Trends in the first series

Why the trends are gentle

Compare a row of the p block with the 3d series. Across period 3, from sodium to chlorine, the atoms shrink fast. Across the 3d series, the ten atoms change little. Why the difference?

In period 3, each new electron goes into the same shell as the outer electrons. Electrons in the same shell shield each other badly, so the pull on the outer electrons rises quickly. In the 3d series, each new electron goes into $3d$, which is inside the $4s$ shell. It screens the $4s$ electrons far better, and it cancels most of the extra proton.

Slater's rules put numbers on this. They are a rough model, but they show the idea. For a $4s$ electron:

• the other $4s$ electron screens about $0.35$;
• each electron in $3s$, $3p$ or $3d$ screens about $0.85$;
• each of the ten electrons in the first two shells screens $1.00$.

For scandium, the screening is $0.35 + 8 \times 0.85 + 1 \times 0.85 + 10 = 18.0$. The effective nuclear charge is $Z_{eff} = 21 - 18.0 = 3.00$. For zinc, there are ten electrons in $3d$, and $Z_{eff} = 30 - 25.65 = 4.35$.

So $Z_{eff}$ rises only from $3.00$ to $4.35$ over ten elements. That is $0.15$ per element, because each step adds $+1$ from the nucleus and takes away $0.85$ through the new $3d$ electron. In period 3, a new electron screens only $0.35$, so $Z_{eff}$ rises by $0.65$ per element, from $2.20$ for sodium to $6.10$ for chlorine. The 3d series changes more than four times more slowly. This one fact explains most of the lesson.

Practise with new numbers

Size and density

Here are the metallic radius, the melting point and the enthalpy of atomisation of each element:

• Sc: radius $164\ \text{pm}$, melts at $1814\ \text{K}$, atomisation $326\ \text{kJ/mol}$
• Ti: radius $147\ \text{pm}$, melts at $1941\ \text{K}$, atomisation $473\ \text{kJ/mol}$
• V: radius $135\ \text{pm}$, melts at $2183\ \text{K}$, atomisation $515\ \text{kJ/mol}$
• Cr: radius $129\ \text{pm}$, melts at $2180\ \text{K}$, atomisation $397\ \text{kJ/mol}$
• Mn: radius $137\ \text{pm}$, melts at $1519\ \text{K}$, atomisation $281\ \text{kJ/mol}$
• Fe: radius $126\ \text{pm}$, melts at $1811\ \text{K}$, atomisation $416\ \text{kJ/mol}$
• Co: radius $125\ \text{pm}$, melts at $1768\ \text{K}$, atomisation $425\ \text{kJ/mol}$
• Ni: radius $125\ \text{pm}$, melts at $1726\ \text{K}$, atomisation $430\ \text{kJ/mol}$
• Cu: radius $128\ \text{pm}$, melts at $1357\ \text{K}$, atomisation $339\ \text{kJ/mol}$
• Zn: radius $137\ \text{pm}$, melts at $692\ \text{K}$, atomisation $126\ \text{kJ/mol}$

The left graph shows four features.

• A steady fall from scandium to chromium. The nuclear charge rises and $Z_{eff}$ climbs, so the atoms shrink.
• Almost no change from iron to copper. The d subshell is now more than half full. The d electrons repel each other, and this repulsion nearly cancels the extra pull.
• A rise at zinc. The $3d$ subshell is full. The repulsion within it is now larger than the extra pull, and zinc has no unpaired d electrons to bond the atoms closely.
• Manganese and zinc are larger than their neighbours. Their arrangements, $3d^5 4s^2$ and $3d^{10} 4s^2$, are specially stable. The d electrons give little to the metal bond, so the atoms in the solid are held less tightly.

The fall in radius is small, about 16 % from scandium to zinc. Mass rises steadily from scandium to zinc while each atom gets a little smaller, so density rises from about $3\ \text{g/cm}^3$ for scandium to about $9\ \text{g/cm}^3$ for nickel and copper. Zinc falls back a little, since its atoms are larger.

