The % (by weight) of methanol in a mixturevof methanol and ethanol is50%.Therefore,the mole fraction of methanol in the mixture is
To find the mole fraction of methanol in the mixture, we will use the following formula:
Mole Fraction of a component = (Number of moles of that component) / (Total number of moles in the mixture)
Given that the weight percentage of methanol is 50%, we can assume we have a 100g mixture. Therefore, we have 50g of methanol in the mixture.
To find the number of moles of methanol, we need to know the molar mass of methanol. The molar mass of methanol (CH3OH) is approximately 32 g/mol (12 g/mol for carbon + 1 g/mol for each of the 3 hydrogen atoms + 16 g/mol for oxygen).
Using the formula:
Number of moles = (Mass of substance) / (Molar mass)
Number of moles of methanol = (50g) / (32 g/mol)
= 1.5625 mol
Now, to find the number of moles of ethanol in the mixture, we subtract the moles of methanol from the total moles in the mixture.
Number of moles of ethanol = Total moles - Moles of methanol
Since we have a 100g mixture and 50g of it is methanol, we have 50g of ethanol.
Number of moles of ethanol = (50g ethanol) / (46 g/mol)
= 1.087 mol
Now, to find the mole fraction of methanol:
Mole fraction of methanol = (Number of moles of methanol) / (Total number of moles in the mixture)
Total moles in the mixture = Number of moles of methanol + Number of moles of ethanol
Total moles in the mixture = 1.5625 mol + 1.087 mol
= 2.6495 mol
Mole fraction of methanol = (1.5625 mol) / (2.6495 mol)
= 0.5894
Therefore, the mole fraction of methanol in the mixture is approximately 0.5894 (or 58.94%).
To calculate the mole fraction of methanol in the mixture, we need to know the mole fractions of both methanol and ethanol.
The weight percentage gives us the ratio of the weight of methanol to the weight of the mixture. In this case, the weight percentage of methanol is 50%. This means that for every 100 units of the mixture, 50 units are methanol.
To calculate the weight of ethanol in the mixture, we can subtract the weight of methanol from the weight of the mixture. Since the weight percentage of methanol is 50%, the weight percentage of ethanol is also 50%.
Now, let's assume that the weight of the mixture is 100g. This means that the weight of methanol is 50g and the weight of ethanol is also 50g.
To calculate the mole fraction of methanol, we need to determine the number of moles of methanol and ethanol.
First, we need to know the molar mass of methanol and ethanol. The molar mass of methanol (CH3OH) is approximately 32 g/mol, and the molar mass of ethanol (C2H5OH) is approximately 46 g/mol.
To calculate the number of moles, we can divide the weight of each alcohol by its molar mass.
For methanol:
Number of moles of methanol = weight of methanol / molar mass of methanol
Number of moles of methanol = 50g / 32 g/mol
Number of moles of methanol ≈ 1.5625 mol
For ethanol:
Number of moles of ethanol = weight of ethanol / molar mass of ethanol
Number of moles of ethanol = 50g / 46 g/mol
Number of moles of ethanol ≈ 1.087 mol
Now, we can calculate the mole fraction of methanol using the formula:
Mole fraction of methanol = number of moles of methanol / (number of moles of methanol + number of moles of ethanol)
Mole fraction of methanol = 1.5625 mol / (1.5625 mol + 1.087 mol)
Mole fraction of methanol ≈ 0.589
Therefore, the mole fraction of methanol in the mixture is approximately 0.589.