Question

(a) What is the difference between adding a subscript 2 to the end of the formula for 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? \(3 \mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}(5)+6 \mathrm{H}_{2} \mathrm{O}(l)\) Why or why not?

Short answer

(a) Adding a subscript 2 to CO creates \(\mathrm{CO}_{2}\) (carbon dioxide), meaning there are two oxygen atoms in the molecule. Adding a coefficient 2 in front of CO represents two molecules of \(\mathrm{CO}\) (carbon monoxide). Subscripts change the composition of the molecule, while coefficients indicate the number of molecules. (b) The given equation, after removing the typo, is: \(3 \mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}+6 \mathrm{H}_{2} \mathrm{O}(l)\). The number of oxygen atoms on both sides is inconsistent, therefore the equation is \textbf{not} consistent with the law of conservation of mass.

Step-by-step solution

Part (a): Understanding subscripts and coefficients

A subscript is a small number written at the lower right corner of the chemical symbol, which indicates the number of atoms of that element present in a molecule. In the molecule CO, the subscript 2 added to the oxygen atom results in the molecule \(\mathrm{CO}_{2}\), which is carbon dioxide. Conversely, a coefficient is a number that appears in front of a chemical formula, which specifies the number of molecules of that substance participating in a chemical reaction. Hence, placing 2 in front of CO gives you \(2 \mathrm{CO}\), which represents two molecules of carbon monoxide instead of altering the chemical composition of it.

Part (b): Consistency with the law of conservation of mass

The law of conservation of mass states that the mass of reactants must be equal to the mass of products in a chemical reaction, which means that the number of atoms of each element should remain the same on both sides of a chemical equation. Given chemical equation: \[3 \mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{H}_{3} \mathrm{PO}_{4}(a q) \longrightarrow \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}(5)+6 \mathrm{H}_{2} \mathrm{O}(l)\] Firstly, the (5) written next to Mg3(PO4)2 is a typo and should be removed. Now, let's check the equation for consistency with the law of conservation of mass. Reactants: 1. Magnesium (Mg): 3 (present in \(\mathrm{Mg}(\mathrm{OH})_{2}\)) 2. Oxygen (O): 6 (present in \(\mathrm{Mg}(\mathrm{OH})_{2}\)) 3. Hydrogen (H): 12 (6 from \(\mathrm{Mg}(\mathrm{OH})_{2}\) and 6 from \(\mathrm{H}_{3} \mathrm{PO}_{4}\)) 4. Phosphorus (P): 2 (present in \(\mathrm{H}_{3} \mathrm{PO}_{4}\)) Products: 1. Magnesium (Mg): 3 (present in \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)) 2. Oxygen (O): 14 (8 from \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) and 6 from \(\mathrm{H}_{2} \mathrm{O}\)) 3. Hydrogen (H): 12 (present in \(\mathrm{H}_{2} \mathrm{O}\)) 4. Phosphorus (P): 2 (present in \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)) There is an inconsistency in the number of Oxygen (O) atoms, which violates the law of conservation of mass. Everything else stays consistent. Thus, as written, the given equation is \textbf{not} consistent with the law of conservation of mass.

Key concepts

Chemical Equations

Chemical equations are representations of chemical reactions. They use symbols and formulas to show the substances involved in a reaction. On the left side of a chemical equation, you find the reactants—these are the starting materials in the reaction. The right side shows the products, which are the substances produced by the reaction.
For example, let's consider the equation for the reaction between magnesium hydroxide and phosphoric acid: \[3 \mathrm{Mg}(\mathrm{OH})_{2} + 2 \mathrm{H}_{3} \mathrm{PO}_{4} \rightarrow \mathrm{Mg}_{3}(\mathrm{PO}_{4})_{2} + 6 \mathrm{H}_{2} \mathrm{O}\]
This equation tells us which substances are reacting and what they will form. It is essential to understand that a chemical equation must be balanced to reflect the real atomic interactions accurately.

Subscripts and Coefficients

Subscripts and coefficients are both integral parts of a chemical equation that convey important information about the chemical species involved.
**Subscripts** are the small numbers found slightly below and to the right of a chemical symbol. They represent the number of atoms of a given element in a molecule. In \(\mathrm{CO}_{2}\), for instance, the subscript 2 indicates there are two oxygen atoms bonded to one carbon atom.
**Coefficients**, on the other hand, are numbers placed in front of the entire chemical formula. They specify how many molecules of that substance are involved in the reaction. For example, in \(2 \mathrm{CO}\), the coefficient 2 means there are two molecules of carbon monoxide. Coefficients are crucial when balancing chemical equations to ensure that the law of conservation of mass is upheld.

Balancing Equations

Balancing chemical equations is essential for reflecting the law of conservation of mass. This scientific principle dictates that matter cannot be created or destroyed in a closed system. Thus, the number of atoms for each element must be the same on both sides of the equation.
To balance an equation, you may need to add coefficients to the reactants or products so that each element has the same number of atoms on both sides. This has to be done carefully because changing subscripts alters the substances, while coefficients adjust the amount without changing the identity.
Returning to our example, if there were initially differing numbers of oxygen atoms on either side, by carefully adjusting coefficients, you can balance the equation to align with the conservation of mass.

Chemical Reactions

A chemical reaction is a process where reactants are transformed into products through the breaking and forming of chemical bonds. Each reaction is governed by specific principles, including energy changes and reaction rates.
During a chemical reaction,

• Bonds between atoms in the reactants are broken.
• New bonds are formed to create the products.

While the atoms are rearranged, the laws of conservation mean the same types and amounts of matter exist before and after the reaction. Whether it involves synthesis, decomposition, single replacement, or double replacement, understanding the type of reaction is key to determining what the products will be.
By observing a reaction's equation, you can predict the identity and quantity of products formed, making this a foundational aspect of chemistry studies.