Question

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

Short answer

The second sample produces 2055.61 grams of fluorine.

Step-by-step solution

Identify Given Information from the First Sample

The first sample decomposes into 1.65 kg of magnesium and 2.57 kg of fluorine. This sets up a ratio of the masses of magnesium to fluorine.

Calculate the Magnesium to Fluorine Ratio

Find the ratio of the mass of fluorine to the mass of magnesium from the first sample. Essentially, divide the mass of fluorine by the mass of magnesium: calculated ratio = (mass of fluorine) / (mass of magnesium) = 2.57 kg / 1.65 kg.

Calculate the Ratio

Perform the division from the previous step to find the exact numerical ratio: calculated ratio = 2.57 kg / 1.65 kg = 1.55758 (rounded to five decimal places).

Determine the Mass of Fluorine in the Second Sample

Using the ratio found and the mass of magnesium from the second sample, calculate the corresponding mass of fluorine. mass of fluorine = calculated ratio * mass of magnesiummass of fluorine in the second sample = 1.55758 * 1.32 kg.

Convert Fluorine Mass to Grams and Perform the Calculation

Since 1 kg equals 1000 grams, and the problem asks for the mass in grams, convert the mass of fluorine from kilograms to grams:mass of fluorine in grams = (1.55758 * 1.32 kg) * 1000 g/kg.

Complete the Calculation

Perform the multiplication to find the mass of fluorine produced by the second sample in grams:mass of fluorine in grams = (1.55758 * 1.32) * 1000 g/kg = 2055.6056 g.

Key concepts

Understanding Chemical Decomposition

Chemical decomposition, often called chemical breakdown, is a fundamental concept in chemistry that involves the separation of a chemical compound into elements or simpler compounds. It's sort of like baking a cake and then breaking it down into its original ingredients—but in reverse. This process is often a result of chemical reactions, heat, or other forms of energy. In a stoichiometry problem involving decomposition, you figure out how much of each element is formed when a compound falls apart. For magnesium fluoride (MgF₂), when it decomposes, we get magnesium (Mg) and fluorine (F₂).

An important tip when dealing with decomposition reactions is to make sure you write down the correct chemical equation for the reaction. This could guide your understanding of how the reactants are related and aid in solving the problem effectively. Remember, stoichiometry relies heavily on the law of conservation of mass, which states that in a chemical reaction, matter is neither created nor destroyed, only transformed.

Mole Ratio Calculation in Stoichiometry

The mole ratio is the heart of stoichiometry. It tells us the proportion of how many moles of one substance react or are produced in relation to another substance. To work with mole ratios, you first need to know the balanced chemical equation for the reaction you're studying. The coefficients in front of the chemical formulas give you the mole ratios.

However, in some exercises like the textbook problem above, you're given masses instead of moles. That's okay, because you can convert masses to moles using molar mass, but sometimes you may work directly with mass ratios if moles are not needed. The important part is to understand the fixed ratio from the balanced equation, whether you are dealing with masses or moles. To calculate the mole ratio, divide the amount of one substance by the amount of another; it's as simple as that.

The Mass-to-Mass Conversion Process

Mass-to-mass conversion is a way to relate the masses of two substances involved in a chemical reaction, adding another layer to our stoichiometry cake. Understanding this conversion is crucial when you're not given the number of moles in a problem. Start by identifying the mass relationship of the compounds from the balanced equation. Then use that relationship to find out how much of one compound is produced or necessary when a certain amount of another is used, as seen in the problem example.

Here's how you go about it: Use the mass ratio calculated from known amounts to find the unknown mass. The first sample from the textbook problem gives us a ratio of magnesium to fluorine, which we apply to the second sample. Don't forget to convert your units appropriately, like kilograms to grams if needed. Keep track of your unit conversions to avoid mistakes—converting units is often where errors creep in. In the end, a good grasp of mass-to-mass conversions can make even complex stoichiometry problems a piece of cake!