______
Name Class Date SkillsWorksheet) ProblemSolving
Gas Laws Chemists found that there were relationships among temperature, volume, pres sure, and quantity of a gas that could be described mathematically. This chapter deals with Boyle’s law, Charles’s law, Gay-Lussac’s law, the combined gas law, and Dalton’s law of partial pressures. These laws have one condition in common. They all assume that the molar amount of gas does not change. In other words, these laws work correctly only when no additional gas enters a system and when no gas leaks out of it. Remember also that a law describes a fact of nature. Gases do not “obey” laws. The law does not dictate the behavior of the gas. Rather, each gas law describes a certain behavior of gas that occurs if conditions are right.
BOYLE’SLAW Robert Boyle, a British chemist who lived from 1627 to 1691 formulated the first gas law, now known as Boyle’s law. This law describes the relationship between the pressure and volume of a sample of gas confined in a container. Boyle found that gases compress, much like a spring, when the pressure on the gas is increased. He also found that they “spring back” when the pressure is lowered. By “springing back” he meant that the volume increases when pressure is low ered. It’s important to note that Boyle’s law is true only if the temperature of the gas does not change and no additional gas is added to the container or leaks out of the container. Boyle’s law states that the volume and pressure of a sample of gas are inverseli proportional to each other at constant temperature. This statement can be expressed as follows.
Proportionality symbol. It means “is Proportionality proportional to. constant
V— and PVk or V=k
Accordmg to Boyle’s law, when the pressure on a gas is increased, the volume of the gas decreases. For example, if the pressure is doubled, the volume decreases by half. If the volume quadruples, the pressure decreases to one-fourth of its original value. The expression PV = k means that the product of the pressure and volume of any sample of gas is a constant, k. If this is true, then P X V under one set of con ditions is equal to P X V for the same sample of gas under a second set of condi tions, as long as the temperature remains constant.
Copyright © by Holt, Rinehart and Winston. All rights reserved. Holt Chemistry 12 Gases Name Class Date
Problem Solving continued
Boyle’s law can be expressed by the followmg mathematical equation.
=
Pressure under Volume under Pressure under Volume under thefirst set of X theflrst set of = the second set X the second set conditions conditions of conditions of conditions
General Plan for Solving Boyl&s-Law Problems
Rearrange the equation 1Ply = 2vP algebraically to solve for the unknown quantity.
An equation that can be used to calculate the unknown quantity It will be one of the following four:
— 1 — — 22 — V p l I V p 2 D ‘ 2 ‘ 1 D ‘ 1 2 2 1
Substitute each of the known quantities, and calculate. I Unknown Por V
Copyright © by Holt, Rinehart and Winston. All rights reserved. I-loftChemistry 13 Gases ______
Name Class Date
Problem Solving continued
Sample Problem 1 A sample of nitrogen collected in the laboratory occupies a volume of 725 mL at a pressure of 0.971 atm. What voimne will the gas occupy at a pressure of 1.40 atm, assuming the temperature remains constant? Solution ANALYZE What is given in the problem? the original volume and pressure of the nitro gen sample, and the new pressure of the sample What are you asked to find? the volume at the new pressure
Items Data Original pressure, F, 0.971 atm Original pressure, 1V 725 mL 2N New pressure, 2P 1.40 atm New volume, 2V ? mE 2N
PLAN What steps are needed to calculate the new volume of the gas? Rearrange the Boyle’s law equation to solve for 172, substitute known quantities, and calculate.
to solvefor V,, divide both sides of the equation by P, to fl isolate I”, - P V =p,v, 2 p1v insert data and solvefor V, p COMPUTE Substitute data for the terms of the equation, and compute the result.
— — 0.971 j1fII X 725 V — mLN V 1P —503— m LN 2 2 “2 1.40I
EVALUATE Are the units correct? Yes; units canceled to give mL .2N Is the number of significant figures correct? Yes; the number of significant figures is correct because data were given to three significant figures. Is the answer reasonable? Yes; pressure increased by about 1/3, volume must decrease by about 1/3.
Copyright © by Holt, Rinehart and Winston. All rights reserved. Hoft Chemistry 14 Gases Name law
According the tional ture ture Kelvin
of ditions,
Holt Copyright
Problem
conditions
Charles’s
The
Charles’s
volume
can
Chemistry
by is ______
to
a temperature
expression
25% ©
as
be
constant,
the by
to long
Solving
expressed Holt,
of
Kelvin will
law
law
absolute
Charles’s
is
Convert the Rinehart
as
if
equal General
reduce
states
can
necessary.
temperatures gas
k, the
V/T
continued
VxT
of
for
be and
to as increases temperature Celsius
pressure
a
that law, =
the
expressed
gas
any
follows.
