Question

An amount of 1 mole of calcium cyanamide and 1 mole of water are allowed to react. The number of moles of ammonia produced is (a) \(3.0\) (b) \(2.0\) (c) \(1.0\) (d) \(0.67\)

Short answer

The number of moles of ammonia produced is (b) 2.0.

Step-by-step solution

Write Down the Chemical Reaction

First, write down the balanced chemical equation for the reaction between calcium cyanamide and water. The reaction is: CaCN2 + 3H2O → CaCO3 + 2NH3.

Relate Moles of Reactants to Moles of Products

Using the balanced equation, determine the stoichiometry of the reaction. For every mole of calcium cyanamide reacting with water, two moles of ammonia (NH3) are produced.

Calculate the Number of Moles of Ammonia Produced

Since there is 1 mole of calcium cyanamide reacting with 1 mole of water, the limiting reactant must be identified. In this case, calcium cyanamide is the limiting reactant as it produces fewer moles of products. According to stoichiometry, 1 mole of calcium cyanamide produces 2 moles of ammonia. Thus, 1 mole of calcium cyanamide will produce 2 moles of ammonia.

Key concepts

Chemical Equation Balancing

To understand any chemical reaction, it is essential to start with a balanced chemical equation. Balancing a chemical equation ensures that the same number of atoms for each element is present on both the reactant and product sides of the equation. This reflects the Conservation of Mass law, which states that matter cannot be created or destroyed in a chemical reaction.

Balancing is achieved by placing coefficients in front of the chemical formulas to indicate the number of molecules or moles of each substance involved in the reaction. For instance, in our textbook exercise, the equation \( \text{CaCN}_2 + 3\text{H}_2\text{O} \rightarrow \text{CaCO}_3 + 2\text{NH}_3 \) is already balanced. It tells us that one mole of calcium cyanamide reacts with three moles of water to produce one mole of calcium carbonate and two moles of ammonia.

Why Balance Chemical Equations?

Without a balanced equation, it would be impossible to make accurate predictions about the amounts of products formed or the amounts of reactants needed. It's similar to baking a cake—using the exact ingredients in the right proportions is essential to get the desired result.

Limiting Reactant Calculation

In chemical reactions, the limiting reactant is the substance that is completely consumed first and thus determines the amount of product that can be formed. This is a crucial concept, as having an excess of one reactant doesn't mean you'll get more products, much like running out of flour will limit the number of cakes you can bake, regardless of how many eggs you have left.

To find the limiting reactant, compare the mole ratio of reactants used in the reaction with the mole ratio in the balanced chemical equation. In our example, even though we started with equal moles of calcium cyanamide and water (1 mole each), calcium cyanamide limits the reaction because it requires three moles of water for complete reaction according to the balanced equation.

Significance of Identifying the Limiting Reactant

Knowing which reactant is limiting is significant in both laboratory and industrial settings as it helps in optimizing resource usage and cost. In addition, estimating the limiting reactant prevents the wastage of other reactants and allows for proper disposition of the excess ones.

Stoichiometric Calculations

Stoichiometric calculations are mathematical techniques used to calculate the relative quantities of reactants and products in a chemical reaction based on the balanced equation. The term 'stoichiometry' comes from the Greek words for 'element' and 'measure' and effectively serves as the 'recipe' for a chemical reaction.

Using the balanced equation, stoichiometry allows us to convert moles of one substance to moles of another. In the exercise, the stoichiometric ratio of calcium cyanamide to ammonia is 1:2. This means that for every mole of calcium cyanamide, two moles of ammonia are expected to be produced, as long as calcium cyanamide is present in excess.

Applying Stoichiometric Principles

These calculations not only help in predicting the outcome of reactions but are also invaluable in troubleshooting when reactions do not go as expected. They are the basis for creating precise formulations in products such as pharmaceuticals, and are vital for ensuring reactions occur safely and efficiently in chemical manufacturing processes.