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?

Chemical decomposition is a critical concept in stoichiometry, where a compound breaks down into its constituent elements or smaller compounds. In the context of the given exercise, magnesium fluoride (MgF₂) undergoes decomposition to yield magnesium (Mg) and fluorine (F₂). This process is governed by the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction. Thus, the total mass of magnesium fluoride will be equal to the sum of the masses of the magnesium and fluorine produced.

Understanding this principle helps to predict the outcomes of decomposition reactions. For example, if a sample of magnesium fluoride decomposes, the masses of magnesium and fluorine produced must add up to the original mass of the magnesium fluoride. This is the underlying reason why we can use the mass ratio between these elements to solve problems related to their decomposition.

The mole ratio is an essential stoichiometry concept that represents the ratio of moles of one substance to the moles of another substance in a chemical reaction. In the given exercise, we infer a mole ratio from the mass-to-mass relationship of the decomposition products. The mole ratio is inherently based on the coefficients of a balanced chemical equation and is critical when predicting the amount of reactants or products involved in a reaction.

However, in situations similar to the textbook exercise, where a chemical equation is not provided, the mole ratio can still be determined using the mass data given. Once you've calculated the mole ratio using the first sample, applying it to the second sample allows you to solve for the unknown quantity with confidence knowing that the underlying stoichiometry remains the same.

Mass-to-mass conversion is a process often used in stoichiometry to predict the mass of one substance that will form or react based on the mass of another substance. In our case, this conversion involves using the constant mass ratio determined from the first sample of magnesium fluoride to find the mass of fluorine in the second sample.

To break it down, following the calculation of the mass ratio using the quantities from the first sample, this ratio is essentially a conversion factor. By multiplying the mass of magnesium in the second sample by this ratio, we effectively convert the known mass of one element (magnesium) to find the corresponding mass of the related element (fluorine), which is what the problem is asking for.

Chemistry problem solving often involves a systematic approach to resolve quantitative chemical questions. The textbook exercise exemplifies this approach in a step-by-step process. It begins with identifying what is known and what needs to be found. In chemistry problems, it's crucial to start by gathering data from the problem statement, which in this case includes known masses of compounds from a decomposition reaction.

After establishing the known data, the next steps involve calculating ratios or conversion factors, applying them to find unknowns, and often converting units for the final answer. It's also vital to recall fundamental principles, such as the law of conservation of mass and stoichiometry, to guide the problem-solving process. This structured approach helps students to logically progress through complex chemistry questions and reach the correct conclusions.