Question

Upon decomposition, one sample of magnesium fluoride produced \(1.65 \mathrm{~kg}\) of magnesium and \(2.57 \mathrm{~kg}\) of fluorine. A second sample produced \(1.32 \mathrm{~kg}\) of magnesium. How much fluorine (in grams) did the second sample produce? Remember that, according to the law of constant composition, the ratio of the masses of the two elements must be the same in both samples.

Short answer

The second sample produced approximately 2056 grams of fluorine.

Step-by-step solution

Understand the Law of Constant Composition

The law of constant composition states that all samples of a pure compound contain the same elements in the same proportion by mass. In this problem, we are dealing with magnesium fluoride, which means that the ratio of the mass of magnesium to the mass of fluorine must be the same in both samples.

Calculate the Mass Ratio of Magnesium to Fluorine in the First Sample

Using the first sample, calculate the mass ratio of magnesium to fluorine. The mass of magnesium is given as 1.65 kg and that of fluorine is 2.57 kg.The mass ratio (magnesium to fluorine) is obtained by dividing the mass of magnesium by the mass of fluorine: Ratio = \( \frac{1.65\mathrm{~kg}}{2.57\mathrm{~kg}} \) = \( \frac{1.65}{2.57} \).

Calculate the Mass of Fluorine in the Second Sample

Use the mass ratio from step 2 to find the mass of fluorine produced in the second sample. Given that the mass of magnesium in the second sample is 1.32 kg, the mass of fluorine (F) can be found by:\( F = 1.32\mathrm{~kg} \times \frac{2.57}{1.65} \).After performing the multiplication, you will find out how many kilograms of fluorine were produced in the second sample. Convert this mass from kilograms to grams by multiplying by 1000.

Execute the Calculations

First, calculate the magnesium to fluorine ratio from step 2:Ratio = \( \frac{1.65}{2.57} \approx 0.6415 \).Next, calculate the mass of fluorine in the second sample using the ratio and the given mass of magnesium (1.32 kg):\( F = 1.32 \times \frac{2.57}{1.65} \approx 2.056 \) kg.Finally, convert the mass of fluorine to grams:\( F_{\text{grams}} = 2.056 \times 1000 \) grams = 2056 grams.

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that involves determining the relative quantities of reactants and products involved in chemical reactions. Imagine stoichiometry as a recipe for a chemical reaction: just as you need a certain amount of flour and sugar to bake cookies consistently, you need the right amounts of reactants to produce a certain amount of product in a chemical reaction.

In the context of the original exercise, stoichiometry helps us understand how much fluorine will be produced from a given amount of magnesium fluoride upon decomposition, based on the consistent ratio dictated by the law of constant composition. If you measure out the right amount of magnesium, using stoichiometry, you can predict the exact amount of fluorine that will be produced.

Chemical Decomposition

Chemical decomposition, also known as analysis or breakdown, is the process in which a chemical compound is split into smaller compounds or individual elements. It's like breaking down a Lego structure into its individual blocks. Decomposition reactions are the opposite of synthesis reactions, where smaller pieces combine to make larger ones.

In our exercise, magnesium fluoride undergoes decomposition, breaking down into magnesium and fluorine. This process obeys the law of constant composition, meaning the products will always consist of magnesium and fluorine in a fixed mass ratio, irrespective of the size of our original magnesium fluoride sample.

Mass Ratio Calculations

Mass ratio calculations are essential in stoichiometry for comparing the masses of different substances involved in a chemical reaction. In the original exercise, the mass ratio is used to compare the amounts of magnesium and fluorine obtained from the decomposition of magnesium fluoride.

It is calculated by dividing the mass of one component by the mass of another. For example, if you have a bag of mixed nuts and you want to know the ratio of almonds to cashews by mass, you'll weigh the almonds and cashews separately and then divide one weight by the other.

• Knowing the mass ratio from the first sample, we can find out how much fluorine the second sample should produce when the given amount of magnesium is decomposed.

Magnesium Fluoride

Magnesium fluoride (MgF2) is an inorganic compound that consists of one magnesium atom and two fluorine atoms. The properties of magnesium fluoride are like those of a basic recipe; it consistently entails two fluorine atoms for each magnesium atom, reflecting the law of constant composition.

Being interested in magnesium fluoride lets us dive deeper into understanding chemical formulas and decomposition. It helps illustrate practical applications of stoichiometry and mass ratio calculations when this compound is decomposed into its elemental parts, magnesium and fluorine, which we have analyzed in our exercise.