VIT Winston. Plan
k
It F =
to
An
means
calculate
volume will when the
will
sample
for
Given
and
for
equation All
volume
be remains
the
by
F double
T Solving rights
the
/ that
one
three by
four
when
the
by =
same the
of TI,
T1 vi /
temperature
Y=k, the
Unknown
T reserved.
of
25%.
the
gas.
same
that
of
quantities:
TorV
V.,
unknown
its Class______
constant. of
17 —
the
pressure
following
Charles’s-Law
sample a
the Rearrange
Substitute result known algebraically the and
T2, V2
T2 volume.
If
can
sample
following
factor.
this =
V2
following
unknown
compute.
be
or
Kto°C
of quantity
needed.
Convert of quantities,
is
used
of
1=y2
remains
T7
Reducing
volume mathematical
of Therefore,
true,
gas
the each
T
a
four:
gas
to sample
to =
V=kT
T2
quantity.
under
if equation
Problems
then solve
of
is
divided
the
constant.
ctirecth,
the
Unknown
VIT
for
another of
Date
doubling
tin°C
gas Kelvin
equation.
under ______
by
increases,
propor
Charles’s
temp
set
tempera
the
one
of
era
con
set
Gases Name Copyright Holt
Problem
Gay-Lussac’s
Chemistry ______© by
Solving Holt,
Kelvin
temperatures
Convert
General Rinehart
if
law
necessary.
temperatures
continued
can
p2 and
Celsius
Plan
be Winston.
It
to
An
calculate
will
expressed
for
Given
equation All
be
Solving
T
\ rights
one
three =
four
the /
T1, l
T1
Unknown / reserved.
of
by /
that
quantities:
TorP P.,
unknown
Gay-Lussac’s-L.aw
Class
of
21
the
the
Rearrange P2
the
Substitute the algebraically known and T2,
T2
can
following ______
following
P2 =
following
unknown
compute.
be
T2 Kto°C
quantity
needed.
quantities, Convert
used
p1
T7
the each _
T,
four:
to
to
mathematical p2
T2
quantity. =
equation if
solve of
Problems ______the
Unknown
for
Date
tin°C ______
equation.
Gases I
volume, Name
be
Copyright t-loIt
Problem
constant.
Chemistry ______
©
and
by
Solving
Holt,
Kelvin
temperature
General
temperatures
Convert
Rinehart
if
necessary.
temperatures
continued
Plan
Celsius
and
Winston.
of
F
to
for
An
calculate
a
Given
gas
equation
Solving
All
‘,.
vary
rights
V1,T, P1V //
five
six
T1
the
/
Unknown
V,T,orP
reserved.
quantities: /
Combined-Gas-Law
that
of Only
P1,
unknown
Class______
J2V
25
the
Rearrange the
algebraically V2,T, Substitute known and
can
the
following
unknown
compute.
be
P2
molar Kto°C
quantity
needed. Convert quantities,
T,
used
the
each
to quantity
to
quantity.
equation if
T2
solve
of
Problems ______
the
Unknown
for
Date
of
tin°C
the
gas
must
Gases Name
Air volume, DALTON’S partial gen,
stated equal
gas technique pressure displaced significant temperatures
TABLE
must You
volume
Copyright
Holt
Problem
Temp in
10 11 12
14 13 15 16
A
is
To
into
20%
°C ______
Chemistry
common
can
a
to
be
mathematically
find
pressures,
1
so ©
a
the
of
by
subtracted use
of VAPOR
by
bottle the
is
LAW
Solving
Vapor amount
in
the at
1.31 1.23 the 1.40
1.60 1.50 1.71 1.82
Holt,
sum
used,
this
kPa any
are
method
true
gas
of Rinehart
OF
filled
PTotai
pressure PRESSURE of
corrected which
given
barometric
at
however,
approximately
alone
continued of
pressure
PARTIAL
the water
and from
that
water
with
and
as
of
=
partial
in
says
so
would
follows.
Winston.
temperature. collecting
PGas
the
Table
is
water
on.
pressure
vapor. the
P
FGas
the
of
OF
that
Temp PRESSURES in pressure
21 17 total 20 22 19 18 23
Total
1
This
pressures
the
All
be. °C gas
+
sum
WATER
1
78%
and
=
the
rights
= PGas
pressure.
