<u>Answer:</u> The total partial pressure of the solution is 131.37 torr.
<u>Explanation:</u>
The number of moles is defined as the ratio of the mass of a substance to its molar mass. The equation used is:
......(1)
Given mass of glucose = 46.8 g
Molar mass of glucose = 180 g/mol
Plugging values in equation 1:
![\text{Moles of glucose}=\frac{46.8g}{180g/mol}=0.26 mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20glucose%7D%3D%5Cfrac%7B46.8g%7D%7B180g%2Fmol%7D%3D0.26%20mol)
Given mass of methanol = 117 g
Molar mass of methanol = 32 g/mol
Plugging values in equation 1:
![\text{Moles of methanol}=\frac{117g}{32g/mol}=3.66 mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20methanol%7D%3D%5Cfrac%7B117g%7D%7B32g%2Fmol%7D%3D3.66%20mol)
Mole fraction is defined as the moles of a component present in the total moles of a solution. It is given by the equation:
.....(2)
where n is the number of moles
Putting values in equation 2:
![\chi_{methanol}=\frac{3.66}{0.26+3.66}=0.934](https://tex.z-dn.net/?f=%5Cchi_%7Bmethanol%7D%3D%5Cfrac%7B3.66%7D%7B0.26%2B3.66%7D%3D0.934)
Raoult's law is the law used to calculate the partial pressure of the individual gases present in the mixture. The equation for Raoult's law follows:
.....(3)
where
is the partial pressure of component A in the mixture and
is the total partial pressure of the mixture
We are given:
![p_{methanol}=122.7torr\\\chi_{methanol}=0.934](https://tex.z-dn.net/?f=p_%7Bmethanol%7D%3D122.7torr%5C%5C%5Cchi_%7Bmethanol%7D%3D0.934)
Putting values in equation 3, we get:
![122.7torr=0.066\times p_T\\\\p_T=\frac{122.7torr}{0.934}=131.37torr](https://tex.z-dn.net/?f=122.7torr%3D0.066%5Ctimes%20p_T%5C%5C%5C%5Cp_T%3D%5Cfrac%7B122.7torr%7D%7B0.934%7D%3D131.37torr)
Hence, the total partial pressure of the solution is 131.37 torr.