Problem 67 - Chemistry The Central Science In Si Units

Question

Write a balanced equation for each of the following reactions: (a) Hydrogen cyanide is formed commercially by passing a mixture of methane, ammonia, and air over a catalyst at \(800^{\circ} \mathrm{C}\). Water is a by-product of the reaction. (b) Baking soda reacts with acids to produce carbon dioxide gas. (c) When barium carbonate reacts in air with sulfur dioxide, barium sulfate and carbon dioxide form.

Step-by-Step Solution

Answer

(a) \(2\text{CH}_4 + 2\text{NH}_3 + 3\text{O}_2 \rightarrow 2\text{HCN} + 6\text{H}_2\text{O}\); (b) \(\text{NaHCO}_3 + \text{H}^+ \rightarrow \text{Na}^+ + \text{H}_2\text{O} + \text{CO}_2\); (c) \(\text{BaCO}_3 + \text{SO}_2 + \frac{1}{2}\text{O}_2 \rightarrow \text{BaSO}_4 + \text{CO}_2\).

Step 1: Write the unbalanced equation for Reaction (a)

For the formation of hydrogen cyanide (HCN), consider the initial reactants: methane (CH₄), ammonia (NH₃), and oxygen from the air. The by-products are HCN and water (H₂O). The unbalanced equation is: \[ \text{CH}_4 + \text{NH}_3 + \text{O}_2 \rightarrow \text{HCN} + \text{H}_2\text{O} \]

Step 2: Balance the equation for Reaction (a)

Balance the elements one by one, starting with carbon, hydrogen, and nitrogen:1. Balance carbon: One CH₄ gives one carbon atom for one HCN.2. Balance hydrogen: Four H from CH₄ and three H from NH₃ gives seven H, with five used in five H₂O molecules and two in one HCN.3. Balance nitrogen: One NH₃ gives one nitrogen for one HCN.4. Balance oxygen: Five H₂O requires five O, and four O from two O₂ molecules are needed. The balanced equation is:\[ 2\text{CH}_4 + 2\text{NH}_3 + 3\text{O}_2 \rightarrow 2\text{HCN} + 6\text{H}_2\text{O} \]

Step 3: Write the unbalanced equation for Reaction (b)

Baking soda (sodium bicarbonate, NaHCO₃) reacts with an acid (H⁺). The products are sodium salt (dependent on the acid used), water, and carbon dioxide (CO₂). The generic unbalanced equation is: \[ \text{NaHCO}_3 + \text{H}^+ \rightarrow \text{Na}^+ + \text{H}_2\text{O} + \text{CO}_2 \]

Step 4: Balance the equation for Reaction (b)

The balance involves only the hydrogen balance, since sodium and carbon atoms are already balanced:Water requires two hydrogen atoms, which are provided directly by the reaction of NaHCO₃ with one proton (H⁺):- The balanced equation: \[ \text{NaHCO}_3 + \text{H}^+ \rightarrow \text{Na}^+ + \text{H}_2\text{O} + \text{CO}_2 \] Already balanced as the reactants and products are in a 1:1:1 molar ratio.

Step 5: Write the unbalanced equation for Reaction (c)

Barium carbonate (BaCO₃) reacts with sulfur dioxide (SO₂) in the presence of oxygen. The products formed are barium sulfate (BaSO₄) and carbon dioxide (CO₂). The unbalanced equation is: \[ \text{BaCO}_3 + \text{SO}_2 \rightarrow \text{BaSO}_4 + \text{CO}_2 \]

Step 6: Balance the equation for Reaction (c)

Balance based on mole quantities:- For barium and sulfate, one BaCO₃ yields one BaSO₄.- Sulfur and oxygen from SO₂ need to account for additional oxygen.- Oxygen atoms: One additional O is needed from O₂ per reaction for full balance: \[ \text{BaCO}_3 + \text{SO}_2 + \frac{1}{2}\text{O}_2 \rightarrow \text{BaSO}_4 + \text{CO}_2 \]Assuming stoichiometric coefficients that satisfy atom counts, balance the equation where necessary.

Key Concepts

Balancing Chemical Equations

In chemistry, balancing chemical equations is an essential skill. Equations need to be balanced to follow the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. To balance an equation, ensure the number of each type of atom is the same on both sides. This keeps the chemical reaction balanced and accurate.There are some steps you can follow to make balancing easier:

• Write the unbalanced equation, listing all reactants and products.
• List each element present on both sides of the equation.
• Adjust coefficients (the numbers in front of molecules or compound formulas) to balance atoms, usually starting with the most complex molecule.
• Continue adjusting until you have the same atom count on each side.

For example, in the case of methane and ammonia forming hydrogen cyanide and water, the final balanced equation is \[2 \text{CH}_4 + 2 \text{NH}_3 + 3 \text{O}_2 \rightarrow 2 \text{HCN} + 6 \text{H}_2\text{O}\]. Learning to balance is a fundamental skill that's not just about using math; it helps visualize what's happening in the reaction.

Stoichiometry

Stoichiometry involves calculating the quantities of reactants and products in a chemical reaction. It's about understanding the relationships between the different elements and compounds in a reaction. Knowing the stoichiometric relationships allows chemists to calculate how much of each substance is needed or produced.Key concepts in stoichiometry include:

• Mole Ratio: This is derived from the coefficients of a balanced equation. It tells you how many moles of one substance are related to moles of another substance.
• Molar Mass: This helps in converting grams of a compound to moles since stoichiometry is based on moles.

For instance, in the reaction where sodium bicarbonate reacts with an acid to produce carbon dioxide, the stoichiometric relationships are directly deduced from the equation \[\text{NaHCO}_3 + \text{H}^+ \rightarrow \text{Na}^+ + \text{H}_2\text{O} + \text{CO}_2\]. Recognizing these relationships helps understand the proportion of reactants needed or products formed, providing a blueprint for laboratory experiments or industrial processes.

Types of Chemical Reactions

Chemical reactions are classified into several types, each with its own characteristics. Identifying the type of reaction can help predict the products and balance the equation more easily. Here's a look at some common types of chemical reactions:

• Synthesis Reaction: Multiple reactants combine to form a single product, like A + B → AB. This is often seen in the formation of compounds.
• Decomposition Reaction: A single compound breaks down into multiple products, such as AB → A + B.
• Single Replacement Reaction: An element swaps places with another in a compound, noted as A + BC → AC + B.
• Double Replacement Reaction: The components of two compounds exchange places, forming two new compounds such as AB + CD → AD + CB.

In the exercise, when barium carbonate reacts with sulfur dioxide and oxygen to form barium sulfate and carbon dioxide, you observe a unique type of reaction that involves both synthesis and decomposition processes. Understanding these types allows chemists to anticipate reaction outcomes and efficiently conduct reactions in practical applications.