As below.
gas
gas
collected P
phenomenon
FG
hi
of
total Total
allow N2,
a
Vapor
in
2.06 reserved. 2.19 1.94 2.34 2.49 2.64 2.81
The 78%
alone,
samples gas-law Class
2
result,
the
28
kPa
+
of
20%
+ —
pressure
vapor
of
pressure
PGas
it ______
“II,,O
the ‘II2O
pressure
in
that
the
to
02,
the
calculations
the
m component
displace
3
pressures
pressure
is
vapor
vapor
pressure
pressure 1%
the
+
bottle
described
of
of
PGas
Ar,
laboratory
a
the
Temp in
mixture 24 25
26 27 28 30 29
and
the
4
contains
of
°C
gas
is
of of
gases.
+
to
water.
the
1%
exerted
water the by
Date
determine
plus
other
water
Dalton’s
Vapor is
in 2.98
3.17 3.36 3.57
4.01 3.78 4.25 of
gas
It ______
a
to
When
the kPa
gases
at
can
small
by
that
bubble
gases
various
vapor
vapor
pressure
intro
be
what
law
this
is
has
but
by
the
of Gases
the Name
The In
volume of volumes of plish STE gas standard gas
equation in
used
always
Copyright
Holt
Skills
Problem
gas
1811,
which
At
The
The
under volume
R P
n V
T
Chemistry Then ______
the
in this Ideal
= = occupies = =
WorksheeD
ideal
value
in of
the
© the
the
the the the the
and of
same
is temperature
by
point,
any moles.
you 22.4
gases
the
Holt, Italian
(22.4 equation.
pressure volume number
ideal
Kelvin
molar
gas
He
Gas
of
other
could
task
L/mol
mathematical
Rinehaxt
22.414
the
if
determined
law
L/mol)
The at
Solving
gas
you
chemist
volume
temperature
is Law
ideal
the set of
of
use
to
is
of
Temperature
constant, most
by
and
Atmospheres (273
Units Kilopascals
know
10
a
moles
a
same . of
calculate
a
already
sample
the using
Winston.
gas mathematical L
sample
conditions. into
K) Amedeo
common
(usually
of
the combined that
statement constant,
of temperature
and
P
the a
All which
of
of
combined number
and gas single
and at
the
of
rights
pressure
ideal
and the
is gas
PV=
standard
rounded Avogadro
gas
present
values
V
volume liters
always .
However,
reserved. combines
gas
liters constant
R,
gas
relationship
of
gas
36
of
nRT
depends
the
into
and
law
moles
used
(1
law. ______
in
to
temperature that
proposed
ideal atm
to kelvins
pressure a
22.4
Value
a
0.082 8.314
standard
for
single
amount
much determine
of
or
on
gas
that
L).
R
a
1
mol- 101.3
LkPa
the
of
mol
gas,
L
are
and
law.
constant.
the simpler
has
R
atm
contain
units
conditions
of
and K .
shown
you
K
kPa)
amount
principle
the the gas
pressure,
Date
can
ofF
way
volume plus
would conditions
The
below.
equal ______
use
of
and
to
the
that
following
gas
occupy the
accom
numbers
one
V of
molar
equal
is
being
the
molar
of
Gases
at
Copyright
Hoft
pheres
pheres
Name
Problem
Chemistry
If you
______
©
or or
by
have
kilopascals.
Holt, kiopascals,
Solving
General
Rinehart
volume
continued
and
Plan
it
units
Winston.
r
F
is
for
the
best
An
be
other
Solving
the
The
All
unknown
equation
used
to
P,
rights
Unknown
PV=
ideal
equation
V,
than
convert
to
n,
reserved.
Ideal-Gas-Law
nRT
Substitute Choose
calculate
in best
algebraically gas
unknown
Rearrange is
Determine
or
37
liters
that
quantity
the
Class
the
T
law
for volume
fits
can
unknown
equation or
______
the
the
quantity.
pressure
each
the
from
gas
units
to
to
equation
Problems
constant,
of
solve
and
liters
quantity.
the
of
the
units
calculate.
the
data
for
and
data
data.
the
R,
which
other
pressure
Date
values that
______
than
to
atmos
atmos Gases Name
An
has cylinder Sample
ANALYZE What Solution
What
Rearrange ties, What
PLAN
Copyright
Holt
Problem
engineer
a ______
Chemistry
and
is
are
capacity
steps
given
C
at
you
calculate.
by
Solving
Problem
the
are
bit,
25°C?
pumps
asked in
Amount
Vo1ume Items Temperature
Ideal Kelvin
ideal-gas-law Pressure
needed
Rinehart of
the
20.0
continued
problem?
to
gas
temperature 5.00
and
of
find?
of
to
1 in
constant,
L.
gas
Winston.
