Phosphorous trichloride (PCl3) is produced
from the reaction of white phosphorous (P4)
and chlorine:
P4(s) + 6Cl2(g) --> 4 PCl3(g) .
A sample of PCl3 of mass 280.7 g was collected from the reaction of 70.86 g of P4 with excess chlorine. What is the percentage yield of the
reaction?
Answer in units of %.
Answer with steps please! Thanks!
To calculate the percentage yield of the reaction, we need to compare the actual yield to the theoretical yield.
Step 1: Calculate the moles of P4 used.
We are given the mass of P4, which is 70.86 g. We can use the molar mass of P4 to convert this mass into moles.
Molar mass of P4 = 4 × atomic mass of phosphorus = 4 × 31.0 g/mol = 124.0 g/mol
moles of P4 = mass of P4 / molar mass of P4 = 70.86 g / 124.0 g/mol = 0.571 moles
Step 2: Use stoichiometry to find the theoretical yield of PCl3.
From the balanced chemical equation, we can see that the stoichiometric ratio between P4 and PCl3 is 1:4. This means that for every mole of P4, we should obtain 4 moles of PCl3.
moles of PCl3 (theoretical) = moles of P4 × (4 moles PCl3 / 1 mole P4) = 0.571 moles × 4 = 2.284 moles
Step 3: Calculate the theoretical mass of PCl3.
We can now use the molar mass of PCl3 to convert the moles of PCl3 into its mass.
Molar mass of PCl3 = (1 × atomic mass of phosphorus) + (3 × atomic mass of chlorine) = 31.0 g/mol + (3 × 35.5 g/mol) = 137.5 g/mol
mass of PCl3 (theoretical) = moles of PCl3 × molar mass of PCl3 = 2.284 moles × 137.5 g/mol = 314.485 g
Step 4: Calculate the percentage yield.
Percentage yield = (actual yield / theoretical yield) × 100
actual yield = mass of PCl3 collected = 280.7 g
percentage yield = (280.7 g / 314.485 g) × 100 = 89.34%
Therefore, the percentage yield of the reaction is 89.34%.
To calculate the percentage yield of the reaction, you need to compare the actual yield (the amount of PCl3 obtained in the experiment) with the theoretical yield (the maximum amount of PCl3 that can be obtained based on stoichiometry).
First, let's calculate the theoretical yield, which requires converting the mass of P4 used to moles and then using the stoichiometry of the balanced equation to determine the moles of PCl3 produced.
Step 1: Convert the mass of P4 used (70.86 g) to moles.
The molar mass of P4 is 123.9 g/mol.
moles of P4 = mass of P4 / molar mass of P4
moles of P4 = 70.86 g / 123.9 g/mol
moles of P4 = 0.571 mol
Step 2: Determine the moles of PCl3 produced using stoichiometry.
According to the balanced equation, 1 mole of P4 produces 4 moles of PCl3.
moles of PCl3 = moles of P4 × (4 moles of PCl3 / 1 mole of P4)
moles of PCl3 = 0.571 mol × (4 mol / 1 mol)
moles of PCl3 = 2.284 mol
Step 3: Calculate the theoretical yield (mass) of PCl3.
The molar mass of PCl3 is 137.33 g/mol.
mass of PCl3 = moles of PCl3 × molar mass of PCl3
mass of PCl3 = 2.284 mol × 137.33 g/mol
mass of PCl3 = 313.6 g
Now, we have calculated the theoretical yield, which is 313.6 g.
Step 4: Calculate the percentage yield.
The percentage yield is given by the formula:
% yield = (actual yield / theoretical yield) × 100%
% yield = (280.7 g / 313.6 g) × 100%
% yield = 89.58%
Therefore, the percentage yield of the reaction is 89.58%.