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Calculate the number of grams of sodium chloride in the solution. (Hint: Remember that sodium chloride is a strong electrolyte.)

creativ13 [48]

The question is incomplete, here is the complete question:

A solution contains 0.115 mol $H_2O$ 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:

$\frac{p^o-p_s}{p^o}=i\times \chi_{\text{solute}}$

where,

$p^o$ = vapor pressure of solvent (water) = 31.8 torr

$p^s$ = vapor pressure of the solution = 25.7 torr

i = Van't Hoff factor = 2

$\chi_{\text{solute}}$ = mole fraction of solute (sodium chloride) = ?

Putting values in above equation, we get:

$\frac{31.8-25.7}{31.8}=2\times \chi_{NaCl}\\\\\chi_{NaCl}=0.0959$

Mole fraction of a substance is calculated by using the equation:

$\chi_A=\frac{n_A}{n_A+n_B}$

$\chi_{\text{NaCl}}=\frac{n_{\text{NaCl}}}{n_{\text{NaCl}}+n_{\text{water}}}$

We are given:

Moles of water = 0.115 moles

$0.0959=\frac{n_{\text{NaCl}}}{n_{\text{NaCl}}+0.115}\\\\n_{\text{NaCl}}=0.0122mol$

To calculate the mass for given number of moles, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Moles of NaCl = 0.0122 moles

Molar mass of NaCl = 58.5 g/mol

Putting values in above equation, we get:

$0.0122mol=\frac{\text{Mass of NaCl}}{58.5g/mol}\\\\\text{Mass of NaCl}(0.0122mol\times 58.5g/mol)=0.714g$

Hence, the mass of sodium chloride in the solution is 0.714 grams

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