Question

Design a concept map for the following reaction. $$\mathrm{CaCO}_{3}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{CaCl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1)+\mathrm{CO}_{2}(\mathrm{g})$$ The concept map should explain how to determine the mass of \(\mathrm{CaCl}_{2}\) produced from a given mass of HCl.

Short answer

To design a concept map for the given reaction and determine the mass of CaCl2 produced from a given mass of HCl, follow these steps: 1. Write down the balanced chemical equation: \(CaCO_3(s) + 2 HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)\) 2. Determine the limiting reactant (HCl in this case) by calculating the moles of HCl: n(HCl) = mass(HCl) / molar mass(HCl) = mass(HCl) / 36.5 g/mol 3. Use stoichiometry to calculate moles of CaCl2 produced: n(CaCl2) = n(HCl) / 2 4. Calculate the mass of CaCl2 produced: mass(CaCl2) = n(CaCl2) * molar_mass(CaCl2) = n(CaCl2) * 111 g/mol

Step-by-step solution

Write down the balanced chemical equation

Write the given balanced chemical equation with correct state symbols: \(CaCO_3(s) + 2 HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)\)

Determine the limiting reactant

To determine the limiting reactant, calculate the moles of each reactant given their masses, and compare their mole ratios to the stoichiometry of the balanced equation. The limiting reactant will be the one with the smallest mole ratio divided by its stoichiometric coefficient. To determine the moles of HCl, use the formula: n(HCl) = mass(HCl) / molar mass(HCl) Suppose the mass of HCl is given. First, find the molar mass of HCl from the periodic table (HCl = 1 g/mol + 35.5 g/mol = 36.5 g/mol). Then, calculate the moles of HCl using the mass provided.

Use stoichiometry to calculate moles of CaCl2 produced

According to the balanced equation, 2 moles of HCl react with 1 mole of CaCO3 to produce 1 mole of CaCl2. So, for every 2 moles of HCl, 1 mole of CaCl2 is produced. Now, use the stoichiometry of the reaction and the moles of HCl calculated in Step 2 to determine the moles of CaCl2 produced: n(CaCl2) = n(HCl) / 2

Calculate the mass of CaCl2 produced

To calculate the mass of CaCl2 produced, use the following formula: mass(CaCl2) = n(CaCl2) * molar_mass(CaCl2) Find the molar_mass of CaCl2 using the periodic table (Ca = 40 g/mol, Cl = 35.5 g/mol). So, molar_mass(CaCl2) = 40 + 2*35.5 = 111 g/mol. Finally, calculate the mass of CaCl2 using the formula mentioned above with the moles of CaCl2 calculated in Step 3. Now you have the mass of CaCl2 produced from the given mass of HCl.

Key concepts

Limiting Reactant

Understanding the concept of a limiting reactant is essential in stoichiometry, as it determines the amount of product formed in a chemical reaction. When you have multiple reactants, one of them will run out first, thereby limiting the extent of the reaction. This reactant is known as the limiting reactant. It is identified by comparing the mole ratio of each reactant to the coefficients in the balanced chemical equation.
To find the limiting reactant, calculate the moles of each substance involved using their respective masses and molar masses. The reactant that produces the least amount of product is the limiting one.

• Calculate moles of each reactant using the formula: \( n = \text{mass} / \text{molar mass} \).
• Compare mole ratios of each reactant to their stoichiometric coefficients from the balanced equation.
• The smallest ratio indicates the limiting reactant, determining the maximum amount of product that can be formed.

Balanced Chemical Equation

A balanced chemical equation accurately represents a chemical reaction using chemical formulas and symbols, illustrating both the reactants and the products succinctly. It provides a direct relationship between the amount of reactants used and the products formed. Balancing a chemical equation involves adjusting the coefficients in front of each substance so that the number of atoms of each element is conserved across both sides of the equation.
This conservation of mass ensures that the reaction abides by the Law of Conservation of Matter.

• Identify the correct state symbols (e.g., (s), (l), (aq), (g)) for each compound.
• Balance the equation by adjusting coefficients, ensuring that the quantity of each element is equal on both sides.
• Keeps the proportional relationships necessary for calculations involving limiting reactants and products.

Molar Mass

Molar mass is a fundamental concept in chemistry which represents the mass of one mole of a substance, and it is expressed in grams per mole (g/mol). To determine the molar mass of a compound, sum up the atomic masses of all the atoms in its chemical formula. This value is crucial for converting between grams of a substance and moles, which is an essential step in stoichiometry processes.
Calculating the molar mass helps in determining the number of moles associated with a given mass of a substance.

• Find atomic masses from the periodic table (e.g., Hydrogen = 1 g/mol, Chlorine = 35.5 g/mol).
• Calculate the molar mass by adding these atomic masses according to the compound's formula.
• Use it to convert between mass and moles, aiding in calculations of limiting reactants and products.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform into different substances called products. These transformations are governed by the rearrangement of atoms, which involve breaking and forming of chemical bonds. Understanding chemical reactions is pivotal for predicting yields and products.

• Reactants convert into products, represented by a balanced chemical equation.
• Reactions may release or absorb energy; hence they can be exothermic or endothermic.
• Inputs like reaction conditions and catalysts can affect the rate and extent of reactions.
• Products formed depend largely on the initial amounts and identities of reactants.

By understanding these fundamental ideas, one can properly analyze reactions, calculate quantities of substances involved, and predict the final outcome of a chemical process.