Question

What is the mass percent of nitrogen in the $\mathrm{Co}(\mathrm{en}{)}_3{}^{3+}$ complex ion?

Short answer

Answer: The mass percent of nitrogen in the Co(en)_3^{3+} complex ion is approximately 35.13%.

Step-by-step solution

Finding the molar mass of the entire complex ion

First, determine the molar mass of each element present in the complex ion. The ion consists of one cobalt (Co) atom and three ethylenediamine (en) molecules. Ethylenediamine has the chemical formula C_2H_8N_2. The molar mass of the elements present in the ion are: - Cobalt (Co): 58.93 g/mol - Carbon (C): 12.01 g/mol - Hydrogen (H): 1.01 g/mol - Nitrogen (N): 14.01 g/mol Now, calculate the molar mass of the complex ion: $$M_{\mathrm{Co}(\mathrm{en}{)}_3}=[1\cdot 58.93]+[(3\cdot 2)\cdot 12.01]+[(3\cdot 8)\cdot 1.01]+[(3\cdot 2)\cdot 14.01]$$

Calculating the molar mass of the complex ion

Evaluate the expression from Step 1 to obtain the molar mass of the complex ion: $$M_{\mathrm{Co}(\mathrm{en}{)}_3}=58.93+72.06+24.24+84.06=239.29\mathrm{g}/\mathrm{mol}$$

Finding the molar mass of nitrogen in the complex ion

As there are 3 ethylenediamine molecules, each containing 2 nitrogen atoms, the complex ion has a total of 6 nitrogen atoms. The molar mass of nitrogen in the complex ion is: $$M_{\mathrm{nitrogen}}=6\cdot 14.01=84.06\mathrm{g}/\mathrm{mol}$$

Calculating the mass percent of nitrogen in the complex ion

Finally, divide the molar mass of nitrogen (84.06 g/mol) by the molar mass of the complex ion (239.29 g/mol) and multiply the result by 100: $$\mathrm{Mass}\mathrm{Percent}\mathrm{of}\mathrm{Nitrogen}\mathrm{in}\mathrm{Co}(\mathrm{en}{)}_3=\frac{84.06}{239.29}\cdot 100$$

Finding the final answer

Evaluate the expression from Step 4 to obtain the mass percent of nitrogen in the Co(en)_3^{3+} complex ion: $$\mathrm{Mass}\mathrm{Percent}\mathrm{of}\mathrm{Nitrogen}\mathrm{in}\mathrm{Co}(\mathrm{en}{)}_3=\frac{84.06}{239.29}\cdot 100\approx 35.13\mathrm{\%}$$ Thus, the mass percent of nitrogen in the $\mathrm{Co}(\mathrm{en}{)}_3{}^{3+}$ complex ion is approximately 35.13%.

Key concepts

Molar Mass

Understanding molar mass is a fundamental step in mastering mass percent calculations. Molar mass, expressed in grams per mole (g/mol), is the mass of one mole of a substance. A mole is a unit in chemistry that represents Avogadro's number, which is approximately 6.022 x 10²³ particles of the substance.

To calculate the molar mass, you sum up the atomic masses of all atoms in a molecule. Each element's atomic mass can be found on the periodic table and is usually expressed in atomic mass units (u) or grams per mole (g/mol). For compounds, multiply the atomic mass of each element by the number of atoms of that element in the compound, and then add these values together. For example, the molar mass of water (H₂O) is 2 times the mass of hydrogen (1.01 g/mol) plus the mass of oxygen (16.00 g/mol), which equals 18.02 g/mol.

What This Means for Our Exercise

In our exercise, the calculation of the molar mass of the Co(en)₃³⁺ ion includes the molar mass of cobalt, carbon, hydrogen, and nitrogen multiplied by their respective number of atoms within the complex, demonstrating the combined mass of the complex in one mole's quantity.

Chemical Composition

Chemical composition signifies the elemental makeup of a compound. It's the identification and proportion of the elements that form a chemical substance. Each compound has a unique composition represented by its chemical formula, which provides information about the number of each type of atom present.

Chemical formulas can be empirical, molecular, or structural. An empirical formula shows the simplest whole-number ratio of atoms in a compound, while a molecular formula shows the actual number of each type of atom found in a molecule of the compound. Lastly, structural formulas show how atoms are connected in a molecule.

Application to Our Mass Percent Calculation

In mass percent calculations, the chemical composition reveals which elements we should focus on. For the complex ion Co(en)₃³⁺, the chemical formula indicates that it contains cobalt, carbon, hydrogen, and nitrogen. To find the mass percent of nitrogen, we examine the formula to determine the number of nitrogen atoms and their contribution to the total mass of the ion.

Stoichiometry

Stoichiometry is a branch of chemistry dealing with the quantitative relationships between reactants and products in a chemical reaction. It involves calculations based on the laws of conservation of mass and the concept of moles. Using stoichiometry, one can predict how much product will form from a given amount of reactants, or vice versa.

Stoichiometric calculations often require balancing a chemical equation to ensure the number of atoms for each element is equal on both the reactant and product sides of the equation. The coefficients in a balanced equation represent the ratio in which substances react or form products.

Stoichiometry in Relation to Mass Percent

The stoichiometric principles apply to our mass percent calculation in the regard that the ratio of the elements in the complex ion Co(en)₃³⁺ must be known to determine the mass contributed by nitrogen atoms specifically. In this case, the stoichiometry of the complex tells us there are six nitrogen atoms present, which we use to calculate the total mass of nitrogen in the ion for the final mass percent value.