- Analyze Reaction 1 (\(? + 2\text{NaBr} \rightarrow 2\text{NaCl} + \text{Br}_2\)) to find it requires \(\text{Cl}_2\) to satisfy mass conservation.
- Analyze Reaction 2 (\(\text{CH}_4 + 2\text{O}_2 \rightarrow ?\)) to find it yields \(\text{CO}_2 + 2\text{H}_2\text{O}\) to satisfy mass conservation.
- The missing components are \(\text{Cl}_2\) and \(\text{CO}_2 + 2\text{H}_2\text{O}\).
- Final answer: \(\boxed{\text{Cl}_2, \text{CO}_2 + 2\text{H}_2\text{O}}\)
Explanation
- Analyzing Reaction 1
To determine the missing components in the chemical reactions, we apply the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. This means the number of atoms of each element must be equal on both sides of the reaction equation.
Reaction 1: \(? + 2\text{NaBr} \rightarrow 2\text{NaCl} + \text{Br}_2\)
Products side has:
- 2 atoms of Sodium (Na)
- 2 atoms of Chlorine (Cl)
- 2 atoms of Bromine (Br)
Reactant side currently has:
- 2 atoms of Sodium (Na)
- 2 atoms of Bromine (Br)
Comparing the two, we see the reactant side is missing 2 atoms of Chlorine (Cl). The reactant that provides two chlorine atoms is \(\text{Cl}_2\). Therefore, the balanced reaction is \(\text{Cl}_2 + 2\text{NaBr} \rightarrow 2\text{NaCl} + \text{Br}_2\).
- Analyzing Reaction 2
Reaction 2: \(\text{CH}_4 + 2\text{O}_2 \rightarrow ?\)
Reactants side has:
- 1 atom of Carbon (C)
- 4 atoms of Hydrogen (H)
- 4 atoms of Oxygen (O) (from \(2\text{O}_2\))
We evaluate the given options to find which one contains 1 Carbon atom, 4 Hydrogen atoms, and 4 Oxygen atoms:
- \(\text{CHO}\): 1C, 1H, 1O (Incorrect)
- \(\text{C}_2\text{H}_2 + \text{CO}_2\): 3C, 2H, 2O (Incorrect)
- \(\text{CO}_2 + 2\text{H}_2\text{O}\): 1C, (2+2)O = 4O, (2 \times 2)H = 4H (Correct)
- \(\text{C} + 2\text{H}_2\text{O}\): 1C, 4H, 2O (Incorrect)
The combustion of methane (\(\text{CH}_4\)) produces carbon dioxide (\(\text{CO}_2\)) and water (\(\text{H}_2\text{O}\)). Balancing the equation \(\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}\) confirms the counts are equal.
- Conclusion
Based on our analysis of both reactions using the law of conservation of mass:
- The missing component for the first reaction is \(\text{Cl}_2\).
- The missing component for the second reaction is \(\text{CO}_2 + 2\text{H}_2\text{O}\).
Thus, the completed equations are:
- \(\text{Cl}_2 + 2\text{NaBr} \rightarrow 2\text{NaCl} + \text{Br}_2\)
- \(\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}\)
The final answers are \(\boxed{\text{Cl}_2}\) and \(\boxed{\text{CO}_2 + 2\text{H}_2\text{O}}\).
Examples
The Law of Conservation of Mass is essential in fields like environmental science and industrial manufacturing. For instance, in an industrial setting, engineers must accurately predict the amount of carbon dioxide produced when burning fuels like methane to design effective carbon capture systems. By calculating the reactants and products precisely, they ensure that the chemical plants operate efficiently and safely, minimizing waste and environmental impact. Understanding these balanced equations allows professionals to track the flow of matter through any chemical process.