Question

A mercury mirror forms inside a test tube as a result of the thermal decomposition of mercury(II) oxide: $$2 \mathrm{HgO}(s) \longrightarrow 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g) \quad \Delta H=181.6 \mathrm{~kJ}$$ (a) How much heat is absorbed to decompose \(555 \mathrm{~g}\) of the oxide? (b) If \(275 \mathrm{~kJ}\) of heat is absorbed, how many grams of \(\mathrm{Hg}\) form? 6.65 Most ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right),\) the starting material for producing polyethylene, comes from petroleum processing. It also occurs naturally as a fruit-ripening hormone and as a component of natural gas. (a) The heat transferred during combustion of \(\mathrm{C}_{2} \mathrm{H}_{4}\). is \(-1411 \mathrm{~kJ} / \mathrm{mol} .\) Write a balanced thermochemical equation. (b) How many grams of \(\mathrm{C}_{2} \mathrm{H}_{4}\) must burn to give \(70.0 \mathrm{~kJ}\) of heat?

Short answer

a) 232.6 kJb) 608.79 g HgCombustion: \(\mathrm{C}_2\mathrm{H}_4(g) + 3\mathrm{O}_2(g) \rightarrow 2\mathrm{CO}_2(g) + 2\mathrm{H}_2\mathrm{O}(l) \quad \Delta H = -1411 \mathrm{~kJ/mol}\); Mass: 1.39 g

Step-by-step solution

Write the known information for part (a)

The decomposition reaction is given: \[2 \mathrm{HgO}(s) \longrightarrow 2 \mathrm{Hg}(l) + \mathrm{O}_2(g) \quad \Delta H = 181.6 \mathrm{~kJ}\] We need to find the heat absorbed for the decomposition of \(555 \mathrm{~g}\) of \(\mathrm{HgO}\).

Calculate the molar mass of HgO

Molar mass of \(\mathrm{HgO}\) = molar mass of Hg + molar mass of O = 200.59 \mathrm{~g/mol} + 16.00 \mathrm{~g/mol} = 216.59 \mathrm{~g/mol}

Convert grams of HgO to moles

Using the molar mass, convert \(555 \mathrm{~g}\) of \(\mathrm{HgO}\) to moles: \[\text{moles of HgO} = \frac{555 \mathrm{~g}}{216.59 \mathrm{~g/mol}} = 2.56 \text{ moles}\]

Calculate the heat absorbed

From the reaction, 2 moles of \(\mathrm{HgO}\) decompose with an absorption of 181.6 \mathrm{~kJ} of heat. Use the ratio to find the heat absorbed for 2.56 moles of \(\mathrm{HgO}\): \[\text{Heat absorbed} = \frac{181.6 \mathrm{~kJ}}{2 \text{ moles}} \times 2.56 \text{ moles} = 232.6 \mathrm{~kJ}\]

Write the known information for part (b)

Given heat absorbed = 275 \mathrm{~kJ}. Find the mass of \(\mathrm{Hg}\) formed.

Calculate the moles of HgO decomposed

Using the ratio from the reaction \[2 \text{ moles of HgO} = 181.6 \mathrm{~kJ} \text{ heat}\] Find moles decomposed for 275 \mathrm{~kJ} heat: \[\text{Moles of HgO} = \frac{275 \mathrm{~kJ}}{\frac{181.6 \mathrm{~kJ}}{2 \text{ moles}}} = 3.03 \text{ moles}\]

Calculate the moles of Hg formed

From the equation, 2 moles of \(\mathrm{HgO}\) produce 2 moles of \(\mathrm{Hg}\). So, 3.03 moles of \(\mathrm{HgO}\) will produce 3.03 moles of \(\mathrm{Hg}\).

