Mole Concept And Molar Masses

Step 1: Concept
One mole of any substance contains Avogadro's number ( ) of constituent particles (atoms, molecules, or ions).
Step 2: Analysis of
One molecule of consists of one Carbon (C) atom and two Oxygen (O) atoms.
Step 3: Calculation
- One mole of molecules contains Carbon atoms. - One mole of molecules contains Oxygen atoms.
Step 4: Conclusion
Thus, one mole of contains atoms of Carbon.
Final Answer: (D)

Step 1: Understanding the Concept:
Number of moles = Mass / Molar mass.

Step 2: Detailed Explanation:
Molar mass of .
Moles = .

Step 3: Final Answer:
0.140 mol

Step 1: Understanding the Concept:
The number of atoms in a given mass is found by dividing the mass by the atomic mass to get moles, then multiplying by Avogadro's number ( atoms/mol).

Step 2: Detailed Explanation:
Atomic mass of Silicon (Si) = 28 g/mol. Mass of chip = 5.68 mg = g. Number of moles of Si = mol. Number of Si atoms = moles = = atoms. This can be written as atoms = atoms, which is not equal to any of the given options.

Step 3: Final Answer:
The calculated number of atoms is , which does not match options (A), (B), or (C). Hence, the correct answer is (D) None of these.

Step 1: Understanding the Concept:
The cost per mole is found by calculating the mass of one mole of the substance (molar mass) and then determining the cost for that mass using the given rate per kg.

Step 2: Detailed Explanation:
Molar mass of sugar (C H O ) = = g/mol = 0.342 kg/mol. Cost per kg = ₹ 50. Cost per mole = = ₹ 17.1.

Step 3: Final Answer:
The cost per mole of sugar is ₹ 17.1, which corresponds to option (A).

Step 1: Understanding the Concept:
The increase in mass of the paper is due to the carbon deposited by the pencil. The number of carbon atoms is then calculated from this mass using the atomic mass of carbon and Avogadro's number.

Step 2: Detailed Explanation:
Mass of carbon atoms deposited = final mass - initial mass = 152 mg - 150 mg = 2 mg = g. Atomic mass of carbon = 12 g/mol. Number of moles of carbon = mol. Number of carbon atoms = moles = = atoms.

Step 3: Final Answer:
The number of carbon atoms is , which corresponds to option (A).

Step 1: Understanding the Concept:
Avogadro's hypothesis states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules. Therefore, the volume ratio is equivalent to the mole ratio.

Step 2: Detailed Explanation:
Let the molecular formula be C H O . The balanced combustion equation is: From the given volume data (1 vol compound : 2 vol CO : 2 vol steam): • Number of carbon atoms: (from 2 volumes of CO ). • Number of hydrogen atoms: (from 2 volumes of steam). • Number of oxygen atoms: From the products, total oxygen atoms = . Oxygen from O is 4 atoms, so the compound must provide 2 oxygen atoms. Thus . Therefore, the molecular formula is C H O .

Step 3: Final Answer:
The molecular formula is C H O , which corresponds to option (A).