Respuesta :
The question is incomplete, here is the complete question:
A solution contains 0.115 mol [tex]H_2O[/tex] and an unknown number of moles of sodium chloride. The vapor pressure of the solution at 30°C is 25.7 torr. The vapor pressure of pure water at this temperature is 31.8 torr. Calculate the number of grams of sodium chloride in the solution. (Hint: Remember that sodium chloride is a strong electrolyte.)
Answer: The mass of sodium chloride in the solution is 0.714 grams
Explanation:
The formula for relative lowering of vapor pressure will be:
[tex]\frac{p^o-p_s}{p^o}=i\times \chi_{\text{solute}}[/tex]
where,
[tex]p^o[/tex] = vapor pressure of solvent (water) = 31.8 torr
[tex]p^s[/tex] = vapor pressure of the solution = 25.7 torr
i = Van't Hoff factor = 2
[tex]\chi_{\text{solute}}[/tex] = mole fraction of solute (sodium chloride) = ?
Putting values in above equation, we get:
[tex]\frac{31.8-25.7}{31.8}=2\times \chi_{NaCl}\\\\\chi_{NaCl}=0.0959[/tex]
Mole fraction of a substance is calculated by using the equation:
[tex]\chi_A=\frac{n_A}{n_A+n_B}[/tex]
[tex]\chi_{\text{NaCl}}=\frac{n_{\text{NaCl}}}{n_{\text{NaCl}}+n_{\text{water}}}[/tex]
We are given:
Moles of water = 0.115 moles
[tex]0.0959=\frac{n_{\text{NaCl}}}{n_{\text{NaCl}}+0.115}\\\\n_{\text{NaCl}}=0.0122mol[/tex]
To calculate the mass for given number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Moles of NaCl = 0.0122 moles
Molar mass of NaCl = 58.5 g/mol
Putting values in above equation, we get:
[tex]0.0122mol=\frac{\text{Mass of NaCl}}{58.5g/mol}\\\\\text{Mass of NaCl}(0.0122mol\times 58.5g/mol)=0.714g[/tex]
Hence, the mass of sodium chloride in the solution is 0.714 grams
