Question

Suggest one method for the estimation of each of the following quantities: (a) \(\Delta_{r} H^{\circ}\) for the conversion: \(\mathrm{GeO}_{2}(\mathrm{quartz}) \rightarrow \mathrm{GeO}_{2}(\text { rutile })\) (b) the Pauling electronegativity value, \(\chi^{P},\) of \(\mathrm{Si}\) (c) the purity of a sample of \(\mathrm{Pb}\left(\mathrm{MeCO}_{2}\right)_{4}\) prepared in a laboratory experiment.

Short answer

Use standard enthalpy of formation for (a), bond dissociation energies for (b), and titration or gravimetric analysis for (c).

Step-by-step solution

Enthalpy Change Estimation

To estimate \( \Delta_{r} H^{\circ} \) for the conversion from \( \mathrm{GeO}_{2} \) (quartz) to \( \mathrm{GeO}_{2} \) (rutile), use the enthalpy values of formation for each form. The equation for the enthalpy change is \( \Delta_{r} H^{\circ} = H_f^{\circ} (\text{products}) - H_f^{\circ} (\text{reactants}) \). Find the standard enthalpies of formation \( H_f^{\circ} \) for both quartz and rutile in tables and compute the difference to estimate \( \Delta_{r} H^{\circ} \).

Pauling Electronegativity Estimation

To estimate the Pauling electronegativity, \( \chi^{P} \), of \( \mathrm{Si} \), use the Pauling scale. The Pauling scale is derived from bond dissociation energies. Find the difference in bond energies between \( \mathrm{Si} \) and a known reference (e.g., hydrogen) in the form \( E(\text{Si-H}) \) and \( E(\text{H-H}) \). The formula \( \chi^{P} = 0.102 \sqrt{E(\text{Si-H})} - 0.102 \sqrt{E(\text{H-H})} \) provides a way to estimate the value.

Sample Purity Estimation

To estimate the purity of a \( \mathrm{Pb(MeCO}_{2})_{4} \) sample, conduct a titration or gravimetric analysis. For example, titrate with a standard solution and determine the endpoint. Calculate the molar amount of lead based on the reacted amount and compare it with the theoretical value from the molecular formula. The ratio gives an estimation of the sample's purity percentage.

Key concepts

Enthalpy Change Estimation

In inorganic chemistry, estimating the change in enthalpy for reactions is an important task. For the conversion of substances like \({\text{GeO}}_2\) from one crystalline form to another, such as from quartz to rutile, this can be determined using standard enthalpy of formation values. These values can be found in reference tables.

The general formula to estimate the standard reaction enthalpy, \(\Delta_{r} H^{\circ}\), is:

• \( \Delta_{r} H^{\circ} = H_f^{\circ}(\text{products}) - H_f^{\circ}(\text{reactants}) \)

For our example, you would look up the enthalpy values for both forms of germanium dioxide. By subtracting the enthalpy of formation for the reactant from that of the product, you obtain an estimate of the enthalpy change for the process.

This method assumes the availability of accurate standard enthalpy values, which are usually averaged values for a given phase of a substance. With these values, you can estimate how much energy is absorbed or released during the phase conversion.

Pauling Electronegativity

Pauling electronegativity is a scale used to predict how atoms will bond based on their affinity for electrons. This is especially useful in inorganic chemistry when evaluating interactions between elements. To estimate the Pauling electronegativity of silicon (Si), you can use information about bond energies.

The Pauling scale uses bond dissociation energies to calculate this property. For instance, to find the electronegativity of Si, examine the bond energies:

• \( E(\text{Si-H}) \)
• \( E(\text{H-H}) \)

You can then apply the formula:

• \( \chi^{P} = 0.102 \sqrt{E(\text{Si-H})} - 0.102 \sqrt{E(\text{H-H})} \)

This method requires accurate bond energy data and uses the difference between the bonds to estimate how strongly Si attracts electrons compared to a standard reference, such as hydrogen. The calculated value of \( \chi^{P} \) provides insight into bonding characteristics, influencing how Si will behave in compounds or reactions.

Purity Estimation Methods

Determining the purity of a chemical sample, such as \( \mathrm{Pb(MeCO}_{2})_{4} \), is critical in research and industry. Accurate purity estimation ensures that experiments and processes using the sample are consistent and reliable. This can be accomplished through techniques like titration and gravimetric analysis.

One common method is titration, where the sample reacts with a titrant of known concentration. As the reaction proceeds, you identify an endpoint, which is when the reactants are stoichiometrically balanced. By calculating the amount of titrant used, you can determine how much lead has reacted.

Another technique is gravimetric analysis, where you precipitate lead from a sample and weigh it. This requires converting all of the lead in the sample to a known form, precipitating it, and accurately measuring its mass. This precision leads to a reliable estimation of the purity of your sample.

• Determine the amount of substance reacted.
• Compare this with theoretical amounts to find purity percentage.

Both methods provide insight into the quality of the sample, with results typically expressed as a percentage reflecting the proportion of the pure substance present. Accurate purity assessment is crucial in ensuring the success of chemical processes.