Chapter 16, Problem 151CP

(a)

Interpretation Introduction

Interpretation: The formula of the four superconductors needs to be determined.

Concept Introduction: The superconductor is a substance which is capable of superconducting at very low temperature values.

Explanation of Solution

The given structures are as follows:

  

  

By considering the color code for spheres, the number of atoms of each element can be counted.

It can be observed that in molecule (a) there is 1 Tl, 2 Ba, 1 Cu and 5 O atoms in 1unit. Thus, the formula of the molecule will be:

  ${\text{TlBa}}_{\text{2}}{\text{CuO}}_{\text{5}}$

Similarly, the atoms in molecule (b) are 1 Tl, 2 Ba, 1 Ca, 1 Cu and 7 O in 1unit. Thus, the formula will be:

  ${\text{TlBa}}_{\text{2}}{\text{CaCu}}_2{\text{O}}_7$

The structure (c) contains 1 Tl, 2 Ba, 2 Ca, 3 Cu and 9 O atoms in 1unit. The formula will be:

  ${\text{TlBa}}_{\text{2}}{\text{Ca}}_2{\text{Cu}}_3{\text{O}}_9$

Similarly, the structure (d) has 1 Tl, 2 Ba, 2 Ca, 4 Cu and 11 O atoms in 1unit thus, the molecular formula will be:

  ${\text{TlBa}}_{\text{2}}{\text{Ca}}_{\text{3}}{\text{Cu}}_{\text{4}}{\text{O}}_{\text{11}}$

(b)

Interpretation Introduction

Interpretation: The four structures needs to be ordered from lowest to highest superconducting temperature.

Concept introduction: The number of sheets in the unit cell is directly proportional to the temperature for the superconductivity.

Explanation of Solution

If the number of sheets in each unit cell increases, the temperature for the superconductivity increases. The number of sheets in the structure (a) is less then (b) which is further less than (c) and (d). Thus, the increasing order of the superconductivity for 4 structures will be as follows:

  $(a)<(b)<(c)<(d)$

(c)

Interpretation Introduction

Interpretation: The oxidation state needs to be assigned to Cu in each mixture. It is assumed that the oxidation state of Tl is +3. Also, the oxidation state of Ca, Ba, O is +2, +2 and -2 respectively.

Concept Introduction: The oxidation state of any atom in the molecule is equal to the charge on it. It can be calculated if oxidation state of all the other atoms is given.

For example, the molecule H₂O₂ is neutral. The oxidation state of H is +1 (general) thus, the oxidation state of O can be calculated as follows:

  $\begin{array}{l}2\left(+1\right)+2x=0\\ 2+2x=0\\ 2x=-2\\ x=-1\end{array}$

Thus, the oxidation state of O in H₂O₂ is -1.

Explanation of Solution

The oxidation state of Cu in structure can be calculated by taking the overall charge on the molecule equal to zero.

The oxidation state of Tl, Ca, Ba and O is assumed +3, +2, +2 and -2 respectively.

For ${\text{TlBa}}_{\text{2}}{\text{CuO}}_{\text{5}}$ :

  $\begin{array}{l}\left(+3\right)+2\left(+2\right)+Cu+5\left(-2\right)=0\\ Cu=+3\end{array}$

Thus, the oxidation state of Cu in molecule (a) is +3.

For ${\text{TlBa}}_{\text{2}}{\text{CaCu}}_2{\text{O}}_7$ :

  $\begin{array}{l}\left(+3\right)+2\left(+2\right)+\left(+2\right)+2Cu+7\left(-2\right)=0\\ Cu=\frac{5}{2}\end{array}$

There are 2 Cu atoms, thus, there is a mixed oxidation state one is $C{u}^{3+}$ and other is $C{u}^{2+}$ per unit formula of molecule (b)

For ${\text{TlBa}}_{\text{2}}{\text{Ca}}_2{\text{Cu}}_3{\text{O}}_9$ :

  $\begin{array}{l}\left(+3\right)+2\left(+2\right)+2\left(+2\right)+3Cu+9\left(-2\right)=0\\ Cu=\frac{7}{3}\end{array}$

Thus, copper has mixed oxidation state that is 1 ${\text{Cu}}^{3+}$ and 2 $C{u}^{2+}$ per formula unit of molecule (c).

For ${\text{TlBa}}_{\text{2}}{\text{Ca}}_{\text{3}}{\text{Cu}}_{\text{4}}{\text{O}}_{\text{11}}$ :

  $\begin{array}{l}\left(+3\right)+2\left(+2\right)+3\left(+2\right)+4Cu+11\left(-2\right)=0\\ Cu=\frac{9}{4}\end{array}$

There will be one $C{u}^{3+}$ and three $C{u}^{2+}$ ions per formula unit of molecule (d).

(d)

Interpretation Introduction

Interpretation: The reason for the copper to display a mixture of oxidation states in the superconductor needs to be explained.

Concept Introduction: The superconductor is a substance which is capable of superconducting at very low temperature values.

Explanation of Solution

There are variable oxidation states of copper due to varying the numbers of Ca, Cu and O atoms in each unit cell. The different oxidation states of Cu are calculated for molecules (b), (c) and (d). In the other superconductor in exercise 79, in YBa₂Cu₃O_7, there is variable oxidation state of copper by omitting oxygen atom at various sites in the lattice.