gas,
cylinder, calculate
mol What
of
hi
Unknown equation
n
gas,
cylinder,
Ideal-gas-law
of All
R
equation, the temperature cylinder,
the PV=
is
of
t
rights
P
carbon
gas,
the
the
II
amount
pressure
P
nRT
for
solve gas-law nRT reserved
to substitute pressure, answer the the and
V
V
Class
new
T
pressure
pressure
38 problem
appropriate
solve solve
the
the
monoxide
in
equation
pressure ideal-
known
hi kPa,
Data 5.00 20.0 25°C
0.0821 (25 8.314 ?
volume
of
asks
for
kPa
moles
so
R,
the
for
+
values,
mol L
choose
in
F,
L•kPaJmolK
273)
L•atmlmolK
gas
substitute kPa
of
of
gas of
K
the
the
gas in
of
into
the
gas?
298
cylinder,
pumped
CO
Date
cylinder
a
K
known
or
inside
cylinder ______
into
and
quanti
the
the
the
that
Gases I Name
Solve
The
COMPUTE Are Yes;
Yes; Is EVALUATE
three Yes; Is
equals
Practice
Copyright
Holt
Problem
1.
the
the
A
ans: of
the problem
the the
the
CliemistFy ______
the
student
significant number
answer
0.899
600.
units
©
ideal
number
1.57 calculation
ideal-gas-law
by
Solving
Holt,
Thus,
atm.
asks
correct?
x
gas
collects reasonable?
of
= Rmehart
102
of
How significant
figures.
constant
5.00 for
619
continued
significant
can
mol
pressure
and
425
many kPa pôl
equation
be
Winston.
02
mL
is
X
was
approximated
figures
moles
in
8.314J.kPaJioM
of
figures
in
All
selected
the
for
oxygen
kPa,
rights
20.0J
of
PV
F,
correct?
right
P=—-
oxygen
the reserved.
is
so
=
Class
39
so at
correct
nRT
use range.
unknown
as
V
a
that ______
temperature
(1/4)
R
did
=
the
because
the x
8314
x
298
quantity.
units
(8
student
x
L
300),
data
of
=
canceled
kPa/mol
619
24°C
collect?
were
Dat.e
or
kPa
and
2400/4,
to
K.
given
a
give
pressure
which
to
kPa.
Gases ______
Name Class______Date
Problem Solving continued
APPLICATIONSOF THE IDEAl. GAS LAW You have seen that you can use the ideal gas law to calculate the moles of gas, n, in a sample when you know the pressure, volume, and temperature of the sample. When you know the amount and identity of the substance, you can use its molar mass to calculate its mass. You did this when you learned how to convert between mass and moles. The relationship is expressed as follows.
Mass in grams
n= m
Molar mass in grams per mole Amount in moles/ If you substitute the expression mIM for n in the ideal-gas-law equation, you get the following equation. PV=RT Al This version of the ideal gas law can be solved for any of the five variables P, V, m, M, or T. It is especially useful in determining the molecular mass of a sub stance. This equation can also be related to the density of a gas. Density is mass per unit volume, as shown in the following equation. D= V Solve for m: m=DV Then, substitute DV for m in the gas law equation: = PLRT M The two V terms cancel and the equation is rearranged to give: PM=DRT or D= RT This equation can be used to compute the density of a gas under any condi tions of temperature and pressure. It can also be used to calculate the molar mass of an unknown gas if its density is known.
Copyright © by Holt, Rinehart and Winston. All rights reserved. Holt Chemistry 41 Gases ______
Name Class______Date
IProblem Solving continued
General Plan for Solving Problems Involving Applications of the Ideal Gas Law
Determine which pv = RT equation fits the D = M problem. RT Rearrange the equation algebraically to solve for the unknown quantity.
An equation that can be used to calculate the unknown quantity
Choose the gas constant, R, that best fits the units of the data. Substitute each of the data values in the equation and calculate.
Unknown P. V. m, M, D or T
Copyright © by Holt, Rinehart and Winston All rights reserved. HoltChemistry 42 Gases Name
Now
reactions Stoichiometry of before kilograms. reactants
Gaseous other. is
amount phases STP,
of Once
simpler related in expression ichiometry mine
chemical mole temperature must the
Skills
Copyright
[loft Problem
measured
gases,
products Reactants
the Reactants
If
There
combined ______
that you
Chemistry
the
volume
the
ratios be
WorksheD
balanced
you
of
to
of way ©
products you
problem
converted will
you
have
by
volume
is
by
equation.
products
its
As
a
can
problems. for
Holt,
one
and
only
gas. at
using
of
and can
and
and need volume.
have has
you
gaseous gas
STP,
the relate
dealing
Rinehart
equation
condition reactants
One
when
products easily Solving
products
pressure.
