Solution:
To calculate the percentage by mass of a solution, we need to divide the mass of the solute (what is being dissolved) by the mass of the solution (sum of the masses of the solute and the solvent) and multiply by 100%.
In this case, the solute is 27.0 grams of HCl and the solvent is 102.0 grams of water. So the mass of the solution is:
mass of the solution = mass of the solute + mass of the solvent
mass of the solution = 27.0 g + 102.0 g
mass of the solution = 129.0 g
Now we can calculate the percentage by mass of the solution as:
percentage by mass = (mass of the solute / mass of the solution) x 100%
Substituting the values we have found, we get:
percentage by mass = (27.0 g / 129.0 g) x 100%
percentage by mass = 20.93%
Therefore, the percentage by mass of the solution formed by dissolving 27.0 grams of HCl in 102.0 grams of water is approximately 20.93%. So the closest answer to this value is 20.9%, which is the second option.