the vapour pressure of a solution having 2g of solute X ( molar mass=32)in 100g of CS2(vapour pressure = 854 torr)is 848.9 torr. The molecular formula of solute is?
To determine the molecular formula of the solute, we can use the concept of Raoult's law and the given information about the solute and the solution.
Raoult's law states that the vapor pressure of a solution is directly proportional to the mole fraction of the solute in the solution. Mathematically, it can be expressed as:
Ptotal = Xsolute * Psolute
Where:
Ptotal is the total vapor pressure of the solution
Xsolute is the mole fraction of the solute
Psolute is the vapor pressure of the pure solute
In the given problem, we know that the vapor pressure of CS2 (carbon disulfide) is 854 torr, and the vapor pressure of the solution containing 2g of solute X in 100g of CS2 is 848.9 torr.
First, we need to calculate the mole fraction of the solute using the given data. To do this, we need to calculate the moles of solute and the moles of CS2.
The moles of solute X can be calculated using the formula:
Moles = Mass / Molar mass
Moles of X = 2g / 32 g/mol (using the given molar mass of 32 g/mol)
The moles of CS2 can be calculated using the formula:
Moles = Mass / Molar mass
Moles of CS2 = 100g / 76 g/mol (using the molar mass of CS2)
Next, we can calculate the mole fraction of the solute:
Mole fraction of solute X = Moles of X / (Moles of X + Moles of CS2)
Now that we have the mole fraction of the solute, we can rearrange Raoult's law to find the vapor pressure of the pure solute, Psolute:
Psolute = Ptotal / Xsolute
Using the given vapor pressure of the solution (848.9 torr) and the mole fraction of the solute, we can substitute the values into the equation to calculate Psolute.
Once we know the vapor pressure of the solute, we can use this information and the given vapor pressure of CS2 (854 torr) to determine the molecular formula of solute X.
Note: In this explanation, we assumed an ideal solution and ideal behavior of the solute and solvent.