A boy drinks \(500\) mL of \(9\%\) glucose solution. The number of glucose molecules he has consumed are [mol. wt. of glucose = \(180\)].

\(1.5 × 10^{23}\)

The correct answer is option 3. \(1.5 × 10^{23}\).

The concentration of the solution in terms of molality, molarity and normality as we already know, determine the amount of solute present in the solution. Similarly, we also have the percentage concentration used to express it.

The percentage concentration of the glucose solution is given to be \(9\), that is, the weight by volume percentage concentration of the solution. So, we have \(9\) grams of glucose in \(100\) ml of solution.

Then, the mass of glucose in \(500\) ml of solution will be \(= \frac{9}{100} ×500 = 45\, \g\)

The molecular mass of a glucose molecule, \(C_6H_{12}O_6 = (6 × 12 + 12 × 1 + 6 × 16) = 180\, \ g/mol\)

Now, we can find the moles of glucose consumed \(= \frac{\text{mass dissolved}}{\text{molecular mass}} = \frac{45}{180} = 0.25\, \ moles\)

As the number of molecules in one mole \(= 6.022 × 10^{23}\, \ \text{molecules/mole\)

Then, the number of molecules present in \(0.25\, \ moles\) \(= 0.25 × 6.022 × 10^{23} = 1.5 × 10^{23}\)

molecules

Therefore, the number of glucose molecules the boy has consumed in 500ml of glucose solution is option (3) \(1.5 × 10^{23}\) molecules in \(0.25\, \ moles\).

So, the correct answer is “Option 3”.