Problem 146 - Chemistry

Question

When \(0.273 \mathrm{~g}\) of \(\mathrm{Mg}\) is heated strongly in a nitrogen \(\left(\mathrm{N}_{2}\right)\) atmosphere, a chemical reaction occurs. The product of the reaction weighs 0.378 g. Calculate the empirical formula of the compound containing \(\mathrm{Mg}\) and \(\mathrm{N}\). Name the compound.

Step-by-Step Solution

Answer

The empirical formula of the compound is Mg3N, and its name is Magnesium Nitride.

Step 1: Convert Mass into Moles

We can convert mass into moles using the formula: n = m/M, where n is the number of moles, m is the mass and M is the molar mass. The molar masses of Mg and N are 24.31 \mathrm{~g/mol} and 14.01 \mathrm{~g/mol} respectively. For Mg: n = 0.273 g / 24.31 g/mol = 0.0112 mol. Since Nitrogen forms diatomic molecules, the molar mass is twice that of a single Nitrogen atom. Therefore the mass of Nitrogen that reacted can be found by subtracting the mass of the original Mg and the final compound: 0.378 g - 0.273 g = 0.105 g. The number of moles of Nitrogen are then: n = 0.105 g / (14.01 g/mol * 2) = 0.00375 mol.

Step 2: Determine the Simplest Ratio

The ratio of the moles of Mg to the moles of N is then: 0.0112 mol / 0.00375 mol = 3. This means that there are 3 moles of Mg for every mole of N in the compound. Therefore, the empirical formula of the compound is Mg3N.

Step 3: Name the Compound

The compound is called Magnesium Nitride. It follows the naming rules for ionic compounds, where the metal (Mg) is named first, followed by the nonmetal (N), which is modified to end with '-ide'.

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance. This is typically expressed in grams per mole (g/mol). The molar mass allows us to convert between the mass of a substance and the number of moles, which is crucial in quantitative chemistry.

To calculate the molar mass of an element or compound:

• Find the atomic mass of each element using the periodic table.
• For compounds, sum the atomic masses of the constituent elements according to their proportions in the formula.

For example, the molar mass of magnesium (Mg) is 24.31 g/mol, and for nitrogen (N), it is 14.01 g/mol. Since nitrogen naturally forms diatomic molecules ( _2"), its molar mass for reactions involving _2 is doubled, becoming approximately 28.02 g/mol.

Mole Conversion

Mole conversion is the process of converting quantities between mass, number of particles, and moles. This is achieved using the conversion formula:\[ n = \frac{m}{M}\]where:

• \(n\) is the number of moles,
• \(m\) is the mass of the substance,
• \(M\) is the molar mass.

This conversion is essential for solving many types of chemistry problems. For instance, in the original problem, the mass of magnesium (0.273 g) is converted into moles using its molar mass (24.31 g/mol) to find that there are 0.0112 moles of Mg. Understanding mole conversion helps in determining the proportions of elements in compounds.

Magnesium Nitride

Magnesium nitride is a chemical compound consisting of magnesium and nitrogen. When magnesium reacts with nitrogen, magnesium nitride is formed. This case illustrates the concept of empirical formulas and compound naming.The empirical formula represents the simplest whole-number ratio of elements in a compound. In magnesium nitride's case, the reaction results in the formation of \(Mg_3N_2\), indicating there are three moles of magnesium for every two moles of nitrogen.

Magnesium nitride is named according to the rules for ionic compounds. The metal (magnesium) is named first, followed by the non-metal (nitrogen) with an '-ide' suffix, resulting in the name 'Magnesium Nitride'.

Chemical Reaction

A chemical reaction involves the transformation of one or more substances into different substances through the breaking and forming of chemical bonds. In the problem, when magnesium is heated in a nitrogen atmosphere, a chemical reaction occurs forming magnesium nitride.

• The magnesium atoms react with nitrogen molecules from the atmosphere.
• New bonds form between magnesium and nitrogen, resulting in magnesium nitride.

Chemical reactions such as this one often involve an energy change, such as the release or absorption of heat. Observations in reactions can include mass changes, as noted in the original problem where the mass of the final compound (0.378 g) differed from just the magnesium's initial mass (0.273 g). This reflects the law of conservation of mass, which states the total mass of reactants equals the total mass of products.