Question

The mass ratio of sodium to fluorinc in sodium fluoride is \(1.21 : 1 . \mathrm{A}\) sample of sodium fluoride produces 28.8 \(\mathrm{g}\) of sodium upon decomposition. How much fluorine (in grams) is formed?

Short answer

23.8 grams of fluorine are formed.

Step-by-step solution

Identify the Mass Ratio

The mass ratio of sodium to fluorine in sodium fluoride is given as 1.21:1. This means that for every 1.21 grams of sodium, there is 1 gram of fluorine.

Calculate the Mass of Fluorine

Using the mass ratio, we set up a proportion to find the mass of fluorine that corresponds to 28.8 grams of sodium. If 1.21 g of Na corresponds to 1 g of F, then 28.8 g of Na corresponds to x g of F. The proportion is \( \frac{1.21g \ Na}{1g \ F} = \frac{28.8g \ Na}{x \ g \ F} \).

Solve the Proportion for Fluorine Mass

To find the value of x, cross multiply and divide. \(x = \frac{28.8g \ Na \times 1g \ F}{1.21g \ Na}\). Calculating this gives the mass of fluorine.

Calculate and Interpret the Result

Perform the calculation to find x: \(x = \frac{28.8g}{1.21}\). After computing, interpret the result which gives the mass of fluorine in grams.

Key concepts

Mass Ratio

Understanding the mass ratio in chemical compounds is crucial when studying stoichiometry. It's a concept that allows us to quantify the comparison between the masses of different elements in a compound. For instance, in the exercise, we're given the mass ratio of sodium to fluorine in sodium fluoride as 1.21:1. This indicates that for every 1.21 grams of sodium, there is exactly 1 gram of fluorine.

To use this information practically, think of the mass ratio as a simple fraction or proportion that can be scaled up or down based on the amount of substance you're dealing with. In the given exercise, if you have 28.8 grams of sodium after decomposition, you apply the mass ratio to find the corresponding mass of fluorine. The process involves setting up a proportional equation and solving for the unknown—which, in this case, would be the mass of fluorine produced.

Real-World Application

Understanding mass ratios has real-world significance, such as in the preparation of chemical solutions, where precise amounts of substances are required. It also plays a role in environmental monitoring, where understanding the relative amounts of pollutants can be vital.

Chemical Decomposition

Chemical decomposition is a type of chemical reaction where a single compound breaks down into two or more simpler substances. These reactions are essential to understanding because they're the inverse of synthesis reactions, where simpler substances combine to form a more complex compound.

In the provided exercise, the decomposition of sodium fluoride (NaF) into its constituent elements, sodium (Na) and fluorine (F), is the focus. Decomposition can occur due to various factors such as heating, light exposure, or use of electricity (electrolysis). The concept of chemical decomposition also finds significance in various industries, such as in the manufacturing of metals, where ores are decomposed to extract the pure metal.

Practical Implications

From the perspective of stoichiometry, knowing the initial compound and the products of decomposition allows you to predict and calculate the amounts of each product that will form. This is especially useful in predicting the outcomes of reactions in chemical engineering, waste management, and materials science.

Mole Concept

The mole concept is a foundational pillar in the study of chemistry, providing a bridge between the atomic scale and the macroscopic world we perceive. A mole represents Avogadro's number (\(6.022 \times 10^{23}\) entities) of any substance. In the context of stoichiometry, the mole concept allows us to convert between mass, number of particles, and volume of gases at Standard Temperature and Pressure (STP).

For the sodium fluoride exercise, even though the mole concept isn't directly mentioned, it's inherently used when dealing with the mass of a substance because mass is related to the amount in moles through the molar mass of the compound or element. The mass ratio helps to keep our calculations on a per-unit-mass basis. Keeping track of the moles ensures that the reaction adheres to the law of conservation of mass, which states that matter is neither created nor destroyed during a chemical reaction.

Link to Everyday Life

The mole concept is not just a scientific abstraction. For example, pharmacists use the mole concept to determine the correct dosage of medication based on body weight, and environmental scientists use it to calculate pollutant concentrations in water or air. It underscores the quantitative aspect of chemical composition in a variety of practical applications.