Problem 77 - Chemistry: The Central Science

Question

Sodium hydroxide reacts with carbon dioxide as follows: $$ 2 \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$ Which is the limiting reactant when \(1.85 \mathrm{~mol} \mathrm{NaOH}\) and \(1.00\) \(\mathrm{mol} \mathrm{} \mathrm{CO}_{2}\) are allowed to react? How many moles of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) can be produced? How many moles of the excess reactant remain after the completion of the reaction?

Step-by-Step Solution

Answer

The limiting reactant is NaOH, and 0.925 moles of Na2CO3 can be produced from the given reactants. After the reaction, 0.075 moles of CO2 remain as the excess reactant.

Step 1: Identify the limiting reactant

To find the limiting reactant, divide the number of moles of each reactant by their respective coefficient in the balanced equation. The reactant with the smallest ratio indicates the limiting reactant. Ratio for NaOH: \(1.85\; moles\; NaOH\div 2 = 0.925\) Ratio for CO2: \(1.00\; moles\; CO2\div 1 = 1.00\) Since 0.925 is smaller than 1.00, NaOH is the limiting reactant.

Step 2: Calculate the moles of Na2CO3 that can be produced

We know the limiting reactant is NaOH, now we can find the maximum moles of Na2CO3 that can be produced using the stoichiometry of the balanced equation. \(1.85\; moles\; NaOH\)(\(1\; mole\; Na_{2}CO_{3}/2\; moles\; NaOH\)) = \(0.925\; moles\; Na_{2}CO_{3}\) 0.925 moles of Na2CO3 can be produced from the given amount of reactants.

Step 3: Find the moles of the excess reactant after the reaction

Since NaOH is the limiting reactant, we need to find out how many moles of CO2 reacted and then subtract that amount from the starting moles of CO2. \(1.85\; moles\; NaOH\)(\(1\; mole\; CO_{2}/2\; moles\; NaOH\)) = \(0.925\; moles\; CO_{2}\) Now, subtract the moles of CO2 that reacted from the initial moles of CO2: \(1.00\; moles\; CO_{2}\) - \(0.925\; moles\; CO_{2}\) = \(0.075\; moles\; CO_{2}\) After the reaction, 0.075 moles of CO2 remain. To summarize, the limiting reactant is NaOH, 0.925 moles of Na2CO3 can be produced from the given reactants, and 0.075 moles of CO2 remain after the completion of the reaction.

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that helps you understand the quantitative relationships in a chemical reaction. When you perform a chemical reaction, you need to know how much of each reactant you need to produce the desired amount of product. This is where stoichiometry comes in handy.

By using a balanced chemical equation, you can determine the ratio of reactants needed to produce a certain amount of product. In other words, stoichiometry allows you to convert moles of one substance in a reaction to moles of another.

• Ratio of reactants: The balanced chemical equation gives you the ratio of moles in which the reactants react.
• Limiting reactant: Identifies which reactant will run out first and therefore limit the amount of product formed.

Understanding stoichiometry is crucial for accurately predicting the outcomes of chemical reactions, just like in the exercise where we used it to identify the limiting reactant and calculate product formation.

Chemical reaction

In every chemical reaction, atoms rearrange to form new substances — these are the products. The original substances are termed reactants. Chemical reactions are depicted through chemical equations, which give us valuable information about the reaction.

• Balanced equations: Ensure the same number of atoms for each element exists on both sides of the equation. This reflects the law of conservation of mass.
• Reaction conditions: Indicate special conditions necessary for the reaction to occur, such as temperature, pressure, or catalysts.

Chemical reactions can involve solids, liquids, gases, or a combination of these phases. In the given problem, the reaction between sodium hydroxide and carbon dioxide forms sodium carbonate and water. Through the balanced equation, we can understand the stoichiometric relationships and determine factors such as the limiting reactant.

Sodium hydroxide

Sodium hydroxide, often known as lye or caustic soda, is a highly caustic base used in many chemical solutions and industrial processes. Its chemical formula is NaOH. Here's what makes sodium hydroxide important:

• As a strong base: It dissociates completely in water to release hydroxide ions, which makes it highly reactive.
• Versatility: Widely used in soap making, paper manufacturing, and as a drain cleaner because it can neutralize acids and precipitate heavy metals.

In the reaction with carbon dioxide, sodium hydroxide acts as a reactant that combines with CO2 under the right conditions to form sodium carbonate. It's fascinating how one compound's property to readily react with other substances makes it so valuable in chemical reactions.

Carbon dioxide

Carbon dioxide, with the chemical formula CO2, is a colorless and odorless gas found in Earth's atmosphere. It is a natural byproduct of burning fossil fuels and respiration in living organisms. Let's look at some key pointers about carbon dioxide:

• Role in nature: Plants use it in photosynthesis to produce oxygen, linking it directly to life on Earth.
• Greenhouse gas: CO2 is known for its capability to trap heat in Earth's atmosphere, contributing to global warming.

In chemistry, CO2 often acts as an acidic oxide and reacts with bases to form carbonates. In the discussed reaction, it's a reactant that combines with sodium hydroxide to produce sodium carbonate and water. Understanding CO2's properties helps chemists predict its behavior in reactions, such as being able to determine its role as the excess reactant.