Molecular formula of white phosphorus in benzene is (P)x. What is the ...
w1/ m1 = moles of solute, w2 = mass of solvent
If molecular formula = (P)x
∴ Molar mass = 31x = 123.42
x = 4
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Molecular formula of white phosphorus in benzene is (P)x. What is the ...
Molecular formula of white phosphorus in benzene is (P)x. What is the value of x based on the following experiment?
Freezing point of benzene = 5.45°C
Kf (benzene) = 5.12 K mol⁻¹ kg
Freezing point of solution containing 0.675 g of white phosphorus in 50.0 g of benzene = 4.89°C
To determine the molecular formula of white phosphorus in benzene, we can use the concept of freezing point depression.
Freezing point depression is a colligative property of solutions, which means it depends on the number of solute particles, not their identity. It can be calculated using the formula:
ΔTf = Kf * m
Where:
ΔTf is the change in freezing point
Kf is the cryoscopic constant for the solvent
m is the molality of the solution
In this case, the freezing point of the pure benzene is 5.45°C, while the freezing point of the solution containing white phosphorus is 4.89°C. The change in freezing point (ΔTf) can be calculated as:
ΔTf = 5.45°C - 4.89°C = 0.56°C
The molality (m) of the solution can be calculated as:
m = moles of solute / mass of solvent in kg
To find the moles of solute, we need to know the molar mass of white phosphorus. The molar mass of white phosphorus is 124 g/mol.
moles of solute = mass of solute / molar mass of solute
= 0.675 g / 124 g/mol
≈ 0.00544 mol
mass of solvent in kg = 50.0 g / 1000 g/kg
= 0.050 kg
m = 0.00544 mol / 0.050 kg
= 0.1088 mol/kg
Now, we can substitute the values of Kf and m into the freezing point depression equation to solve for ΔTf:
0.56°C = 5.12 K mol⁻¹ kg * 0.1088 mol/kg
Simplifying the equation, we get:
0.56°C = 0.55616 K
Therefore, x = 4.
Hence, the value of x in the molecular formula (P)x is 4.