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 \(0.378 \mathrm{~g}\). Calculate the empirical formula of the compound containing \(\mathrm{Mg}\) and \(\mathrm{N}\). Name the compound.

Short answer

The empirical formula is \(\text{Mg}_3\text{N}_2\) and the compound is magnesium nitride.

Step-by-step solution

Determine the mass of nitrogen that reacted

First, we need to find out how much nitrogen reacted during the process. We do this by subtracting the mass of magnesium from the mass of the product. \[\text{Mass of nitrogen} = \text{Mass of product} - \text{Mass of magnesium} = 0.378 \text{ g} - 0.273 \text{ g} = 0.105 \text{ g}\]

Convert masses to moles

To find the empirical formula, convert the masses of magnesium and nitrogen into moles.For magnesium (Mg):\[\text{Moles of Mg} = \frac{0.273 \text{ g}}{24.31 \text{ g/mol}} \approx 0.01123 \text{ mol}\]For nitrogen (N):\[\text{Moles of N} = \frac{0.105 \text{ g}}{14.01 \text{ g/mol}} \approx 0.0075 \text{ mol}\]

Determine the simplest mole ratio

Divide the number of moles of each element by the smallest number of moles calculated:For Mg:\[\frac{0.01123}{0.0075} \approx 1.497 \approx 1.5\]For N:\[\frac{0.0075}{0.0075} = 1\]The simplest ratio is approximately Mg : N = 1.5 : 1.

Multiply to get whole numbers

To get integers from the fraction, multiply both ratios by 2 to eliminate the fraction:Mg : N = 1.5 : 1 becomes 3 : 2, thus indicating the empirical formula is \(\text{Mg}_3\text{N}_2\).

Name the compound

The compound \(\text{Mg}_3\text{N}_2\) is named magnesium nitride.

Key concepts

Moles Conversion

Converting the mass of a substance into moles is a crucial step in understanding the composition of a compound. The relationship between mass and moles is governed by the molar mass of the substance, which is the mass per mole of its atoms. To convert grams into moles, we use the formula:\[\text{Moles} = \frac{\text{Mass in grams}}{\text{Molar mass in g/mol}}.\]This conversion is helpful because chemical reactions happen at the level of moles, not grams. It's like comparing apples to apples in chemistry!

In the context of the exercise, converting the mass of magnesium (Mg) and nitrogen (N) into moles allows us to find the basic building blocks of the compound formed in the reaction. Always remember to use the correct molar mass for each element for accurate conversion.

Mole Ratio

The mole ratio is the proportion of moles of one element to another in a compound. It is essential for determining the simplest whole number ratio of atoms and, consequently, the empirical formula of a compound. Calculating the mole ratio involves dividing the number of moles of each element by the smallest number of moles obtained.

This step helps establish a baseline for comparison. The ratio from the exercise was Mg : N = 1.5 : 1, which couldn't directly be used to form a whole number empirical formula. As a solution, we adjusted the ratio to achieve whole numbers by multiplying all components by the same factor, resulting in Mg : N = 3 : 2. Such adjustive measures are vital in deriving accurate empirical formulas.

• Ensure those ratios are as simple and close to whole numbers as possible.
• Multiply across if needed, to reach integer ratios.

Understanding mole ratios help in grasping the fundamental relationships in compounds.

Chemical Reaction

Chemical reactions are processes in which substances undergo chemical changes, resulting in the formation of new substances with new properties. In our exercise, the reaction between magnesium (Mg) and nitrogen (\(\text{N}_2\)) is a classic example of a synthesis reaction.

During a synthesis reaction, simple substances combine to form more complex compounds. For instance, when Mg is heated in nitrogen gas, they bond to form a solid compound, magnesium nitride (\(\text{Mg}_3\text{N}_2\)). This transformation occurs through the reorganization of electrons and changes in the arrangement of atoms.

• Reactants: The starting materials such as Mg and \(\text{N}_2\).
• Product: A new compound like magnesium nitride.

Understanding the specifics of this reaction aids in predicting product formation and methods for balancing chemical equations.

Magnesium Nitride

Magnesium nitride (\(\text{Mg}_3\text{N}_2\)) is a chemical compound formed through the reaction between magnesium and nitrogen. It stands as an example of a binary compound, consisting of two different elements.

Let's look into its characteristics:

• It is usually a powdery or crystalline solid and is yellow-brown in appearance.
• As a nitride, it contains nitride ions (\(\text{N}^{3-}\)), interacting with magnesium ions (\(\text{Mg}^{2+}\)).

This compound's empirical formula, \(\text{Mg}_3\text{N}_2\), reflects the simplest whole number ratio of its constituent atoms. Moreover, magnesium nitride can react further with water to produce ammonia (NH3), making it quite useful in various chemical processes. Understanding the formation and properties of \(\text{Mg}_3\text{N}_2\) is a stepping stone towards mastering inorganic chemistry.