Convert moles of Hg to grams

Molar mass of \(\mathrm{Hg}\) = 200.59 \mathrm{~g/mol} \[\text{Mass of Hg} = 3.03 \text{ moles} \times 200.59 \mathrm{~g/mol} = 608.79 \mathrm{~g}\]

Write the balanced thermochemical equation for ethylene combustion

Given that the heat transferred during combustion of \(\mathrm{C}_2\mathrm{H}_4\) is \(-1411 \mathrm{~kJ/mol}\): \[\mathrm{C}_2\mathrm{H}_4(g) + 3\mathrm{O}_2(g) \rightarrow 2\mathrm{CO}_2(g) + 2\mathrm{H}_2\mathrm{O}(l) \quad \Delta H = -1411 \mathrm{~kJ/mol}\]

Calculate the molar mass of \(\mathrm{C}_2\mathrm{H}_4\)

Molar mass of \(\mathrm{C}_2\mathrm{H}_4\): \[2 \times 12.01 \mathrm{~g/mol} + 4 \times 1.01 \mathrm{~g/mol} = 28.05 \mathrm{~g/mol}\]

Calculate the moles of \(\mathrm{C}_2\mathrm{H}_4\) burned

Using the given heat: \[\text{Moles of } \mathrm{C}_2\mathrm{H}_4 = \frac{70 \mathrm{~kJ}}{1411 \mathrm{~kJ/mol}} = 0.0496 \text{ moles}\]

Convert moles of \(\mathrm{C}_2\mathrm{H}_4\) to grams

Using the molar mass: \[\text{Mass of } \mathrm{C}_2\mathrm{H}_4 = 0.0496 \text{ moles} \times 28.05 \mathrm{~g/mol} = 1.39 \mathrm{~g}\]

Key concepts

Thermal Decomposition

Thermal decomposition is a chemical reaction where a compound breaks down into simpler substances when heated. In the given problem, mercury(II) oxide \((\text{HgO})\) decomposes into mercury \((\text{Hg})\) and oxygen gas \((\text{O}_2)\) when heated: \({2 \text{HgO} (s) \rightarrow 2 \text{Hg}(l) + \text{O}_2(g)} \). This type of reaction is crucial in various industrial processes and laboratory experiments. Each substance involved changes its state as a result of the heat applied, demonstrating how energy in the form of heat can break chemical bonds.

Enthalpy Change

Enthalpy change \((\Delta H)\) refers to the heat absorbed or released during a chemical reaction at constant pressure. It's an essential parameter in thermochemical equations. In this exercise, the enthalpy change for the decomposition of mercury(II) oxide is \({\Delta H = 181.6 \text{kJ}}\). This value indicates that 181.6 kJ of heat is absorbed for every 2 moles of \({\text{HgO}}\) decomposed. By understanding \({\Delta H}\), we can calculate the heat required for any amount of \({\text{HgO}}\) to decompose, making it a vital tool for predicting energy requirements in reactions.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). Calculating the molar mass is the first step in converting between grams and moles. For mercury(II) oxide \((\text{HgO})\), the molar mass is computed as follows: \({\text{molar mass of HgO} = \text{molar mass of Hg} + \text{molar mass of O}}\)
Given that the molar mass of Hg is 200.59 g/mol and O is 16.00 g/mol, the molar mass of HgO is 216.59 g/mol. Accurate molar mass calculations ensure that stoichiometric calculations yield correct results.

Combustion Reaction

A combustion reaction involves a fuel reacting with an oxidant (typically oxygen) to release energy in the form of heat and light. The combustion of ethylene \(\text{C}_2\text{H}_4}\) is represented by the balanced thermochemical equation: \(\text{C}_2\text{H}_4(g) + 3\text{O}_2(g) \rightarrow 2\text{CO}_2(g) + 2\text{H}_2\text{O}(l) \Delta H = -1411 \text{kJ/mol}\). Here, \({\Delta H=-1411 \text{kJ/mol}}\) indicates that 1411 kJ of heat is released per mole of ethylene burned. Combustion reactions are crucial for energy production in engines, power plants, and even in our metabolism.

Stoichiometry

Stoichiometry is the study of quantitative relationships between the amounts of reactants and products in a chemical reaction. It allows us to make precise calculations based on the balanced chemical equation. For instance, the decomposition of HgO involves a 1:1 molar ratio of HgO to Hg formed, as shown: \({2 \text{HgO} \rightarrow 2 \text{Hg} + \text{O}_2}\). Given this ratio and the reaction \({\Delta H}\), you can use stoichiometry to calculate how much heat is needed to decompose a certain mass of HgO, or how many grams of Hg are produced when a specific amount of heat is absorbed.