Calculate the molarity of a solution having density = 1.5 g/mL %(w/w) of solute is 36% and molecular weight of solute is 36 g/mol.

The correct answer is 15.

To find the molarity of the solution, let us break down the problem step-by-step using standard chemical formulas.

Step 1: Understand the given parameters
Density of the solution ($d$) = 1.5 g/mL
Mass percentage (% w/w) of solute = 36%
Molar mass (molecular weight) of solute ($M{W}_{\text{solute}}$) = 36 g/mol

Step 2: Assume a standard mass of the solution
Let the mass of the solution be 100 g.

Based on the percentage by mass (36% w/w):
Mass of solute = 36 g

Step 3: Calculate the moles of solute
The number of moles of solute ($n$) is calculated as:

$n=\frac{\text{Mass of solute}}{\text{Molar mass of solute}}$

$n=\frac{36\text{g}}{36\text{g/mol}}=1\text{mol}$

Step 4: Calculate the volume of the solution
Using the density formula, $\text{Density}=\frac{\text{Mass}}{\text{Volume}}$, we can find the volume of 100 g of solution:

$\text{Volume of solution (in mL)}=\frac{\text{Mass of solution}}{\text{Density of solution}}$

$\text{Volume}=\frac{100\text{g}}{1.5\text{g/mL}}=\frac{100}{1.5}\text{mL}$

To convert this volume into Liters (L):

$\text{Volume of solution (in L)}=\frac{100}{1.5\times 1000}\text{L}=\frac{1}{15}\text{L}$

Step 5: Calculate Molarity
Molarity ($M$) is defined as the total moles of solute per liter of solution:

$M=\frac{\text{Moles of solute}}{\text{Volume of solution (in L)}}$

$M=\frac{1}{1/15}=15\text{M}$

Alternatively, using the direct relationship formula for molarity from mass percent and density:

$M=\frac{\%(w/w)\times \text{Density}\times 10}{M{W}_{\text{solute}}}$

$M=\frac{36\times 1.5\times 10}{36}=15\text{M}$

Thus, the molarity of the solution is 15 M.