Ch.2 - Atoms & Elements

Problem 34

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Chapter 2, Problem 34

Upon decomposition, one sample of magnesium fluoride produces 1.65 kg of magnesium and 2.57 kg of fluorine. A second sample produces 1.32 kg of magnesium. How much fluorine (in grams) does the second sample produce?

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Step 1: Identify the given information. The first sample decomposes to produce 1.65 kg of magnesium and 2.57 kg of fluorine. The second sample produces 1.32 kg of magnesium and we need to find the amount of fluorine it produces.

Step 2: Convert all the given masses from kilograms to grams because the question asks for the answer in grams. Remember that 1 kg = 1000 g. So, the first sample produces 1650 g of magnesium and 2570 g of fluorine. The second sample produces 1320 g of magnesium.

Step 3: Determine the ratio of the mass of fluorine to the mass of magnesium in the first sample. This ratio is constant because it is based on the stoichiometry of the decomposition reaction of magnesium fluoride. The ratio is 2570 g of fluorine / 1650 g of magnesium.

Step 4: Use this ratio to find the mass of fluorine in the second sample. Multiply the mass of magnesium in the second sample by the ratio of the mass of fluorine to the mass of magnesium. This gives the mass of fluorine in the second sample.

Step 5: The result from step 4 is the mass of fluorine in the second sample, in grams. This is the answer to the problem.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a reaction based on balanced chemical equations. In this case, understanding the stoichiometric ratios of magnesium and fluorine from the decomposition of magnesium fluoride is essential to determine the amount of fluorine produced from the second sample.

Law of Conservation of Mass

The Law of Conservation of Mass states that mass is neither created nor destroyed in a chemical reaction. This principle implies that the total mass of the reactants must equal the total mass of the products. In the context of the question, this law helps in understanding that the mass of magnesium and fluorine produced from the decomposition of magnesium fluoride must correspond to the mass of the original sample, allowing for calculations of the second sample's fluorine yield.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. In this problem, knowing the molar masses of magnesium and fluorine will aid in determining the mass of fluorine produced from the second sample based on the amount of magnesium obtained.

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Molar Mass Concept

Related Practice

Two samples of carbon tetrachloride are decomposed into their constituent elements. One sample produces 38.9 g of carbon and 448 g of chlorine, and the other sample produces 14.8 g of carbon and 134 g of chlorine. Are these results consistent with the law of definite proportions? Explain your answer.

Two samples of sodium chloride are decomposed into their constituent elements. One sample produces 6.98 g of sodium and 10.7 g of chlorine, and the other sample produces 11.2 g of sodium and 17.3 g of chlorine. Are these results consistent with the law of definite proportions? Explain your answer.

Textbook Question

The mass ratio of sodium to fluorine in sodium fluoride is 1.21:1. A sample of sodium fluoride produces 28.8 g of sodium upon decomposition. How much fluorine (in grams) forms?

Two different compounds containing osmium and oxygen have the following masses of oxygen per gram of osmium: 0.168 and 0.3369 g. Show that these amounts are consistent with the law of multiple proportions.

Palladium forms three different compounds with sulfur. The mass of sulfur per gram of palladium in each compound is listed here. Show that these masses are consistent with the law of multiple proportions. Compound Grams S per Gram Pd A 0.603 B 0.301 C 0.151

Sulfur and oxygen form both sulfur dioxide and sulfur trioxide. When samples of these are decomposed, the sulfur dioxide produces 3.49 g oxygen and 3.50 g sulfur, while the sulfur trioxide produces 6.75 g oxygen and 4.50 g sulfur. Calculate the mass of oxygen per gram of sulfur for each sample and show that these results are consistent with the law of multiple proportions.

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