The question is incomplete, here is the complete question:
A solution contains 0.115 mol
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.)
<u>Answer:</u> The mass of sodium chloride in the solution is 0.714 grams
<u>Explanation:</u>
The formula for relative lowering of vapor pressure will be:
![\frac{p^o-p_s}{p^o}=i\times \chi_{\text{solute}}](https://tex.z-dn.net/?f=%5Cfrac%7Bp%5Eo-p_s%7D%7Bp%5Eo%7D%3Di%5Ctimes%20%5Cchi_%7B%5Ctext%7Bsolute%7D%7D)
where,
= vapor pressure of solvent (water) = 31.8 torr
= vapor pressure of the solution = 25.7 torr
i = Van't Hoff factor = 2
= mole fraction of solute (sodium chloride) = ?
Putting values in above equation, we get:
![\frac{31.8-25.7}{31.8}=2\times \chi_{NaCl}\\\\\chi_{NaCl}=0.0959](https://tex.z-dn.net/?f=%5Cfrac%7B31.8-25.7%7D%7B31.8%7D%3D2%5Ctimes%20%5Cchi_%7BNaCl%7D%5C%5C%5C%5C%5Cchi_%7BNaCl%7D%3D0.0959)
Mole fraction of a substance is calculated by using the equation:
![\chi_A=\frac{n_A}{n_A+n_B}](https://tex.z-dn.net/?f=%5Cchi_A%3D%5Cfrac%7Bn_A%7D%7Bn_A%2Bn_B%7D)
![\chi_{\text{NaCl}}=\frac{n_{\text{NaCl}}}{n_{\text{NaCl}}+n_{\text{water}}}](https://tex.z-dn.net/?f=%5Cchi_%7B%5Ctext%7BNaCl%7D%7D%3D%5Cfrac%7Bn_%7B%5Ctext%7BNaCl%7D%7D%7D%7Bn_%7B%5Ctext%7BNaCl%7D%7D%2Bn_%7B%5Ctext%7Bwater%7D%7D%7D)
We are given:
Moles of water = 0.115 moles
![0.0959=\frac{n_{\text{NaCl}}}{n_{\text{NaCl}}+0.115}\\\\n_{\text{NaCl}}=0.0122mol](https://tex.z-dn.net/?f=0.0959%3D%5Cfrac%7Bn_%7B%5Ctext%7BNaCl%7D%7D%7D%7Bn_%7B%5Ctext%7BNaCl%7D%7D%2B0.115%7D%5C%5C%5C%5Cn_%7B%5Ctext%7BNaCl%7D%7D%3D0.0122mol)
To calculate the mass for given number of moles, we use the equation:
![\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20moles%7D%3D%5Cfrac%7B%5Ctext%7BGiven%20mass%7D%7D%7B%5Ctext%7BMolar%20mass%7D%7D)
Moles of NaCl = 0.0122 moles
Molar mass of NaCl = 58.5 g/mol
Putting values in above equation, we get:
![0.0122mol=\frac{\text{Mass of NaCl}}{58.5g/mol}\\\\\text{Mass of NaCl}(0.0122mol\times 58.5g/mol)=0.714g](https://tex.z-dn.net/?f=0.0122mol%3D%5Cfrac%7B%5Ctext%7BMass%20of%20NaCl%7D%7D%7B58.5g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20NaCl%7D%280.0122mol%5Ctimes%2058.5g%2Fmol%29%3D0.714g)
Hence, the mass of sodium chloride in the solution is 0.714 grams