Answer
A)The volume decreases by a factor of 4
B), the volume has increased by factor of 2
Explanation:
A)Given:
P1= 760Kpa
P2 =202Kpa
The temperature changes from37C to155C
There is increase In pressure from P1 to P2
P1= 760torr.
We need to convert to Kpa
But, 1atm= 760torr
Then 760torr 101000pa
Then 101000pa = 101Kpa
We need to convert the temperature from Celsius to Kelvin
T1= 37+273= 310K
But from ideal gas, we know that PV = nRT where nR is constant
Where P= pressure
V= volume
T= temperature
n = number of moles
(P1V1/T1)=(P2V2/T2)
V1/V2 = P2/P1 * T1/T2
V1/V2 = (202/101)*(310/155)
V1/V2=4
Therefore, the volume has decreased by factor of 4
B)
Given:
P1= 2atm
P2 =101Kpa
The temperature changes from 305K to 32C
There is increase In pressure from P1 to P2
P1= 2atm
We need to convert to Kpa
But, 1atm= 760torr
Then 760torr 101000pa
Then 101000pa = 101Kpa
P1= 202.65kpa
We need to convert the temperature from Celsius to Kelvin
T2= 32+273= 305K
But from ideal gas, we know that PV = nRT
Where P= pressure
V= volume
T= temperature
n = number of moles
(P1V1/T1)=(P2V2/T2)
V1/V2 = P2/P1 * T1/T2
V1/V2 = (202/101)
V1/V2 = (101/202.65)*(305/305)
V1/V2 = 1/2
Therefore, the volume has increased by factor of 2
Answer:
1. 9.57 × 10^-9 moles.
2. 7.38mol
Explanation:
1.) To find the number of moles there are in the number of particles in an atom, we divide the number of particles (nA) by Avagadro's constant (6.02 × 10^23)
Hence, to find the number of moles (n) of Manganese (Mn), we say:
5.76 x 10^15 atoms ÷ 6.02 × 10^23
5.76/6.02 × 10^(15-23)
= 0.957 × 10^-8
= 9.57 × 10^-9 moles.
2.) Mole = mass/molar mass
Molar mass of sodium chloride (NaCl) = 23 + 35.5
= 58.5g/mol
mole = 431.6 g ÷ 58.5g/mol
mole = 7.38mol
It's a combination of factors:
Less electrons paired in the same orbital
More electrons with parallel spins in separate orbitals
Pertinent valence orbitals NOT close enough in energy for electron pairing to be stabilized enough by large orbital size
DISCLAIMER: Long answer, but it's a complicated issue, so... :)
A lot of people want to say that it's because a "half-filled subshell" increases stability, which is a reason, but not necessarily the only reason. However, for chromium, it's the significant reason.
It's also worth mentioning that these reasons are after-the-fact; chromium doesn't know the reasons we come up with; the reasons just have to be, well, reasonable.
The reasons I can think of are:
Minimization of coulombic repulsion energy
Maximization of exchange energy
Lack of significant reduction of pairing energy overall in comparison to an atom with larger occupied orbitals
COULOMBIC REPULSION ENERGY
Coulombic repulsion energy is the increased energy due to opposite-spin electron pairing, in a context where there are only two electrons of nearly-degenerate energies.
So, for example...
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−− is higher in energy than
↑
↓
−−−−−
↓
↑
−−−−−
↑
↓
−−−−−
To make it easier on us, we can crudely "measure" the repulsion energy with the symbol
Π
c
. We'd just say that for every electron pair in the same orbital, it adds one
Π
c
unit of destabilization.
When you have something like this with parallel electron spins...
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−−
It becomes important to incorporate the exchange energy.
EXCHANGE ENERGY
Exchange energy is the reduction in energy due to the number of parallel-spin electron pairs in different orbitals.
It's a quantum mechanical argument where the parallel-spin electrons can exchange with each other due to their indistinguishability (you can't tell for sure if it's electron 1 that's in orbital 1, or electron 2 that's in orbital 1, etc), reducing the energy of the configuration.
For example...
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−− is lower in energy than
↑
↓
−−−−−
↓
↑
−−−−−
↑
↓
−−−−−
To make it easier for us, a crude way to "measure" exchange energy is to say that it's equal to
Π
e
for each pair that can exchange.
So for the first configuration above, it would be stabilized by
Π
e
(
1
↔
2
), but the second configuration would have a
0
Π
e
stabilization (opposite spins; can't exchange).
PAIRING ENERGY
Pairing energy is just the combination of both the repulsion and exchange energy. We call it
Π
, so:
Π
=
Π
c
+
Π
e
Inorganic Chemistry, Miessler et al.
Inorganic Chemistry, Miessler et al.
Basically, the pairing energy is:
higher when repulsion energy is high (i.e. many electrons paired), meaning pairing is unfavorable
lower when exchange energy is high (i.e. many electrons parallel and unpaired), meaning pairing is favorable
So, when it comes to putting it together for chromium... (
4
s
and
3
d
orbitals)
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−−
compared to
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−−
↑
↓
−−−−−
is more stable.
For simplicity, if we assume the
4
s
and
3
d
electrons aren't close enough in energy to be considered "nearly-degenerate":
The first configuration has
Π
=
10
Π
e
.
(Exchanges:
1
↔
2
,
1
↔
3
,
1
↔
4
,
1
↔
5
,
2
↔
3
,
2
↔
4
,
2
↔
5
,
3
↔
4
,
3
↔
5
,
4
↔
5
)
The second configuration has
Π
=
Π
c
+
6
Π
e
.
(Exchanges:
1
↔
2
,
1
↔
3
,
1
↔
4
,
2
↔
3
,
2
↔
4
,
3
↔
4
)
Technically, they are about
3.29 eV
apart (Appendix B.9), which means it takes about
3.29 V
to transfer a single electron from the
3
d
up to the
4
s
.
We could also say that since the
3
d
orbitals are lower in energy, transferring one electron to a lower-energy orbital is helpful anyways from a less quantitative perspective.
COMPLICATIONS DUE TO ORBITAL SIZE
Note that for example,
W
has a configuration of
[
X
e
]
5
d
4
6
s
2
, which seems to contradict the reasoning we had for
Cr
, since the pairing occurred in the higher-energy orbital.
But, we should also recognize that
5
d
orbitals are larger than
3
d
orbitals, which means the electron density can be more spread out for
W
than for
Cr
, thus reducing the pairing energy
Π
.
That is,
Π
W
