To determine the cost of one mole of table sugar (C12H22O11), we need to calculate the molar mass of the sugar and then use this to find its cost per mole. Here is the step-by-step solution:
1. Calculate the Molar Mass of Table Sugar:
- The molecular formula for table sugar is C12H22O11, which consists of:
- 12 Carbon (C) atoms
- 22 Hydrogen (H) atoms
- 11 Oxygen (O) atoms
2. Determine the Atomic Masses:
- Carbon (C) has an atomic mass of approximately 12 grams per mole.
- Hydrogen (H) has an atomic mass of approximately 1 gram per mole.
- Oxygen (O) has an atomic mass of approximately 16 grams per mole.
3. Calculate the Molar Mass:
- Molar mass of C12H22O11 = (12 atoms of Carbon 12 g/mol) + (22 atoms of Hydrogen 1 g/mol) + (11 atoms of Oxygen 16 g/mol)
- Molar mass of C12H22O11 = (12 12) + (22 1) + (11 16)
- Molar mass of C12H22O11 = 144 + 22 + 176
- Molar mass of C12H22O11 = 342 grams per mole.
4. Convert the Molar Mass to Kilograms:
- Since there are 1000 grams in a kilogram, the molar mass in kilograms is:
- Molar mass of sugar in kilograms = 342 grams / 1000
- Molar mass of sugar in kilograms = 0.342 kg.
5. Given Data:
- The cost of 1 kilogram of table sugar is Rs. 70.
6. Calculate the Cost of One Mole of Sugar:
- The cost of one mole of sugar = cost per kg molar mass in kg
- The cost of one mole of sugar = Rs. 70 0.342
- The cost of one mole of sugar = Rs. 23.94
Therefore, the cost of one mole of table sugar (C12H22O11) is [tex]\(\boxed{\text{Rs. 23.94}}\)[/tex]. Thus, the correct answer is:
c. Rs. 23.94
