Question

(a) What is the difference between adding a subscript 2 to the end of the formula for \(\mathrm{CO}\) to give \(\mathrm{CO}_{2}\) and adding a coefficient in front of the formula to give \(2 \mathrm{CO} ?\) (b) Is the following chemical equation, as written, consistent with the law of conservation of mass? $$ \begin{aligned} 3 \mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow & \\ \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$ Why or why not?

Short answer

(a) A subscript in a chemical formula (e.g., \(\mathrm{CO}_{2}\)) indicates the number of atoms of a specific element within a molecule or ion, while a coefficient in front of a formula (e.g., \(2 \mathrm{CO}\)) represents the number of molecules or ions involved in a reaction. (b) The given chemical equation is not consistent with the law of conservation of mass because the number of phosphorus (P) atoms is not conserved between the reactants and products, as there are 2 (reactants) and 6 (products).

Step-by-step solution

a) Difference between adding a subscript and adding a coefficient

Adding a subscript to a chemical formula indicates that there are multiple atoms of a specific element within a single molecule or ion. In the example given, \(\mathrm{CO}_{2}\) indicates a molecule of carbon dioxide, composed of one carbon atom (C) and two oxygen atoms (O). On the other hand, adding a coefficient in front of a chemical formula represents the number of molecules or ions involved in a chemical reaction. For example, \(2 \mathrm{CO}\) means there are two molecules of carbon monoxide, each consisting of one carbon atom (C) and one oxygen atom (O). So, the difference between a subscript and a coefficient is that a subscript refers to the number of atoms of a certain element within a molecule or ion, whereas a coefficient refers to the number of molecules or ions participating in a chemical reaction.

b) Checking consistency with the law of conservation of mass

To determine if the given chemical equation obeys the law of conservation of mass, we need to count the number of atoms of each element on both the reactants (left) and products (right) side of the equation and see if they are equal. The reactants side of the equation is: $$ 3 \mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{H}_{3} \mathrm{PO}_{4}(a q) $$ Counting the atoms, we have: - 3 magnesium (Mg) atoms - 6 oxygen (O) atoms (as there are 3 \(\mathrm{Mg}(\mathrm{OH})_{2}\) molecules, each with 2 oxygen atoms) - 6 hydrogen (H) atoms (as there are 3 \(\mathrm{Mg}(\mathrm{OH})_{2}\) molecules, each with 2 hydrogen atoms) - 6 hydrogen (H) atoms (as there are 2 \(\mathrm{H}_{3} \mathrm{PO}_{4}\) molecules, each with 3 hydrogen atoms) - 2 phosphorus (P) atoms (as there are 2 \(\mathrm{H}_{3} \mathrm{PO}_{4}\) molecules, each with 1 phosphorus atom) - 8 oxygen (O) atoms (as there are 2 \(\mathrm{H}_{3} \mathrm{PO}_{4}\) molecules, each with 4 oxygen atoms) On the products side of the equation, we have: $$ \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ Counting the atoms, we have: - 3 magnesium (Mg) atoms - 6 phosphorus (P) atoms (as there are 2 \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) formula units, each with 3 phosphorus atoms) - 12 oxygen (O) atoms (as there are 2 \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) formula units, each with 6 oxygen atoms) - 12 hydrogen (H) atoms (as there are 6 \(\mathrm{H}_{2} \mathrm{O}\) molecules, each with 2 hydrogen atoms) - 6 oxygen (O) atoms (as there are 6 \(\mathrm{H}_{2} \mathrm{O}\) molecules, each with 1 oxygen atom) Comparing the number of atoms in reactants and products: - Mg: 3 (reactants) = 3 (products) - H: 6 + 6 (reactants) = 12 (products) - O: 6 + 8 (reactants) = 12 + 6 (products) - P: 2 (reactants) = 6 (products) We can see that the number of atoms for magnesium (Mg), hydrogen (H), and oxygen (O) is conserved, but the number of atoms for phosphorus (P) is not conserved. Therefore, the given chemical equation is not consistent with the law of conservation of mass.

Key concepts

Subscripts in Chemical Formulas

Understanding subscripts in chemical formulas is fundamental to grasping the basics of chemistry. For example, in the chemical formula \(\mathrm{CO}_{2}\), the subscript '2' tells us there are two oxygen atoms for every one carbon atom in a molecule of carbon dioxide. Subscripts provide specific information about the proportions of atoms in a compound.

Contrary to changing the entire compound, altering a single subscript can significantly modify the substance. For instance, \(\mathrm{CO}\), which lacks the subscript '2', represents carbon monoxide, a different compound with unique properties and reactivity. As seen in the exercise, subscripts are essential for accurate representation of chemical species, highlighting their importance in understanding chemical composition and reactions.

Coefficients in Chemical Reactions

While subscripts refer to the individual molecules or ions, coefficients in chemical reactions provide a different layer of information. They indicate the quantity of the molecules or ions present. In the expression \(2 \mathrm{CO}\), '2' is the coefficient, indicating two separate molecules of carbon monoxide are involved. This concept extends beyond counting molecules; it also relates to balancing chemical equations.

By adjusting coefficients, chemists ensure both sides of the reaction have the same number of atoms for each element, upholding the law of conservation of mass. This law, which states that matter is not created or destroyed in a chemical reaction, is crucial for the proper balance of a reaction equation, just like the one presented in the exercise.

Law of Conservation of Mass

The law of conservation of mass is a cornerstone of chemistry, positing that in any chemical reaction, the mass of the reactants must equal the mass of the products. This principle guided us when checking the chemical equation provided in the exercise. Upon examination, it was discovered that while there is a balance in the number of magnesium, hydrogen, and oxygen atoms, there is a discrepancy in the number of phosphorus atoms.

Identifying that the number of phosphorus atoms on the reactants side (2) does not match the number on the products side (6) indicates that the equation is imbalanced and violates the law of conservation of mass. Such error highlights the need to adjust coefficients to preserve the mass balance in the equation. This law underpins the quantitative analysis of reactions and reinforces the importance of meticulous attention to detail when presenting chemical equations.