been of
which
know,
and
the
law
to worked
ideal
and to of
you
one
the use
mole
Therefore,
and No the
mole
reactants
for
converted the
reactants, with
put Gases
reactants.
will
gas
gas you you
Winston
quantities
can
the
conversion
conditions
to
this
that
that
volumes
that
with
of
If these
ratio,
law
the from need
solve
must
are
ideal
they be
any
conversion.
must
are
are
All
relationships
stoichiometric
can
above; used
trying
the
to
just
gaseous
to
the
only gas rights
are
convert
stoichiometry gas
not V2
gases
by
work
are
amount
be be
mole
of n=— from
volume
as
at
as
not, — —
reserved.
law using
Avogadro’s
gases _____
to
Class
observed. related
the
measured the
STP
volume
49
V1PT2
are
RT Pv
solve in
T1P2
products,
ratios
volume then these to
molar
other ______
stoichiometry
a
in
occupies usually are
determine
of among
balanced
moles to
amounts. and
involves
the
another
ratios
of
usually
problems
gas.
Gas amount
under
law
to
gases
volume liquids
or
measured
moles,
amount
you
Usually
volumes
to
22.4
of
both.
or
chemical
the
to
the only measured
gas
Look
relate
given
those
liquid can
of
are calculations.
involving
L. amounts
of
number
mass,
same in
a
gases,
is If
you
use
Date one
gas related
again
a
in
can by
the
gases
the
required
products
balanced
equation.
liters.
the
conditions
the will and is ______
of
in
volume
be
gas
there
of in
directly at multiple
the
grams
to
mole to
coefficients
related
volumes
need
moles
moles.
the
is
Many
If
solve
each
to
gases
not and
is
the
and
deter ratios
a or
to
of
at
gas
by
sto
Gases
use Name
Problem Copyright
I-bit
Chemistry
©
molar
by
using
Solving
Convert
solid,
Holt,
substance
General
if
Volume
substance
of
mass
it
the
Rinehart
A. is
Mass
liquid,
a
continued
gas
of
Plan
of
and A
A—
or
Winston.
set
gas
exist
for
two
same
convert
of
Solving
The
under
conditions.
All gases
as
the rights
Convert
volume
the
using
between
A
are
different
mole
reserved.
Gas
and
Class
mole
50
under
the
ratio
using
If
ratio Stoichiometry B.
the
ratio
gas
conditions,
the
is
two
the
laws.
if
same
the
gases
solid,
substance
Problems
Mass
liquid,
convert if gas
substance
if Volume
Date
Convert
of using molar
B
it
of
laws. is
is B.
B
or
a
a —
the
gas,
gas
using
mass
gas
of
B
Gases Name Ammonia
to If Sample that ANALYZE
What Solution
What
The What
The of under PLAN
Copyright
Holt
Problem
1.78
the
02?
Chemistry
volume
coefficients ______
temperature
is
are
steps
the
following
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conditions
equation
of
volume
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51
N,
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ratio,
volume
fact
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nitrogen
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of
that
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=LN2
of
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when
nitrogen
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produced
the 02 3 Data NA NA NA
NA NA ÷ 1.78
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formed
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two
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gases
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volume
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are
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Are COMPUTE
Yes; EVALUATE Yes; Is
Is three Yes;
Practice
Copyright HoIt
Problem
1.
2.
the
the
In monoxide
volume
What
conditions.
Fluorine the
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of conditions.
units
the
the
______Chemistry
significant number
answer
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units
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number volume
volume
volumes
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canceled
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Holt,
gas
correct?
reasonable?
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and
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of
ans:
ans:
Rinehart
of
of
reacts
significant
figures.
of
mL
will
water.
of of
N2
continued
significant
to
3500 oxygen
1.20
4NH3(g) to
manufacturing
of 03
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give
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3F2(g)
violently the
fluorine
and
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x L produced?
1.78
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following
02,
wifi figures
HF
N2.
be
+ +
figures
2800
mL All
be
gas? 3H20(1) 502(g) gas 2/3
with
rights
used
X
03,
correct?
the
would
nitric
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L
All
equation.
water
is
reserved.
NO
7.20
Class
volumes —> volume
in
correct 52
gases
—*
acid,
4N0(g)
a
be
6HF(g)
to
x ______
=
reaction
produced
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produce
1.19 are
ammonia
of
because
are
mL
02. measured
+
L
+
measured
N2
6H20(1)
of
ifF
03(g)
by 2800
the
is
the
oxidized
under
data
L
Date
under complete
of
fluoride
NH3? were ______
the
to
the
same
nitrogen given
What
reaction
same
and
to
Gases