What mass of [tex]$Cl _2$[/tex] reacted when 0.243 g Mg reacted completely to form [tex]$0.953 g MgCl _2$[/tex]?
Answer (2)
The mass of chlorine gas (Cl_2) that reacted when 0.243 g of magnesium (Mg) formed 0.953 g of magnesium chloride (MgCl_2) is 0.710 g. This is determined by applying the law of conservation of mass. The calculation follows the steps of identifying the chemical reaction, rearranging the mass equation, and substituting the given values.
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The reaction is M g + C l 2 → M g C l 2 .
Apply the law of conservation of mass: m M g + m C l 2 = m M g C l 2 .
Rearrange the equation to solve for the mass of C l 2 : m C l 2 = m M g C l 2 − m M g .
Calculate the mass of C l 2 : m C l 2 = 0.953 g − 0.243 g = 0.710 g . The mass of C l 2 reacted is 0.710 g .
Explanation
Problem Analysis We are given that 0.243 g of Mg reacts completely to form 0.953 g of M g C l 2 . We need to find the mass of C l 2 that reacted.
Reaction Equation The reaction is: M g + C l 2 → M g C l 2
Conservation of Mass According to the law of conservation of mass, the mass of reactants must equal the mass of products. Therefore, the mass of M g plus the mass of C l 2 must equal the mass of M g C l 2 . We can write this as: m M g + m C l 2 = m M g C l 2
Solving for Mass of Chlorine We are given m M g = 0.243 g and m M g C l 2 = 0.953 g . We want to find m C l 2 . We can rearrange the equation to solve for m C l 2 : m C l 2 = m M g C l 2 − m M g
Calculating Mass of Chlorine Now, we can plug in the given values: m C l 2 = 0.953 g − 0.243 g m C l 2 = 0.710 g
Final Answer Therefore, the mass of C l 2 that reacted is 0.710 g.
Examples
In chemistry, understanding the mass relationships in chemical reactions is crucial for various applications. For instance, in industrial processes, knowing the exact amount of reactants needed to produce a specific amount of product is essential for optimizing efficiency and minimizing waste. This problem demonstrates a fundamental concept in stoichiometry, which is the quantitative relationship between reactants and products in a chemical reaction. By applying the law of conservation of mass, we can determine the amount of chlorine required to react with a given amount of magnesium to produce magnesium chloride, a compound used in various applications such as dust control and fireproofing.
