Q14.146CP - Chemistry: Molecular Nature Of Matter And Change

Question

The main reason alkali metal dihalides (MX2) do not form is the high  IE₂ of the metal.

 (a) Why is IE₂ so high for alkali metals?

 (b) The IE₂ for Cs is 2255 kJ/mol, low enough for CsF2 to form exothermically $\left(\Delta {\mathbf{H}}^0\mathbf{f} =-\mathbf{125}\mathbf{kJ}/\mathbf{mol}\right)$ . This compound cannot be synthesized, however, because CsF forms with a much greater release of heat $\left(\Delta H^{0}f =-530\mathrm{kJ}/\mathrm{mol}\right)$  . Thus, the breakdown of CsF2 to CsF happens readily. Write the equation for this breakdown, and calculate the heat of reaction per mole of CsF.

Step-by-Step Solution

Answer

1. Because the electron is being taken from the inner shell, securely bound by the nucleus, the second ionization energy for alkali metals is high.
2. The equation for this breakdown is:  $2{\mathrm{CsF}}_{2\left(\mathrm{s}\right)}\to 2{\mathrm{CsF}}_{2\left(\mathrm{s}\right)}+{\mathrm{F}}_{2\left(\mathrm{g}\right)}$ and the heat of creation of the ${\mathrm{CsF}}_2$ breakdown process is -405 kJ/mol.

Step 1: (a) Why is IE 2 so high for alkali metals?

Alkali metals have an ns¹  valance electron configuration.

The initial ionization energy (IE1) is the energy necessary to remove one electron from a mole of gaseous atoms' outermost shell (valence shell).

The energy required to remove the second electron from the outermost shell is the second ionization energy (IE2).

Because the electron is being taken from the inner shell, securely bound by the nucleus, the second ionization energy for alkali metals is high.

Step 2: (b) Calculate the heat of reaction per mole of CsF and the equation for this breakdown.

The following is the reaction that converts CsF₂  to CsF :

${\text{2CsF}}_{\text{2(s)}}\to {\text{2CsF}}_{\text{(s)}}{\text{ + F}}_{\text{2(g)}}\text{ \_\_\_\_\_\_\_\_\_\_\_}\left(\text{1}\right)$

 

The following is the equation for the production of CsF2 and the related enthalpy:

${\mathrm{Cs}}_{\left(\mathrm{s}\right)}+{{\mathrm{F}}_2}_{\left(\mathrm{g}\right)}\to \mathrm{Cs}{{\mathrm{F}}_2}_{\left(\mathrm{s}\right)}{\mathrm{\Delta H}}_{\mathrm{f}}^0=-125\mathrm{kJ}/\mathrm{mol}\_\_\_\_\_\_\_\left(2\right)$

 

The following is the equation for the production of CsF and the related enthalpy:

 ${\mathrm{Cs}}_{\left(\mathrm{s}\right)}+\frac{1}{2}{{\mathrm{F}}_2}_{\left(\mathrm{g}\right)}\to {\mathrm{CsF}}_{\left(\mathrm{s}\right)}{\mathrm{\Delta H}}_{\mathrm{f}}^0=-530\mathrm{kJ}/\mathrm{mol}\_\_\_\_\_\_\_\left(3\right)$

Multiply equation (2) by 2 and rewrite it in the other direction.

$2{\mathrm{CsF}}_{2\left(\mathrm{s}\right)}\to 2{\mathrm{Cs}}_{\left(\mathrm{s}\right)}+2{\mathrm{F}}_{2\left(\mathrm{g}\right)} {\mathrm{\Delta H}}_{\mathrm{f}}^0=250 \mathrm{kJ}/\mathrm{mol}\_\_\_\_\_\_\_\_\_\left(4\right)$

 

Divide equation (3) by two.

$2{\mathrm{Cs}}_{\left(\mathrm{s}\right)}+{\mathrm{F}}_{2\left(\mathrm{g}\right)}\to 2{\mathrm{CsF}}_{2\left(\mathrm{s}\right) }{\mathrm{H}}_{\mathrm{f}}^0=-1060 \mathrm{kJ}/\mathrm{mol}\_\_\_\_\_\_\_\_\_\left(5\right)$

Combine equations (4) and (5). 

$$\begin{gathered} 2{\mathrm{CsF}}_{2\left(\mathrm{s}\right)}\to 2{\mathrm{Cs}}_{\left(\mathrm{s}\right)}+2{\mathrm{F}}_{2\left(\mathrm{g}\right)} \\ 2{\mathrm{Cs}}_{\left(\mathrm{s}\right)}+{\mathrm{F}}_{2\left(\mathrm{g}\right)}\to 2{\mathrm{CsF}}_{2\left(\mathrm{s}\right)} \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ 2{\mathrm{CsF}}_{2\left(\mathrm{s}\right)}\to 2{\mathrm{CsF}}_{2\left(\mathrm{s}\right)}+{\mathrm{F}}_{2\left(\mathrm{g}\right)}\_\_\_\_\_\_\_\_\_\_\_\_\_\_\left(6\right) \end{gathered}$$

 

The sum of the enthalpies of the two reactions (4) and (5) is the enthalpy change for the consequent reaction (6). 

$\begin{array}{rcl}∆\mathrm{H}& =& \left(250 \mathrm{kJ}/\mathrm{mol}\right)+\left(-1060 \mathrm{kJ}/\mathrm{mol}\right)\\ & =& -810 \mathrm{kJ}/\mathrm{mol}\\ & & \end{array}$

As a result, the heat of formation of the reaction of two moles of CsF2 breakdown is -810 kJ/mol.

Calculate the heat of creation of 1 mole of CsF2 breakdown process as follows:

$\frac{-810 \mathrm{kJ}/\mathrm{mol}}{2}=-405 \mathrm{kJ}/\mathrm{mol}$

As a result, the heat of creation of the CsF₂  breakdown process is -405 kJ/mol.