/Schif-SiO2
70
70
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
n-Heptane
n-Hexane
Cyclohexane
Toluene
Toluene
Toluene
n.r.
21
n.r.
n.r.
72
91
87
37
33
72
n.r.
92
85
–
–
–
–
2
60
–
30
–
0
10
–
3
70
–
4
25
–
–
–
–
5
50
43
75
45
53
7
21
15
30
12
12
12
–
28
5
8
6
70
5
7
90
2
23
5
8
70
30
12
21
–
9
70
6
10
11a
12a
13a
70
64
–
3
70
–
120
120
91
2
4
5
0
90
0
8
Reaction condition: nitrobenzene (1 mmol), benzaldehyde (1 mmol), FA (10 mmol), catalyst (1.5 mol%
Au), solvent (10 mL), 40 min
aReaction condition: nitrobenzene (1 mmol), benzaldehyde (1 mmol), H2 (2 MPa), catalyst (1.5 mol% Au),
solvent (10 mL), 2 h
bGC analysis using anisole as internal standard. Conversion is based on nitrobenzene. n.r. no reaction
were investigated over Au/Schif-SiO2 (entry 6 and 8–10,
Table 2). The results showed that toluene and cyclohex-
ane as solvent beneits much to achieve imines. We have
also tested the catalytic performance with H2 gaseous as
hydrogen source, as shown in Table 2 entry 11 and 12. It
was found that no conversion of nitrobenzene occurs at the
same reaction condition. The conversion of nitrobenzene
can be achieved at 92% with 91% selectivity to imines until
the reaction conditions raised up to higher temperature
(120°C), higher pressure (2 MPa) and prolonged the reac-
tion time (2 h).
eicient synthesis of partial-hydrogenation in heterogene-
ous catalysis.
Acknowledgements This work was supported by the National Nat-
ural Science Foundation of China (21676045, 21176037, 21373037,
51273030 and 21403026), the Fundamental Research Funds for the
Central Universities (DUT15LK29 and DUT16RC(4)03).
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In summary, a partial-hydrogenation strategy was devel-
oped with formic acid as hydrogen source over the Schif
base modiied gold catalyst with many merits in catalytic
transformation. First, the excess of formic acid can be
removed by the direct dissociation of formic acid over Au/
Schif-SiO2 catalyst with CO2 emission into atmosphere,
which leads to a hydrogen resource as clean as hydrogen
gaseous, but with a much more high activity and selectiv-
ity under mild reaction process. Second, such Schif-based
gold nano-catalysts exhibits excellent activity and partial-
hydrogenation selectivity, with a high yield (>99%) for
phenylacetylene partial-hydrogenation, and achieving a
75% chemoselelctivity for imines at a relative low tem-
perature and atmospheric pressure. Our result will provide
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