Question

The sodium salt of methyl orange has 7% sodium. What is the minimum molecular weight of the compound?

Answer 1

The basic knowledge of mole concept to be used here. Conversion from moles to weight of the methyl orange compound is required.
- One mole of sodium weighs $23g$.
- Minimum assumption to be taken of one mole of sodium present in one mole of the given compound to find the molecular weight of the compound.

Complete Solution :
So, following the points mentioned in the hint. let us assume the minimum molecular weight of the compound to be $M$.
And according to the question, $7$ % of this molecular weight is sodium.
So, weight of sodium on the compound=$\dfrac{7}{100}\times M$
$\Rightarrow 0.07M$

- As we know the molecular weight of a substance constitutes one mole of that substance.
And according to this $M$ mass is one mole of methyl orange compound.
So, for minimum condition, at least one mole of sodium must be present in one mole of compound
Weight of one mole sodium = $23g$

$\Rightarrow 0.07M = 23$
$M = \dfrac{23}{0.07}$
$\Rightarrow M = 329g/mol$.
This must be the minimum weight of the compound to satisfy the condition given in question.

Note: The assumption of number of moles of sodium in accordance with mole of given compound is a point where one needs to be careful.
- The number of moles in a given sample of an element/compound can be calculated by dividing the total mass of the sample by the molar mass of the element/compound.
- One mole of a substance contains a constant number of particles which is termed as Avogadro’s constant.