Problem 19 - Chemistry The Central Science In Si Units

Question

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;\) (b) barium carbonate decomposes into barium oxide and carbon dioxide gas when heated; \((\mathbf{c})\) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l),\) is combusted in air; \((\mathbf{d})\) dimethylether, \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(g),\) is combusted in air.

Step-by-Step Solution

Answer

(a) \(\mathrm{Mg}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{MgCl}_2(s)\); (b) \(\mathrm{BaCO}_3(s) \rightarrow \mathrm{BaO}(s) + \mathrm{CO}_2(g)\); (c) \(\mathrm{C}_8\mathrm{H}_8(l) + 10\mathrm{O}_2(g) \rightarrow 8\mathrm{CO}_2(g) + 4\mathrm{H}_2\mathrm{O}(l)\); (d) \(2\mathrm{CH}_3\mathrm{OCH}_3(g) + 6\mathrm{O}_2(g) \rightarrow 4\mathrm{CO}_2(g) + 6\mathrm{H}_2\mathrm{O}(g)\).

Step 1: Determine Reactants and Products for Mg and Cl2

In reaction (a), the reactants are magnesium (\(\mathrm{Mg}(s)\) and chlorine gas (\(\mathrm{Cl}_{2}(g)\)). Magnesium will react with chlorine gas to form magnesium chloride (\(\mathrm{MgCl}_2\)).

Step 2: Balance the Mg and Cl2 Reaction

For the reaction \(\mathrm{Mg}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{MgCl}_2(s)\), we see that there is one magnesium atom on both sides but two chlorine atoms and two required for the product magnesium chloride. The balanced equation is \(\mathrm{Mg}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{MgCl}_2(s)\).

Step 3: Identify Decomposition Products for Barium Carbonate

In reaction (b), barium carbonate (\(\mathrm{BaCO}_3\)) decomposes upon heating to produce barium oxide (\(\mathrm{BaO}\)) and carbon dioxide (\(\mathrm{CO}_2\)).

Step 4: Balance Barium Carbonate Decomposition

The decomposition reaction \(\mathrm{BaCO}_3(s) \rightarrow \mathrm{BaO}(s) + \mathrm{CO}_2(g)\) is already balanced, as there is one of each type of atom on both sides of the equation.

Step 5: Identify Products of Styrene Combustion

In reaction (c), the combustion of styrene (\(\mathrm{C}_8\mathrm{H}_8(l)\)) in air involves oxygen gas (\(\mathrm{O}_2\)) to form carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)).

Step 6: Balance Styrene Combustion Equation

The reaction is \(\mathrm{C}_8\mathrm{H}_8(l) + 10\mathrm{O}_2(g) \rightarrow 8\mathrm{CO}_2(g) + 4\mathrm{H}_2\mathrm{O}(l)\). This equation balances the carbon (8 in styrene), hydrogen (8 in styrene), and oxygen atoms (16 for CO2, and 4 for H2O) on both sides.

Step 7: Identify Products of Dimethylether Combustion

In reaction (d), when dimethylether (\(\mathrm{CH}_3\mathrm{OCH}_3(g)\)) is combusted in air, it reacts with oxygen gas to produce carbon dioxide and water.

Step 8: Balance Dimethylether Combustion

The balanced reaction is \(\mathrm{2CH}_3\mathrm{OCH}_3(g) + 6\mathrm{O}_2(g) \rightarrow 4\mathrm{CO}_2(g) + 6\mathrm{H}_2\mathrm{O}(g)\). This ensures that oxygen, carbon, and hydrogen atoms are equal on both sides (4 carbon, 12 hydrogen, and 12 oxygen).

Key Concepts

Chemical Reactions

A chemical reaction occurs when substances transform into new substances.
This change involves breaking and forming bonds among atoms. In a chemical equation, reactants are the starting substances and products are the new substances formed. For example, when magnesium reacts with chlorine gas, they form magnesium chloride: \( \mathrm{Mg}(s) + \mathrm{Cl}_2(g) \rightarrow \mathrm{MgCl}_2(s) \).
The equation must be balanced to reflect that atoms are not created or destroyed during the reaction.
To balance a chemical equation means ensuring an equal number of each type of atom on both sides.

• Reactants are listed on the left side of the arrow.
• Products are listed on the right side of the arrow.
• Equations must be balanced using coefficients, not altering chemical formulas.

Stoichiometry

Stoichiometry is a key concept in chemistry that involves the calculation of reactants and products in chemical reactions.
It uses balanced chemical equations to measure the amount of each substance.
This ensures that the law of conservation of mass is followed. Every atom present in the reactants must also be present in the products, just rearranged.
Let's look at the third reaction from our exercise: the combustion of dimethylether. The balanced equation is: \( 2\mathrm{CH}_3\mathrm{OCH}_3(g) + 6\mathrm{O}_2(g) \rightarrow 4\mathrm{CO}_2(g) + 6\mathrm{H}_2\mathrm{O}(g) \).

• We see that two molecules of dimethylether react with six molecules of oxygen.
• They produce four molecules of carbon dioxide and six molecules of water.
• Each element's atoms are conserved and tracked from reactants to products.

Using stoichiometry ensures precision in predicting amounts needed or formed in any reaction.

Combustion Reactions

Combustion reactions are a specific type of chemical reaction where a substance combines with oxygen, often producing energy in the form of heat and light.
They are crucial in many everyday scenarios, such as generating electricity, powering engines, and even in heating. A common example from our exercise is the combustion of styrene: \( \mathrm{C}_8\mathrm{H}_8(l) + 10\mathrm{O}_2(g) \rightarrow 8\mathrm{CO}_2(g) + 4\mathrm{H}_2\mathrm{O}(l) \).
Key aspects of combustion reactions include:

• Reactants usually include a hydrocarbon and oxygen.
• The main products are carbon dioxide and water.
• They release energy, making them exothermic reactions.

The balancing of combustion reactions is often more complex because it requires balancing large numbers of atoms, especially oxygen and hydrogen. Understanding combustion helps in fields like environmental science, to better grasp concepts like carbon emissions and energy efficiency.