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 reagent is the limiting reactant when \(1.85 \mathrm{~mol}\) \(\mathrm{NaOH}\) and \(1.00 \mathrm{~mol} \mathrm{CO}_{2}\) 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?

Short answer

In conclusion, the limiting reactant is NaOH, 0.925 moles of Na2CO3 can be produced, and 0.075 moles of CO2 remain after the completion of the reaction.

Step-by-step solution

Identify the stoichiometric relationship between reactants and products in the balanced chemical equation

Using the balanced equation, we can identify the stoichiometric relationship between the reactants and the products: 2 NaOH (s) + CO2 (g) → Na2CO3 (s) + H2O (l) This equation shows that for every 2 moles of NaOH, 1 mole of CO2 is required, and 1 mole of Na2CO3 is produced.

Determine the limiting reactant

To find the limiting reactant, we can compare the mole ratio of each reactant to the stoichiometric ratio: For NaOH: \(1.85 \ mol \ / \ 2 = 0.925 \) For CO2: \(1.00 \ mol \ / \ 1 = 1.00 \) Based on these results, we can conclude that the limiting reactant is NaOH as its mole ratio is lower than that of CO2.

Calculate the moles of Na2CO3 that can be produced

Using the stoichiometry of the balanced chemical equation, we can determine how many moles of Na2CO3 can be produced from the limiting reactant, NaOH: 2 moles NaOH → 1 mole Na2CO3 So, when using all the available NaOH: \(1.85 \ mol \ NaOH \times (1 \ mol \ Na2CO3 / 2 \ mol \ NaOH) = 0.925 \ mol \ Na2CO3 \) Thus, a maximum of 0.925 moles of Na2CO3 can be produced.

Calculate the remaining moles of excess reactant

Now that we know the amount of Na2CO3 produced, we can determine how many moles of the excess reactant, CO2, are left after the reaction: 1 mole CO2 → 2 moles NaOH So, the moles of CO2 consumed in the reaction can be calculated as: \(0.925 \ mol \ Na2CO3 \times (1 \ mol \ CO2 / 1 \ mol \ Na2CO3) = 0.925 \ mol \ CO2 \) We started with 1.00 mole of CO2, so the remaining moles of the excess reactant are: \( 1.00 \ mol \ CO2 - 0.925 \ mol \ CO2 = 0.075 \ mol \ CO2 \) In conclusion, the limiting reactant is NaOH, 0.925 moles of Na2CO3 can be produced, and 0.075 moles of CO2 remain after the completion of the reaction.

Key concepts

Stoichiometry

Stoichiometry is the backbone of calculating chemical reactions and understanding the relationships between different substances in a reaction. At its core, stoichiometry involves using a balanced chemical equation to determine the ratios in which reactants combine to form products. In this exercise, the equation is balanced as \(2 \ \mathrm{NaOH}(s) + \mathrm{CO}_{2}(g) \rightarrow \mathrm{Na}_{2}\mathrm{CO}_{3}(s) + \mathrm{H}_{2}\mathrm{O}(l)\). Here, the coefficients indicate the mole ratios: 2 moles of NaOH react with 1 mole of CO2 to produce 1 mole of Na2CO3.

The key steps in stoichiometry include:

• Balancing the chemical equation to understand the ratio of reactants to products.
• Identifying the stoichiometric ratio, which in this case is 2:1 between NaOH and CO2, and the same 1:1 ratio between CO2 and Na2CO3.
• Using these ratios to predict the outcome of a chemical reaction, including figuring out how much product can be formed from given amounts of reactants.

Understanding these principles allows us to perform mole calculations and predict how much of each substance is consumed and produced in a reaction.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. For a better grasp, imagine a reaction as baking a cake, where ingredients (reactants) mix and are baked to create a cake (product). In the provided reaction equation, sodium hydroxide and carbon dioxide are the ingredients reacting to form sodium carbonate and water.

Chemical reaction types can vary, including synthesis, decomposition, single replacement, and double replacement. Here, the reaction is a synthesis type due to two reactants combining to form one compound. The presence of a limiting reactant is crucial, as it determines the extent of the reaction, similar to having limited flour for baking a cake, which limits how many cakes can be produced. The limiting reactant is completely consumed when the reaction goes to completion.

In this exercise, identifying the limiting reactant, NaOH, is essential, as this limits the amount of Na2CO3 produced. Understanding chemical reactions helps predict outcomes and implement strategies such as optimizing reactant use in industrial processes, reducing waste, or even adjusting conditions to favor the formation of desired products.

Mole Calculations

Mole calculations are a fundamental part of understanding chemical reactions and involve quantifying moles, which serve as a bridge between the atomic scale and real-world quantities. The concept of the mole allows us to count particles like atoms and molecules by weighing them. In the context of our exercise, mole calculations help determine how much of each substance is present and predict the procedures within the reaction.

Here's a breakdown of how mole calculations are applied:

• First, you need the balanced chemical equation to understand how many moles of reactants and products are involved.
• Next, calculate the initial number of moles for each reactant, as done with 1.85 moles of NaOH and 1.00 mole of CO2.
• Use the mole ratio from the balanced equation to determine the limiting reactant by comparing these quantities.
• Finally, calculate how many moles of products can be formed and how many moles of the excess reactant remain after the reaction.

In the exercise, we computed that 0.925 moles of Na2CO3 can be produced, with remaining moles of CO2 as the excess reactant after calculating the consumed and remaining amounts. Mastery of mole calculations is a critical skill for any chemistry student and is essential in lab settings, where precise measurements are necessary to carry out reactions safely and effectively.