A surprise waits further down. The $4d$ series is larger than the $3d$ series, as you would expect. The $5d$ series is not larger than the $4d$ series. Zirconium is $160\ \text{pm}$ and hafnium is $159\ \text{pm}$. The fourteen lanthanoids between them are the reason, and they have a topic of their own.

Strong metals: melting point and atomisation

The table above also lists the melting point and the enthalpy of atomisation, the energy needed to turn one mole of the solid metal into gaseous atoms. Both are high for the d block, because the metal bond is strong. Compare this with potassium, which melts at only $337\ \text{K}$.

The reason is that the $3d$ electrons join the $4s$ electrons in the metal bond. More unpaired d electrons mean more bonding. So the values rise from scandium to a peak at vanadium and chromium, where each atom has three to six unpaired electrons to bond.

Two elements fall below the trend.

• Manganese. Its half-filled $3d^5$ subshell holds its electrons tightly. They bond less well, and manganese melts at $1519\ \text{K}$ with an atomisation enthalpy of only $281\ \text{kJ/mol}$.
• Zinc. Its $3d^{10}$ subshell is full, so only the two $4s$ electrons bond. Zinc melts at $692\ \text{K}$ with an atomisation enthalpy of $126\ \text{kJ/mol}$. Cadmium and mercury are lower still. Mercury is a liquid.

Choose property 3, then property 4. The peak and the two low points sit in the same places. The reason is the same: the strength of the metal bond.

Practise with new numbers

Ionisation enthalpies

The first, second and third ionisation enthalpies of each element are:

• Sc: $631\ \text{kJ/mol}$, $1235\ \text{kJ/mol}$, $2393\ \text{kJ/mol}$
• Ti: $656\ \text{kJ/mol}$, $1309\ \text{kJ/mol}$, $2657\ \text{kJ/mol}$
• V: $650\ \text{kJ/mol}$, $1414\ \text{kJ/mol}$, $2830\ \text{kJ/mol}$
• Cr: $653\ \text{kJ/mol}$, $1592\ \text{kJ/mol}$, $2990\ \text{kJ/mol}$
• Mn: $717\ \text{kJ/mol}$, $1509\ \text{kJ/mol}$, $3260\ \text{kJ/mol}$
• Fe: $762\ \text{kJ/mol}$, $1561\ \text{kJ/mol}$, $2962\ \text{kJ/mol}$
• Co: $758\ \text{kJ/mol}$, $1644\ \text{kJ/mol}$, $3243\ \text{kJ/mol}$
• Ni: $736\ \text{kJ/mol}$, $1752\ \text{kJ/mol}$, $3402\ \text{kJ/mol}$
• Cu: $745\ \text{kJ/mol}$, $1958\ \text{kJ/mol}$, $3556\ \text{kJ/mol}$
• Zn: $906\ \text{kJ/mol}$, $1734\ \text{kJ/mol}$, $3829\ \text{kJ/mol}$

The first ionisation enthalpy rises slowly, from $631\ \text{kJ/mol}$ to $906\ \text{kJ/mol}$. This agrees with the slow rise of $Z_{eff}$. Zinc is the highest, because its electron comes from a full $4s^2$ subshell next to a full $3d$ subshell.

The second enthalpy has two jumps. Chromium rises by $178\ \text{kJ/mol}$ above vanadium, and copper rises by $206\ \text{kJ/mol}$ above nickel. The reason is the ion that is left. $\text{Cr}^+$ is $3d^5$ and $\text{Cu}^+$ is $3d^{10}$, and both are specially stable. The second electron must come out of that stable subshell, which costs more.

The third enthalpy is large for manganese and zinc. The ions $\text{Mn}^{2+}$ ($3d^5$) and $\text{Zn}^{2+}$ ($3d^{10}$) resist losing another electron. Iron is easier: it loses its third electron to reach $3d^5$.

