Answer :
To answer the question, let's analyze the given information step-by-step:
1. Identify Compounds and Their Masses:
- [tex]\(A = 12\)[/tex] grams (mass of carbon)
- [tex]\(B = 44\)[/tex] grams (mass of carbon dioxide)
- [tex]\(C = 32\)[/tex] grams (mass of oxygen)
2. Identify What Needs to be Verified:
We are asked to support a statement that indicates the combustion of coal follows the law of conservation of mass. The law of conservation of mass states that in a chemical reaction, the total mass of the reactants equals the total mass of the products.
3. List and Analyze Each Statement:
- Statement 1: The total mass of [tex]\(A\)[/tex] and [tex]\(C\)[/tex], which are carbon dioxide and oxygen, is equal to the mass of [tex]\(B\)[/tex], which is carbon.
- This statement incorrectly describes the masses associated with [tex]\(A\)[/tex] and [tex]\(C\)[/tex]. Therefore, it cannot be correct.
- Statement 2: The total mass of [tex]\(A\)[/tex] and [tex]\(C\)[/tex], which are carbon and oxygen, is equal to the mass of [tex]\(B\)[/tex], which is carbon dioxide.
- This means comparing the sum of the masses of carbon and oxygen ([tex]\(A\)[/tex] and [tex]\(C\)[/tex]) to the mass of carbon dioxide ([tex]\(B\)[/tex]):
[tex]\[\text{Total mass of } A + C = 12 \, \text{grams} + 32 \, \text{grams} = 44 \, \text{grams}\][/tex]
[tex]\[\text{Mass of } B = 44 \, \text{grams}\][/tex]
Since these masses are equal, this statement supports the law of conservation of mass.
- Statement 3: The total mass of [tex]\(B\)[/tex] and [tex]\(C\)[/tex], which are carbon and oxygen, is greater than the mass of [tex]\(A\)[/tex], which is carbon dioxide.
- Let’s calculate:
[tex]\[\text{Total mass of } B + C = 44 \, \text{grams} + 32 \, \text{grams} = 76 \, \text{grams}\][/tex]
[tex]\[\text{Mass of } A = 12 \, \text{grams}\][/tex]
This statement does not support the law of conservation of mass as it claims a situation that is not equal.
- Statement 4: The total mass of [tex]\(A\)[/tex] and [tex]\(B\)[/tex], which are carbon and oxygen, is greater than the mass of [tex]\(C\)[/tex], which is carbon dioxide.
- Let’s calculate:
[tex]\[\text{Total mass of } A + B = 12 \, \text{grams} + 44 \, \text{grams} = 56 \, \text{grams}\][/tex]
[tex]\[\text{Mass of } C = 32 \, \text{grams}\][/tex]
This statement too does not support the law of conservation of mass as it compares unrelated quantities.
4. Conclusion:
Based on the analysis, Statement 2 correctly supports the conclusion that the combustion of coal follows the law of conservation of mass as it verifies that the total mass of carbon and oxygen used up ( [tex]\(A + C\)[/tex] ) equals the mass of carbon dioxide formed ( [tex]\(B\)[/tex] ). Thus, the correct statement is:
The total mass of [tex]\(A\)[/tex] and [tex]\(C\)[/tex], which are carbon and oxygen, is equal to the mass of [tex]\(B\)[/tex], which is carbon dioxide.
1. Identify Compounds and Their Masses:
- [tex]\(A = 12\)[/tex] grams (mass of carbon)
- [tex]\(B = 44\)[/tex] grams (mass of carbon dioxide)
- [tex]\(C = 32\)[/tex] grams (mass of oxygen)
2. Identify What Needs to be Verified:
We are asked to support a statement that indicates the combustion of coal follows the law of conservation of mass. The law of conservation of mass states that in a chemical reaction, the total mass of the reactants equals the total mass of the products.
3. List and Analyze Each Statement:
- Statement 1: The total mass of [tex]\(A\)[/tex] and [tex]\(C\)[/tex], which are carbon dioxide and oxygen, is equal to the mass of [tex]\(B\)[/tex], which is carbon.
- This statement incorrectly describes the masses associated with [tex]\(A\)[/tex] and [tex]\(C\)[/tex]. Therefore, it cannot be correct.
- Statement 2: The total mass of [tex]\(A\)[/tex] and [tex]\(C\)[/tex], which are carbon and oxygen, is equal to the mass of [tex]\(B\)[/tex], which is carbon dioxide.
- This means comparing the sum of the masses of carbon and oxygen ([tex]\(A\)[/tex] and [tex]\(C\)[/tex]) to the mass of carbon dioxide ([tex]\(B\)[/tex]):
[tex]\[\text{Total mass of } A + C = 12 \, \text{grams} + 32 \, \text{grams} = 44 \, \text{grams}\][/tex]
[tex]\[\text{Mass of } B = 44 \, \text{grams}\][/tex]
Since these masses are equal, this statement supports the law of conservation of mass.
- Statement 3: The total mass of [tex]\(B\)[/tex] and [tex]\(C\)[/tex], which are carbon and oxygen, is greater than the mass of [tex]\(A\)[/tex], which is carbon dioxide.
- Let’s calculate:
[tex]\[\text{Total mass of } B + C = 44 \, \text{grams} + 32 \, \text{grams} = 76 \, \text{grams}\][/tex]
[tex]\[\text{Mass of } A = 12 \, \text{grams}\][/tex]
This statement does not support the law of conservation of mass as it claims a situation that is not equal.
- Statement 4: The total mass of [tex]\(A\)[/tex] and [tex]\(B\)[/tex], which are carbon and oxygen, is greater than the mass of [tex]\(C\)[/tex], which is carbon dioxide.
- Let’s calculate:
[tex]\[\text{Total mass of } A + B = 12 \, \text{grams} + 44 \, \text{grams} = 56 \, \text{grams}\][/tex]
[tex]\[\text{Mass of } C = 32 \, \text{grams}\][/tex]
This statement too does not support the law of conservation of mass as it compares unrelated quantities.
4. Conclusion:
Based on the analysis, Statement 2 correctly supports the conclusion that the combustion of coal follows the law of conservation of mass as it verifies that the total mass of carbon and oxygen used up ( [tex]\(A + C\)[/tex] ) equals the mass of carbon dioxide formed ( [tex]\(B\)[/tex] ). Thus, the correct statement is:
The total mass of [tex]\(A\)[/tex] and [tex]\(C\)[/tex], which are carbon and oxygen, is equal to the mass of [tex]\(B\)[/tex], which is carbon dioxide.
