Problem 49 - Chemistry The Central Science In Si Units

Question

Write the chemical formula for each of the following compounds, and indicate the oxidation state of nitrogen in each: (a) sodium azide, (b) ammonium ion, (c) nitrous acid, (d) magnesium nitride, \((\mathbf{e})\) diazene, \((\mathbf{f})\) sodium nitrate, (g) nitrogen trifluoride, \((\mathbf{h})\) nitric acid.

Step-by-Step Solution

Answer

Sodium azide: \( \text{NaN}_3 \), \( -\frac{1}{3} \); Ammonium ion: \( \text{NH}_4^+ \), \( -3 \); Nitrous acid: \( \text{HNO}_2 \), \( +3 \); Magnesium nitride: \( \text{Mg}_3\text{N}_2 \), \( -3 \); Diazene: \( \text{N}_2\text{H}_2 \), \( -1 \); Sodium nitrate: \( \text{NaNO}_3 \), \( +5 \); Nitrogen trifluoride: \( \text{NF}_3 \), \( +3 \); Nitric acid: \( \text{HNO}_3 \), \( +5 \).

Step 1: Sodium Azide Formula

The formula for sodium azide is \( \text{NaN}_3 \). In sodium azide, nitrogen exists in the form of \( \text{N}_3^- \). The average oxidation state of nitrogen in \( \text{N}_3^- \) can be calculated by considering the total oxidation state as \( -1 \). Since there are three nitrogen atoms, the oxidation state \( x \) is given by the equation: \( 3x = -1 \), resulting in \( x = -\frac{1}{3} \).

Step 2: Ammonium Ion Formula

The ammonium ion is represented by the formula \( \text{NH}_4^+ \). In this compound, hydrogen has an oxidation state of \( +1 \). Since the charge of the ammonium ion is \( +1 \), the oxidation state of nitrogen \( x \) can be found using the equation: \( x + 4(+1) = +1 \), which simplifies to \( x = -3 \).

Step 3: Nitrous Acid Formula

Nitrous acid has the chemical formula \( \text{HNO}_2 \). The hydrogen here has a \( +1 \), and each oxygen has a \( -2 \) oxidation state. To find the oxidation state of nitrogen \( x \), use the equation: \( (+1) + x + 2(-2) = 0 \), leading to \( x = +3 \).

Step 4: Magnesium Nitride Formula

Magnesium nitride can be written as \( \text{Mg}_3\text{N}_2 \). Magnesium has a \( +2 \) oxidation state. To balance the total charge of \( 3(+2) \), the combined oxidation states of the two nitrogen atoms must be \( -6 \). Hence, each nitrogen atom is \( -3 \).

Step 5: Diazene Formula

Diazene has the formula \( \text{N}_2\text{H}_2 \). Each hydrogen has a \( +1 \) oxidation state. Therefore, the oxidation state of nitrogen \( x \) is determined by the equation: \( 2x + 2(+1) = 0 \), giving \( x = -1 \).

Step 6: Sodium Nitrate Formula

The formula for sodium nitrate is \( \text{NaNO}_3 \). Sodium has a \( +1 \) oxidation state and each oxygen is \( -2 \). Using the equation: \( (+1) + x + 3(-2) = 0 \), the oxidation state of nitrogen \( x \) is \( +5 \).

Step 7: Nitrogen Trifluoride Formula

Nitrogen trifluoride is represented by \( \text{NF}_3 \). Fluorine, being the most electronegative element, has a \( -1 \) oxidation state. The equation \( x + 3(-1) = 0 \) gives an oxidation state of nitrogen as \( +3 \).

Step 8: Nitric Acid Formula

Nitric acid is written as \( \text{HNO}_3 \). With hydrogen at \( +1 \) and each oxygen at \( -2 \), the equation for nitrogen's oxidation state \( x \) is: \( (+1) + x + 3(-2) = 0 \), resulting in \( x = +5 \).

Key Concepts

Oxidation States

Oxidation states, sometimes known as oxidation numbers, represent the degree of oxidation or reduction of an atom within a compound. They help in understanding electron transfer during chemical reactions and in determining the chemical formula for compounds. To find the oxidation state of an element like nitrogen, you balance the charge in the molecule or ion by using known oxidation states of other elements in the compound. For example, in sodium azide (\( \text{NaN}_3 \)). Sodium typically has an oxidation state of \( +1 \). In \( \text{NaN}_3 \), the nitrogen exists as the azide ion \( \text{N}_3^- \). The overall charge of the azide ion is \( -1 \), which helps calculate the average oxidation state of nitrogen as \( -\frac{1}{3} \) per nitrogen atom. This is found by solving the equation \( 3x = -1 \), where \( x \) is the oxidation state of each nitrogen atom. Understanding oxidation states is essential as it provides insight into the redox behavior of compounds and helps deduce molecular structures.

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons between each other, often resulting in a metal bonding with a non-metal. Such bonds are created through electrostatic forces between positively charged cations and negatively charged anions. These compounds generally have high melting and boiling points, and they conduct electricity when molten or dissolved in water. A perfect example of an ionic compound is magnesium nitride (\( \text{Mg}_3\text{N}_2 \)). Magnesium, a metal, loses electrons to become \( \text{Mg}^{2+} \), while nitrogen gains electrons to form the ion \( \text{N}^{3-} \). Magnesium nitride demonstrates the transfer of electrons from magnesium to nitrogen, resulting in a stable ionic compound. The chemical formula \( \text{Mg}_3\text{N}_2 \) reflects the balance of total charges, where the total positive charge from magnesium balances the total negative charge from nitrogen, ensuring neutrality.

Covalent Compounds

Covalent compounds are created when two or more non-metals share electrons to achieve a full outer electron shell. This type of bonding results in molecules with defined shapes and often lower melting and boiling points compared to ionic compounds. Covalent bonds are characterized by the sharing of electron pairs between atoms rather than a transfer. For instance, nitrogen trifluoride (\( \text{NF}_3 \)) showcases covalent bonding. Here, a nitrogen atom shares electrons with three fluorine atoms. Each fluorine forms a single covalent bond by sharing one of its electrons with nitrogen, leading to nitrogen having a \( +3 \) oxidation state as calculated from the compound's molecular formula. This sharing creates a stable molecular structure where the atoms involved reach a lower energy state.

Nitrogen Compounds

Nitrogen is a versatile element that forms a variety of compounds with different elements, showing a range of oxidation states due to its ability to lose, gain, or share electrons. These compounds can be ionic or covalent, and they play crucial roles in various chemical and biological processes.One notable nitrogen compound is nitric acid (\( \text{HNO}_3 \)). It is an example where nitrogen reaches its highest oxidation state of \( +5 \). In nitric acid, the nitrogen is bonded to three oxygen atoms and one hydrogen atom, forming a highly reactive and strong acid used in fertilizers and explosives. Nitrogen compounds like ammonium ion \( \text{NH}_4^+ \) further demonstrate the range of forms nitrogen can take. In this ion, nitrogen has an oxidation state of \( -3 \), showcasing a completely different set of properties compared to its oxides and acids. Understanding nitrogen compounds is essential for fields ranging from agriculture to pharmaceuticals, highlighting the importance of nitrogen in various chemical contexts.