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In chemistry, a balanced chemical equation is crucial for understanding the relationship between reactants and products in a chemical reaction. A chemical equation shows the substances involved in a reaction and their relative amounts. Balancing this equation ensures the law of conservation of mass is respected - meaning the number of atoms of each element is the same on both sides of the equation.

For example, in the electrolytic decomposition of calcium chloride (\text{CaCl\(_2\)}), the balanced equation is represented as: \[ 2 \text{CaCl}_2 \rightarrow 2 \text{Ca} + \text{Cl}_2 \] This tells us that 2 molecules of \text{CaCl\(_2\)} decompose to produce 2 atoms of calcium (\text{Ca}) and 1 molecule of chlorine gas (\text{Cl\(_2\)}).

It's important to ensure the equation is balanced before moving on to perform any further calculations. Balancing helps in predicting the amount of products formed from given reactants and vice versa. The coefficients in the balanced equation (like the '2' in front of \text{CaCl\(_2\)}) indicate the molar ratio of the reactants and products.

Molar mass is used to convert between grams and moles, an essential step in stoichiometry. The molar mass of a compound is the total mass of all the atoms in one mole of that compound. It's calculated by adding up the atomic masses of all the atoms present in the molecular formula. For the decomposition of calcium chloride (\text{CaCl\(_2\)}), we calculate the molar mass as follows:

- Molar mass of \text{CaCl\(_2\)} is \[ 40.08 + 2 \times 35.45 = 110.98 \text{ g/mol} \] \text{Calcium} has a molar mass of 40.08 g/mol and \text{chlorine} has a molar mass of 35.45 g/mol.

Knowing the molar masses of \text{CaCl\(_2\)}, \text{Ca}, and \text{Cl\(_2\)} allows us to convert masses into moles, making it easier to use the stoichiometric ratios to determine how much of each product will be formed from a given amount of reactant. For instance, with \text{Cl\(_2\)}, the molar mass is \[ 2 \times 35.45 = 70.90 \text{ g/mol} \]

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the mole ratios of reactants and products. For the decomposition of calcium chloride, we use stoichiometric principles to find out how much chlorine gas (\text{Cl\(_2\)}) and calcium (\text{Ca}) can be produced from a given amount of calcium chloride (\text{CaCl\(_2\)}).

Steps in stoichiometric calculations:

• Determine moles of \text{CaCl\(_2\)}: \[ \text{Moles of CaCl\(_2\)} = \frac{874 \text{ g}}{110.98 \text{ g/mol}} = 7.875 \text{ mol} \]
• Find moles of \text{Cl\(_2\)} produced: According to the balanced equation, 2 moles of \text{CaCl\(_2\)} produce 1 mole of \text{Cl\(_2\)}. So, \[ \text{Moles of Cl\(_2\)} = \frac{7.875 \text{ mol}}{2} = 3.9375 \text{ mol} \]
• Convert moles of \text{Cl\(_2\)} to grams: \[ \text{Mass of Cl\(_2\)} = 3.9375 \text{ mol} \times 70.90 \text{ g/mol} = 279.26 \text{ g} \]
• For calcium, 2 moles of \text{CaCl\(_2\)} produce 2 moles of \text{Ca}. So, \[ \text{Moles of Ca} = 7.875 \text{ mol} \]
• Then convert moles of \text{Ca} to grams: \[ \text{Mass of Ca} = 7.875 \text{ mol} \times 40.08 \text{ g/mol} = 315.67 \text{ g} \]

Using stoichiometry helps predict the quantities of products formed and ensure that no reactant is wasted. It aligns chemical calculations with the balanced equation, providing precise results.