Express the relationship between molarity and strength in ${\text{g/L}}$.

Hint: To solve this we must know that the molarity is used to express the concentration of the solution. The molarity of a solution is equal to the number of moles of solute divided by the litres of a solution.while dealing with such questions,we must take care of the units and unit conversion formulas.

Formulae used: ${\text{Molarity}}\left( {\text{M}} \right) = \dfrac{{{\text{Number of moles of solute}}\left( {{\text{mol}}} \right)}}{{{\text{Volume of solution}}\left( {\text{L}} \right)}}$

${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass of solute}}\left( {\text{g}} \right)}}{{{\text{Molecular mass}}\left( {{\text{g/mol}}} \right)}}$

Complete step by step solution:
We know that the molarity of a solution is equal to the number of moles of solute divided by the litres of a solution.
The formula to calculate the molarity of the solution is as follows:
${\text{Molarity}}\left( {\text{M}} \right) = \dfrac{{{\text{Number of moles of solute}}\left( {{\text{mol}}} \right)}}{{{\text{Volume of solution}}\left( {\text{L}} \right)}}$ …… (1)
We know that the number of moles of any substance is the ratio of mass of the solute in grams to its molecular mass.
The formula to calculate the number of moles is as follows:
${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass of solute}}\left( {\text{g}} \right)}}{{{\text{Molecular mass}}\left( {{\text{g/mol}}} \right)}}$ …… (2)
From equation (1) and equation (2), the equation for molarity is as follows:
${\text{Molarity}}\left( {\text{M}} \right) = \dfrac{{\dfrac{{{\text{Mass of solute}}\left( {\text{g}} \right)}}{{{\text{Molecular mass}}\left( {{\text{g/mol}}} \right)}}}}{{{\text{Volume of solution}}\left( {\text{L}} \right)}}$ …… (3)
The strength of a solution is the amount of solute present in one litre of the solution.
The formula to calculate the strength of the solution is as follows:
${\text{Strength}}\left( {{\text{g/L}}} \right) = \dfrac{{{\text{Mass of solute}}\left( {\text{g}} \right)}}{{{\text{Volume of solution}}\left( {\text{L}} \right)}}$ …… (4)
From equation (3) and equation (4), the equation for strength of a solution is as follows:
${\text{Strength}}\left( {{\text{g/L}}} \right) = {\text{Molarity}} \times {\text{Molecular mass}}$

Thus, the strength of a solution is the product of the molarity of the solution and its molecular mass.

Note: For example, consider $1{\text{ M}}$ solution of glucose. The strength of glucose solution can be calculated using the formula as follows:
${\text{Strength}}\left( {{\text{g/L}}} \right) = {\text{Molarity}} \times {\text{Molecular mass}}$
Substitute $1{\text{ M}}$ for the molarity of the glucose solution, $180{\text{ g/mol}}$ for the molecular mass of glucose and solve for the strength of the solution. Thus,
${\text{Strength}}\left( {{\text{g/L}}} \right) = 1{\text{ M}} \times 180{\text{ g/mol}} = 180{\text{ g/L}}$
Thus, the strength of $1{\text{ M}}$ glucose solution is $180{\text{ g/L}}$.