- This is a coupled reaction problem. The coupled reaction is
The maximum ratio of PEP to pyruvate is obtained when
, so we want
The activity of phosphate is irrelevant (at least, in this
problem) so we have
This is not a very large ratio, but it is considerably better
than what would be obtained without ATP and may be sufficient
if only a small amount of phosphoenolpyruvate is needed.
-
- There are at least two different approaches to this
problem:
- Method 1
- Boiling has to do with the process
. We begin by
computing the equilibrium constant at 298K:
At the boiling point, K=1. (Make sure you
understand why that is before proceeding.)
We use the formula which relates equilibrium
constants to temperature, which we rearrange to
the form
- Method 2
- At the normal boiling point, liquid water is
in equilibrium with 1atm of steam thus K=1
for the process .
This implies that . Therefore
.
(This is Trouton's rule.)
Since we can calculate (as
above) and , we can compute
the temperature T at which
, i.e. the boiling
point:
- Both of these methods underestimate the boiling point by
for essentially the same reason:
Both assume that is independent of
temperature, which is not quite right. The second
method also assumes that is
independent of temperature.
- We start with dE. dE=dq+dw.
If we take a reversible path, and , so
. Since H=E+PV,
Therefore
.
Note: If I put a differential derivation
on a test or exam, it will be an
optional question. If you learn how to do these, they are quite
easy. However, make sure that you can at least interpret a
differential (i.e. relate the differential to derivatives of
state functions) that is given to you.
-
- Imagine taking a sample of water at 298K and warming or cooling
it reversibly to temperature T. Adding the change in
entropy to the entropy at the starting temperature, we
get
where T is in Kelvin and the entropy is in
.
- Take a Taylor series near :
where .
- Here are some entropies calculated with the two equations:
The approximation is valid to 1% for up to
about 80K, although the approximation is better on the
high-temperature side than on the low-T side.
- The hydrogen bonds should result in considerable organization
of the molecules in solution. Accordingly, HF should be less
available for chemical or physical processes than its
concentration would indicate. We therefore expect its activity
coefficient to be less than 1.
- Let us say that the Debye-Hückel correction is only significant
if . (This is somewhat arbitrary and you could
of course pick a different number.)
To obtain a conservative estimate of the maximum ionic strength
for ideal behaviour, take the largest reasonable values for
and : There are few anions stable in solution whose
charges are other than -1 or -2 so take . There are
some +3 and +4 cations so take . The critical ionic
strength is therefore
Below an ionic strength of , we can be
reasonably assured of ideal behaviour. We also know that above
0.01mol/L, the Debye-Hückel equation yields poor results so
we should use Debye-Hückel theory when
.
- Let s be the solubility in mol/L. Omitting the division by the
standard concentration, we have
or
Since the charges on the calcium and oxalate ions are +2 and
-2, . Accordingly
Start iteration with the guesstimate :
The molar mass of calcium oxalate is 128.10g/mol so the
solubility is .
Note that the ionic strength of the saturated solution is
, which is well within the
range of applicability of Debye-Hückel theory.
- We want a freezing point depression of
. Using the freezing-point depression formula,
the total concentration of solutes should therefore
be
Since NaCl dissociates into and ,
this is twice the concentration of either sodium or chloride
ions (i.e. twice the formal concentration of sodium chloride).
The formal concentration of sodium chloride should therefore be
1.4mol/kg.
We have 18000kg of solvent so
- The first step is to compute the concentration of the solution
from the osmotic pressure measurement:
In the more conventional concentration units, this is
. Since 100mL of water
(0.100L) of water was used, the number of moles of the
forensic sample is .
The mass was 2.841mg so the molar mass of the unknown
substance is
From the chemical formula, we know that the molar mass of MDA is
179.218g/mol.
It seems quite likely that the material brought in by the police
officer is MDA. Further tests on the sample should be ordered.
- If the osmotic pressure is rising, then the total concentration of
solutes must be increasing. This suggests that the starch is
breaking down into its constituent units.