Use the program below to see this as a ratio. It compares the energy to reach $\text{M}^{3+}$ with the energy to reach $\text{M}^{2+}$. The ratio is highest for manganese and zinc, and lowest for iron. These numbers decide which oxidation states are stable, in the next lesson.

Electrode potentials and reactivity

The standard electrode potentials $E^\circ$ for $\text{M}^{2+}/\text{M}$ are:

• Ti $-1.63\ \text{V}$, V $-1.18\ \text{V}$, Cr $-0.91\ \text{V}$, Mn $-1.18\ \text{V}$
• Fe $-0.44\ \text{V}$, Co $-0.28\ \text{V}$, Ni $-0.25\ \text{V}$
• Cu $+0.34\ \text{V}$, Zn $-0.76\ \text{V}$

As you learned in Class 11, a metal with a negative $E^\circ$ releases hydrogen from dilute acid. All of these metals do, except copper. Some react slowly, because an oxide film protects them.

The values rise from titanium to copper, with two exceptions. Manganese and zinc are more negative than the trend. To see why, follow the three energy steps that make $E^\circ$ for $\text{M}^{2+}/\text{M}$:

• atomise the solid metal, $\Delta_a H$, which costs energy;
• remove two electrons, $\Delta_i H_1 + \Delta_i H_2$, which costs energy;
• hydrate the $\text{M}^{2+}$ ion, which releases energy.

The hydration enthalpy becomes more negative only slowly across the series, as the ion gets smaller. So the first two costs mostly decide $E^\circ$. For copper they add up to $339 + 745 + 1958 = 3042\ \text{kJ/mol}$, the largest of the series. Hydration cannot repay it, so $E^\circ$ is positive. Compare nickel, $2918\ \text{kJ/mol}$, and zinc, $2766\ \text{kJ/mol}$.

Manganese and zinc have much smaller sums than their neighbours: $2507\ \text{kJ/mol}$ for manganese against $2642\ \text{kJ/mol}$ for chromium and $2739\ \text{kJ/mol}$ for iron. Their stable $3d^5$ and $3d^{10}$ subshells give low atomisation enthalpies, and manganese also loses its second electron easily. That is why their $E^\circ$ values are more negative than those of the neighbours.

Try it in Python

The program uses the data for the radius and the ionisation enthalpies. It also works out the effective nuclear charge from Slater's rules and the ratio that we met above.

Common mistakes

• Saying that the nuclear charge stays the same. It rises by one at each step. The change is small because the new $3d$ electron screens the $4s$ electrons.
• Expecting the radius to fall steadily to zinc. It falls at the start, is almost flat in the middle, and rises at the end.
• Explaining the low melting point of manganese by saying it has few electrons. It has seven outer electrons. The stable $3d^5$ subshell holds them tightly.
• Saying that copper is unreactive to every acid. Dilute hydrochloric acid does nothing to copper, but nitric acid oxidises it.

Remember these

• $Z_{eff}$ rises by only about $0.15$ per element across the 3d series, against $0.65$ in period 3. So the radius, density and ionisation enthalpy change slowly.
• The radius falls, is almost flat in the middle, and rises at zinc. Mn and Zn are larger than their neighbours.
• Melting point and atomisation enthalpy peak near V and Cr and are low for Mn and Zn.
• The second ionisation enthalpy jumps at Cr and Cu, and the third is large for Mn and Zn.
• $E^\circ$ for $\text{M}^{2+}/\text{M}$ is positive only for copper, because its atomisation and ionisation costs are the largest.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Why does the metallic radius change very little from iron to copper?

2. The second ionisation enthalpy of copper is much higher than that of nickel. Why?

3. Which has the higher melting point, vanadium or zinc, and why?

4. Why is $E^\circ$ for $\text{Cu}^{2+}/\text{Cu}$ positive while that for $\text{Ni}^{2+}/\text{Ni}$ is negative?