Question

Consider the unbalanced chemical equation $$\mathrm{CaH}_{2}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{H}_{2}(g)$$ Balance the equation and then write the mole ratios that would allow you to calculate the number of moles of each product that would form for a given number of moles of water reacting.

Short answer

The balanced chemical equation is \(CaH_{2}(s) + 2 H_{2}O(l) \rightarrow Ca(OH)_{2}(aq) + 2 H_{2}(g)\). The mole ratios are: CaH2:H2O = 1:2, CaH2:Ca(OH)2 = 1:1, and CaH2:H2 = 1:2. To calculate the number of moles of products that would form for a given number of moles of water reacting, for Ca(OH)2, divide the moles of water by 2, and for H2, the moles of water reacted is equal to the moles of H2 formed.

Step-by-step solution

Balance the chemical equation

To balance the equation, we must make sure that the number of atoms of each element on the reactant side is equal to the number of atoms of that element on the product side. We'll start by comparing the number of atoms for each element in the unbalanced equation: CaH2(s) + H2O(l) -> Ca(OH)2(aq) + H2(g) Calcium (Ca): 1 (reactants) == 1 (products) Hydrogen (H): 2 (reactants) != 4 (products) Oxygen (O): 1 (reactants) == 1 (products) The only element that is not already balanced is hydrogen. To balance hydrogen, we can add a coefficient of 2 to the water molecule (H2O) on the reactant side. This gives the balanced equation: CaH2(s) + 2 H2O(l) -> Ca(OH)2(aq) + 2 H2(g) Now the equation is balanced, and we can proceed to the next step.

Find the mole ratios

The mole ratios can be determined by the coefficients in the balanced equation. The mole ratios for the reactants and products are: CaH2:H2O = 1:2 CaH2:Ca(OH)2 = 1:1 CaH2:H2 = 1:2 H2O:Ca(OH)2 = 2:1 H2O:H2 = 2:2

Analyzing the mole ratios for a given number of moles of water reacting

To calculate the number of moles of each product that would form for a given number of moles of water reacting, we can use the mole ratios from the balanced equation: 1. For Ca(OH)2, the mole ratio with water (H2O) is 2:1. So, for every 2 moles of H2O reacting, 1 mole of Ca(OH)2 is formed. To calculate moles of Ca(OH)2 formed, divide the given number of moles of water by 2. 2. For H2, the mole ratio with water (H2O) is 2:2, which is 1:1. So, for every mole of H2O reacting, 1 mole of H2 is formed. To calculate moles of H2 formed, the number of moles of water reacted is equal to the number of moles of H2 formed.

Key concepts

Stoichiometry

Stoichiometry is the study of the quantitative relationships or ratios between the reactants and products in a chemical reaction. Essential to understanding chemistry, stoichiometry is often referred to as the math behind chemistry. It involves calculations derived from the balanced chemical equation and is based on the Principle of Conservation of Mass, which states that in a chemical reaction, matter is neither created nor destroyed.

Understanding stoichiometry means you can predict the results of a chemical reaction, determine the amounts of substances consumed and produced, and calculate yields. Key components include understanding the mole concept, molar mass, and Avogadro's number, which provides a bridge between the atomic scale and the macro scale in the form of the mole ratio. The mole ratio is a foundational concept used for stoichiometric calculations as it connects the reactants to the products through the coefficients in a balanced chemical equation.

Mole Ratio

The mole ratio is derived from the balanced chemical equation and provides the proportions in which reactants combine and products form. Knowing the mole ratio is crucial for converting between moles of one substance and moles of another. It is found by taking the coefficients from the balanced chemical equation and placing them in ratio form.

For example, in our balanced equation of calcium hydride reacting with water to form calcium hydroxide and hydrogen gas, there are simple mole ratios such as 1 mole of CaH₂ reacts with 2 moles of H₂O, or 1 mole of CaH₂ produces 2 moles of H₂ gas. Having correct mole ratios is imperative as they allow for accurate stoichiometric calculations, ensuring that all mass is accounted for and that the physical constraints of the chemical reaction are respected.

Chemical Reaction Calculations

Conducting chemical reaction calculations is the practical application of stoichiometry involving mole ratios. It allows chemists to determine the amount of reactants required or products formed in a given reaction. These calculations involve several steps, beginning with writing and balancing the chemical equation.

Once the equation is balanced, as in our exercise with the reaction between calcium hydride and water, we can then use the mole ratios to convert moles of one substance to moles of another. For instance, to find the amount of hydrogen gas produced from a certain amount of water, we use the mole ratio of H₂O to H₂ derived from the balanced equation (2:2 in this case), which simplifies to 1:1. This means that for each mole of water that reacts, one mole of hydrogen gas is produced. Using mole ratios in this manner allows for precise calculations and predictions concerning the outcome of a chemical reaction.