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The mole fraction of methanol in the mixture is 0.444
We'll begin by calculating the number of mole of water.
- Molar mass of water = 18 g/mol
Mole = mass / molar mass
Mole of water = 45 / 18
Mole of water = 2.5 moles
Finally, we shall determine the mole fraction of methanol.
- Mole of water = 2.5 moles
- Mole of methanol = 2 moles
- Total mole = 2 + 2.5 = 4.5 moles
Mole fraction of methanol =?
Mole fraction = mole / total mole
Mole fraction of methanol = 2 / 4.5
Mole fraction of methanol = 0.444
Thus, the mole fraction of methanol is 0.444
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Answer: Heat of the solution = mass water × specific heat water × change in temperature
mass water = 260ml (1.00g/ml ) = 260g
specific heat of water = c(water) = 4.184J/ g°C
Heat change of water = final temperature - initial temperature
= 26.5 - 21.2
= 5.3 °C
H = 260 g ( 4.184J/g°C ) (5.3°C) = 5765J
Molar heat = 
= 16473J/mol
Explanation: finding molar heat requires first to look at specific heat of water and the change of water temperature
C₀=2 mol/l
c₁=0.400 mol/l
v₁=100.0 ml = 0.1 l
c₁v₁=c₀v₀
v₀=c₁v₁/c₀
v(H₂O)=v₁-v₀
v₀=0.1*0.400/2=0.02 l = 20 ml
v(H₂O)=100 - 20 = 80 ml
It is necessary to mix 20 ml of the feed solution and 80 ml of water.