JEE Chemistry 2023 Question with Solution

Given: Molarity of $CH_2Cl_2$ is $2.6 \times 10^{-3} \, M$, volume is $671.141 \, \text{mL} = 0.671141 \, \text{L}$, and density of $CHCl_3$ is $1.49 \, \text{g cm}^{-3}$.

Find: Concentration of $CH_2Cl_2$ in ppm by mass.

First, calculate the molar mass of $CH_2Cl_2$:

$$\text{Molar mass of } CH_2Cl_2 = 12 + 2(1) + 2(35.5) = 85 \, \text{g mol}^{-1}$$

Using molarity,

$$M = \frac{\text{moles of solute}}{\text{volume of solution in L}}$$

So, moles of $CH_2Cl_2$ are

$$\text{moles} = 2.6 \times 10^{-3} \times 0.671141 = 1.745 \times 10^{-3} \, \text{mol}$$

Hence, mass of $CH_2Cl_2$ is

$$\text{mass} = 1.745 \times 10^{-3} \times 85 = 0.148 \, \text{g}$$

Mass of $CHCl_3$ is

$$\text{mass of solvent} = 1.49 \times 671.141 = 1000.0 \, \text{g}$$

Therefore, ppm by mass is calculated as

$$\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solvent}} \times 10^6 = \frac{0.148}{1000.0} \times 10^6 = 148$$

So the concentration is $148$ ppm.

The solution shows 221 ppm, but that arithmetic is inconsistent with its own preceding values. The defensible final answer is $148$.

Given: The extracted working gives mass of solute as $0.148 \, \text{g}$ and mass of solvent as $1000.0 \, \text{g}$.

Find: The correct ppm value from these numbers.

For dilute solutions, ppm by mass is

$$\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6$$

Using total mass of solution,

$$\text{mass of solution} = 1000.0 + 0.148 = 1000.148 \, \text{g}$$

Therefore,

$$\text{ppm} = \frac{0.148}{1000.148} \times 10^6 \approx 147.98$$

which rounds to

$$148$$

Thus, the value 221 ppm stated in the solution is not supported by the calculation. The correct numerical answer is $148$.