Extra Credit 40

Q17.5.8

Using the information thus far in this chapter, explain why battery-powered electronics perform poorly in low temperatures.

Answer:

The Nernst Equation, which is

\(E\ =\ E^{\circ}\ -\ (\dfrac{RT}{nF})\ \times\ \ln(Q)\)

the temperature T, is directionally proportional to E. Thus, as T increases, the value of E will also increase. If T decreases, E will also decrease. E is the cell voltage measured from the battery to the device. A decreased value of E means less voltage coming from the battery to the device. Therefore, we come to the conclusion that E is directly proportional to temperature.

You can prove this to yourself by simply plugging in different values for T, and see that lower values of T yield lower values of E, and higher values of T yield higher values of E.

Q12.3.3

Tripling the concentration of a reactant increases the rate of a reaction nine times. With this knowledge, answer the following questions:

1. What is the order of the reaction with respect to that reactant?
2. Increasing the concentration of a reactant by a factor of four increases the rate of a reaction four times. What is the order of the reaction with respect to that reactant?

Answer:

1: The order of the reaction with respect to that reactant is 2. Given the information that the tripling the concentration of a reactant increases the rate of the reaction nine times, we see that the

\[Rate\propto \left [ A \right ]^{2\displaystyle }\]

If we multiply the concentration of the arbitrary reactant concentration by 3, we see that

\[Rate\propto \left [ 3A \right ]^{2\displaystyle }\]

Here, it is evident that tripling the concentration of the reactant will yield the reaction

\[Rate\propto \left [ 9A ^{2}\right ]\displaystyle \]

2. Seeing that increasing the concentration of the reactant by a factor of four increases the reaction four times tells us that the order of the reaction with respect to the reactant is one. We know this because the new rate of the reaction is

\[Rate\propto \left [ 4A \right ]\displaystyle \]

Originally, the rate of the reaction was

\[Rate\propto \left [ A \right ]\displaystyle \]

However, the concentration of the reactants is increased by a factor of four. According to the given information, the new rate of the reaction was \[Rate\propto \left [ 4A \right ]\displaystyle \]. We know that the order of the reaction is equal to the exponent, and since the exponent is one, the order of the reaction is one.

Q12.5.12

In terms of collision theory, to which of the following is the rate of a chemical reaction proportional?

1. the change in free energy per second
2. the change in temperature per second
3. the number of collisions per second
4. the number of product molecules

In terms of the collision theory, the rate of the chemical reaction is proportional to the change in temperature per second and the number of collision per second. The collision theory states that there are three conditions that must be met for two species to react:

1) They must collide with each other

2) They must collide with enough energy to break the chemical bonds in the reactants

3) Both particles must collide with the correct orientation.

Conditions 1 and 2 are dependent on the the change in temperature, since the higher the temperature means the increased kinetic energy which means more collisions. The change in temperature changes the amount of energy each reactant has. The number of collisions per second pertain to conditions 1 and 3 because the more the particles collide, the more likely they will be to collide and thus the higher the chances of colliding with proper orientation. The number of product molecules and the change in free energy per second have no relation to the collision theory because there is no relations between free energy and the number of product molecules and the reaction rate.

Q21.4.7

Which of the following nuclei is most likely to decay by positron emission? Explain your choice.

1. chromium-53
2. manganese-51
3. iron-59

The nuclei that is most likely to decay by positron emission is Manganese-51. First of all, to obtain the amount of neutrons in each of the atoms, we would take the mass number (the superscript in the top left) and then subtract the atomic number to get the neutrons. To get the neutron proton ratio, take the number of neutrons, and divide it by the number of electrons. The neutron proton ratio for Cr-53 is: \[{29\over 24} \displaystyle = 1.21\] For Mn-51 it is \[{26\over 25} \displaystyle = 1.04\] And for Fe-59 is \[{29\over 24} \displaystyle = 1.28\]. Positron emission occurs most when the neutron to proton ratio is the low. This is because during positron emission, there is a gain of a neutron which would thus increase the neutron proton ratio. Besides the fact that Mn-51 has the lowest neutron proton ratio, Cr-53 is a stable isotope and Fe-59 decays by beta emission.

Q20.2.11

Using the activity series, predict what happens in each situation. If a reaction occurs, write the net ionic equation; then write the complete ionic equation for the reaction.

1. Platinum wire is dipped in hydrochloric acid.
2. Manganese metal is added to a solution of iron(II) chloride.
3. Tin is heated with steam.
4. Hydrogen gas is bubbled through a solution of lead(II) nitrate.

Answer:

1. When the platinum wire is dipped in hydrochloric acid, there is no net ionic reaction. This is because platinum is low on the activity series, meaning it is not reactive.

2. When manganese metal is added to a solution of iron(II) chloride, a reaction will occur because FeCl₂ dissociates in solution and MnCl₂ forms.

a. Net Ionic Equation: \[Mn(s)+2Cl(g)\rightarrow MnCl_{2}(s)\displaystyle\]

b. Complete Ionic Equation: \[Fe^{2+}(aq)+Mn(s)+2Cl(g)\rightarrow MnCl_{2}(s)+Fe^{2+}(aq)\displaystyle\]

3. When tin is heated with steam, no reaction will occur since according to the activity series, tin only reacts with simple acids to make bimolecular hydrogen.

4. When hydrogen gas is bubbled through a solution of lead(II) nitrate, a reaction will occur since lead(II) nitrate is soluble in water and will form nitric acid.

a. Net Ionic Equation: \[H_{2}(g)+NO_{3}(aq)\rightarrow 2HNO_{3}(aq)\displaystyle\]

b. Complete Ionic Equation:\[Pb^{2+}(aq)+H_{2}(g)+NO_{3}(aq)\rightarrow 2HNO_{3}(aq)+Pb^{2+}(aq)\displaystyle\]

Q20.5.6

Although the sum of two half-reactions gives another half-reaction, the sum of the potentials of the two half-reactions cannot be used to obtain the potential of the net half-reaction. Why? When does the sum of two half-reactions correspond to the overall reaction? Why?

Answer: Although the sum of the two half reactions gives another half reaction, the sum of the potential of the two half reactions cannot be used to obtain the potential of the net half reaction because the cell potentials are not a state function. A state function is when the value depends on the state of the substance. Cell potentials are not state functions since the process in which the substance reached its present state varies in different reactions. However, the sum of the half reactions equals the cell potential of the overall reaction when the substances are in standard state conditions. Standard state conditions are when there is a 1M for all solutions present, 1 atm for all gases, and the temperature is 25°C.

Q24.6.2

In CFT, what causes degenerate sets of d orbitals to split into different energy levels? What is this splitting called? On what does the magnitude of the splitting depend?

Answer: In the crystal field theory, the electron-electron repulsion causes the degenerate sets of d orbitals to split into different energy levels. The splitting is called the d-orbital splitting because it is the splitting of the electrons in the d orbital. The magnitude of splitting depends on the geometry of the molecule, (i.e. octahedral splitting compared to square planar compared to tetrahedral) and also the spin of the electrons. The geometry of the molecule is different, allowing there to be electron distributions. The spin of the electrons depends on the ligand to which the metal is bound and whether it is weak or strong field.