Final answer:
To determine the number of moles of sodium chloride in the solution, Raoult's Law and the concept of mole fraction are used to relate the change in vapor pressure to the amount of solute present. After performing the calculations, the solution is found to contain approximately 0.027 moles of sodium chloride.
Step-by-step explanation:
The subject of this question is determining the number of moles of sodium chloride in a solution based on the change in vapor pressure of water when a solute is added. This concept falls under the domain of Chemistry, specifically colligative properties in solutions. To find the number of moles of NaCl, we use Raoult's Law which connects the vapor pressure of the solvent in a solution to the molality of the solution. According to Raoult's Law, the vapor pressure of a solvent in a solution (Psolution) is equal to the vapor pressure of the pure solvent (Psolvent) multiplied by the mole fraction of the solvent (Xsolvent).
First, we calculate the mole fraction of water (solvent) in the solution:
XH2O = Psolution / Psolvent
XH2O = 25.7 torr / 31.8 torr
XH2O = 0.808. Now we can calculate the mole fraction of NaCl:
XNaCl = 1 - XH2O = 1 - 0.808 = 0.192
Since we know the total moles of H2O (0.115 mol), we can calculate the moles of NaCl using mole fraction:
0.192 = moles of NaCl / (moles of NaCl + 0.115 moles H2O)
After solving for moles of NaCl, we find that the number of moles of sodium chloride in the solution is approximately 0.027 moles.