Question

Units of parts per million (ppm) or parts per billion (ppb) are often used to describe the concentrations of solutes in very dilute solutions. The units are defined as the number of grams of solute per million or per billion grams of solvent. Bay of Bengal has 1.89 ppm of lithium ions. The molality of ${\text{L}}{{\text{i}}^ + }$ in this water is (atomic number of Li=7)
A: $1.5 \times {10^{ - 4}}{\text{m}}$
B: $1.7 \times {10^{ - 4}}{\text{m}}$
C: $2.5 \times {10^{ - 4}}{\text{m}}$
D: $2.7 \times {10^{ - 4}}{\text{m}}$

Answer 1

Hint: x parts per million means = x part of a compound is present in 1 million parts of it’s solution and use of formula to find the molality.
1.89 ppm of ${\text{L}}{{\text{i}}^ + }$ ions means 1.89 gm is present in 1000000 g in solvent.
1000000 g=1000 kg;
\[\
  {\text{Number of moles of L}}{{\text{i}}^ + }{\text{ = }}\dfrac{{1.89}}{7}{\text{ = 0}}{\text{.27 moles}} \\
  {\text{Molality(m) = }}\dfrac{{{\text{Number of moles}}}}{{{\text{Mass of solvent in kg}}}}{\text{ = }}\dfrac{{0.27}}{{1000}} \\
  {\text{ = 2}}{\text{.7}} \times {\text{1}}{{\text{0}}^{ - 4}}{\text{m }} \\
\ \]

Hence,option D is the correct answer.

Additional Information:
Molality : It is defined as the ratio of number of moles of solute to the mass of solvent in kilograms.
Molarity: It is defined as the ratio of number of moles per litre of the solution.
Molarity and Molality are measures of concentration. They are intensive properties (like temperature or pressure). Hence, 1 litre of a solution and 100 gallons of a solution can have the same molarity/molality .

Note:
Students often make mistakes for taking molality and molarity.
Molarity depends upon the volume of the solution which is unlike molality which only depends upon the mass of the solvent, meanwhile molarity also depends upon temperature and pressure.