Question

Cost of sugar \[({{C}_{12}}{{H}_{22}}{{O}_{11}})\] is Rs. 40 per kg. Calculate its cost per mole.

Answer 1

Hint: In order to find the cost of sugar per mole, we must first know the molecular weight of the sugar. Later find how many moles of sugar is one kg, with that value we can find the cost of one mole of sugar.

Complete Solution :
We can easily calculate the cost of sugar per mole, if we know how to find the molecular weight of sugar\[({{C}_{12}}{{H}_{22}}{{O}_{11}})\].

- Molecular weight is also known as the molar mass. Molar mass is defined as the mass of one mole of the substance. It is expressed in the unit g/mol.
Molar mass of sugar \[({{C}_{12}}{{H}_{22}}{{O}_{11}})\]
\[=12\times 12+22\times 1+11\times 16\]
\[=144+22+176\]
\[=342g/mol\]

- Molar mass of sugar\[({{C}_{12}}{{H}_{22}}{{O}_{11}})\] is equal to \[342g/mol\].
1000g of sugar\[({{C}_{12}}{{H}_{22}}{{O}_{11}})\] contains \[=\dfrac{1000}{342}=2.92mole\]
Cost of 1kg of sugar\[({{C}_{12}}{{H}_{22}}{{O}_{11}})\] = Rs. 40
Therefore, Cost of 2.92 mole of sugar = Rs. 40
Cost of one mole of sugar\[({{C}_{12}}{{H}_{22}}{{O}_{11}})\] \[=\dfrac{40}{2.92}=13.7\]
Cost of one mole of sugar\[({{C}_{12}}{{H}_{22}}{{O}_{11}})\] is Rs. 13.7

Additional Information:
- Mole is defined as the amount of substance that contains Avogadro Number of molecules. Avogadro Number is \[6.022\times {{10}^{23}}\] and it is represented by the symbol \[{{N}_{A}}\].

Note: - The number of moles of a pure sample can be calculated using the formula
\[n=\dfrac{N}{{{N}_{A}}}\]
- One mole of a pure sample of Carbon-12 ($^{12}C$) will have a mass of exactly 12 grams of Carbon and Avogadro number \[6.022\times {{10}^{23}}\] of$^{12}C$ atoms.