Question

Cost of sugar $({{C}_{12}}{{H}_{22}}{{O}_{11}})$ is Rs.50 per kg. Calculate its cost per mol.
A) Rs.17.1 per mol
B) Rs.27.1 per mol
C) Rs.14.1per mol
D) None of the above

Answer 1

Hint: The answer to this question includes the basic concept of chemistry that involves calculation of molar mass of sugar using its molecular formula and the dividing this value with the given weight of sugar.

Complete step by step answer:
In the lower classes of physical chemistry part, we have studied the calculation of molar mass, normality, molarity etc., of the given compounds.
Now, let us see what is meant by the molar mass of the compound and its calculation.
- Molar mass of a compound is the mass of one mole of a substance.
It can be calculated as shown below for the sugar having the formula $({{C}_{12}}{{H}_{22}}{{O}_{11}})$
Molar mass = (Number of carbon atoms $\times $ its mass) + (Number of hydrogen atoms $\times $ Its mass) + (number of oxygen atoms $\times $Its mass)
Therefore, the values can be substituted as,
Molar mass of sugar = (12$\times $12) + (22$\times $1) + (11$\times $16)

Simplifying this values we get,
Molar mass = 144 + 22 + 176
Molar mass of sugar = 342 g

Now, we have the data given as, 1 kg = 1000 g of sugar costs Rs.50 and we have to calculate the cost of sugar for 342 g
Therefore, by the cross multiplication formula of mathematics we have’
Cost of 342 g of sugar = $\dfrac{50}{1000}\times 342$
Therefore cost of 342 g of sugar = Rs. 17.1
So, the correct answer is “Option A”.

Note: Do not get confused about molar mass and molecular mass of compounds are the same. These two are different quantities where molar mass is the mass of 1 mole of a substance and molecular mass is the mass of a single molecule.