Question

Given the following two reactions and thermodynamic data from Appendix 4, estimate \(\Delta H_{\mathrm{m}}\) for the hydrogenation of acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) with one mole of hydrogen gas to make ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) \(\mathrm{HC}=\mathrm{CH}(g)+2 \mathrm{H}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{3}(g)\) Acetylene Ethane \(\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{3}(g)\) Ethylene Ethane

Short answer

Question: Calculate the enthalpy change for the hydrogenation of acetylene to ethylene using the given thermodynamic data: \(\Delta H_1 = -312 \,kJ/mol\) and \(\Delta H_2 = -137 \,kJ/mol\). Answer: Using the formula \(\Delta H_{\mathrm{m}} = \Delta H_1 - \Delta H_2\), we can find the enthalpy change for the hydrogenation of acetylene to ethylene: \(\Delta H_{\mathrm{m}} = -312 \,kJ/mol - (-137 \,kJ/mol) = -312 \,kJ/mol + 137 \,kJ/mol = -175 \,kJ/mol\) The enthalpy change for the hydrogenation of acetylene to ethylene is -175 kJ/mol.

Step-by-step solution

Determine the required reaction to obtain ethylene from acetylene

The hydrogenation of acetylene should result in the addition of one hydrogen molecule to acetylene, forming ethylene as follows: C\(_2\)H\(_2\) (g) + H\(_2\) (g) → C\(_2\)H\(_4\) (g) Now we will find the enthalpy change for this reaction using the given thermodynamic data.

Analyze the given two reactions

The two given reactions are: 1) C\(_2\)H\(_2\) (g) + 2 H\(_2\) (g) → C\(_2\)H\(_6\) (g) - Acetylene → Ethane 2) C\(_2\)H\(_4\) (g) + H\(_2\) (g) → C\(_2\)H\(_6\) (g) - Ethylene → Ethane Our goal is to find the enthalpy change for the reaction: A) C\(_2\)H\(_2\) (g) + H\(_2\) (g) → C\(_2\)H\(_4\) (g) - Acetylene → Ethylene Using the two given reactions, we can manipulate them to obtain the desired reaction A. Let the enthalpy changes for the given reactions be \(\Delta H_1\) and \(\Delta H_2\) respectively.

Manipulate the given reactions to find the desired reaction

Reversing reaction 2 will yield ethylene in the products: 2R) C\(_2\)H\(_6\)(g) → C\(_2\)H\(_4\)(g) + H\(_2\)(g) - Ethane → Ethylene The enthalpy change for the reverse reaction, \(\Delta H_2{}_{R}\), would be the opposite of the enthalpy change for the forward reaction 2: \(\Delta H_2{}_R = -\Delta H_2\) Now, add reaction 1 and reaction 2R to obtain the desired reaction A: 1) C\(_2\)H\(_2\)(g) + 2 H\(_2\)(g) → C\(_2\)H\(_6\)(g) - Acetylene → Ethane 2R) C\(_2\)H\(_6\)(g) → C\(_2\)H\(_4\)(g) + H\(_2\)(g) - Ethane → Ethylene -------------------------------------------------------------- A) C\(_2\)H\(_2\)(g) + H\(_2\)(g) → C\(_2\)H\(_4\)(g) - Acetylene → Ethylene

Find the enthalpy change for the desired reaction using Hess's law

Hess's law states that the enthalpy change for a reaction depends only on the initial and final states, which means the enthalpy change should be equal by adding the enthalpy changes of the intermediate reactions. Therefore, the enthalpy change for the desired reaction A (\(\Delta H_{\mathrm{m}}\)) can be calculated as follows: \(\Delta H_{\mathrm{m}} = \Delta H_1 + \Delta H_2{}_R\) Substituting the given enthalpy changes into the formula, we will get: \(\Delta H_{\mathrm{m}} = \Delta H_1 - \Delta H_2\) Now you can use this formula to calculate the enthalpy change (\(\Delta H_{\mathrm{m}}\)) for the hydrogenation of acetylene to ethylene by substituting the given thermodynamic data for \(\Delta H_1\) and \(\Delta H_2\).

Key concepts

Hydrogenation

Hydrogenation is a chemical reaction where hydrogen molecules add to other compounds. This process is highly significant in both industrial and chemical contexts. It typically involves hydrogen gas (\( H_2 \)) combining with unsaturated compounds, like alkenes or alkynes, to form saturated compounds.

In simplest historical terms, hydrogenation has been used to saturate fats in the culinary industry. For example, liquid oils, when hydrogenated, can turn into solid fats like margarine. In the context of organic chemistry, hydrogenation involves breaking multiple bonds such as double or triple carbon-carbon bonds and adding hydrogen atoms. This reaction usually requires a catalyst, such as platinum, palladium, or nickel, to proceed effectively.

Hydrogenation reactions can be categorized based on the type of bond being hydrogenated. For alkynes like acetylene (\( C_2H_2 \)), the reaction of hydrogenation is unique as it can be stopped at the stage of forming an alkene (ethylene) or continued further to form an alkane (ethane). Understanding how this process works is fundamental for chemists when transforming chemical substances.

Acetylene to Ethylene

The transformation of acetylene (\( C_2H_2 \)) to ethylene (\( C_2H_4 \)) is an example of a hydrogenation process. Starting with acetylene, an alkyne with a triple bond, hydrogenation involves the addition of a hydrogen molecule (\( H_2 \)).

This reaction is fairly straightforward: \[C_2H_2 (g) + H_2 (g) \rightarrow C_2H_4 (g)\]During this reaction, the triple bond in acetylene (\( C\equiv C \)) is converted to a double bond, forming ethylene with a \( C=C \) bond. This means acetylene loses its characteristic triple-bond structure and takes up a new configuration as an alkene (ethylene).

Without the careful control of conditions, such as temperature and pressure, the reaction might proceed further to form ethane (\( C_2H_6 \)). However, with the right catalyst and conditions, the reaction can be selectively controlled to stop at the ethylene stage, which is crucial for industrial applications such as plastic manufacturing.

Hess's Law

Hess's Law is a foundational principle in thermodynamics and chemistry. It states that the total enthalpy change in a chemical reaction is the same, regardless of the pathway the reaction takes, provided the initial and final conditions are identical.

This principle allows chemists to determine enthalpy changes for reactions that are difficult to measure directly by using known enthalpies of related reactions. In the case of hydrogenation from acetylene to ethylene, Hess's Law aids the calculation of the enthalpy change by treating the desired reaction as a combination of simpler, known reactions.

Using Hess's Law, chemists can express the enthalpy change for the desired conversion of acetylene to ethylene (\( \Delta H_m \)) as:\[\Delta H_m = \Delta H_1 - \Delta H_2\]Here, \( \Delta H_1 \) and \( \Delta H_2 \) are the enthalpy changes of the intermediary reactions. By manipulating and combining these reactions, one can accurately estimate the enthalpy change for the direct hydrogenation of acetylene to ethylene. This elegant approach simplifies calculations and ensures accurate results for both academic studies and practical applications.