if you start with 20.0g of phosphorus 30.0g of oxygen gas, and 15.0g water, what is the maximum mass of phosphoric acid that can be formed?
To answer this question, we need to write the balanced chemical equation for the reaction between phosphorus, oxygen gas, and water to form phosphoric acid.
The balanced equation is as follows:
P4 + 5O2 + 6H2O -> 4H3PO4
From the balanced equation, we can see that 4 moles of phosphoric acid (H3PO4) are produced for every mole of phosphorus (P4) reacted.
To find the maximum mass of phosphoric acid that can be formed, we need to determine which reactant limits the amount of product that can be obtained. This can be done by comparing the moles of each reactant using their molar masses.
1. Calculate the moles of each reactant:
Moles of phosphorus (P4) = mass / molar mass
Moles of oxygen (O2) = mass / molar mass
Moles of water (H2O) = mass / molar mass
Using the molar masses:
Molar mass of P4 = 123.895 g/mol
Molar mass of O2 = 31.998 g/mol
Molar mass of H2O = 18.015 g/mol
Substituting the given values:
Moles of P4 = 20.0 g / 123.895 g/mol ≈ 0.161 mol
Moles of O2 = 30.0 g / 31.998 g/mol ≈ 0.938 mol
Moles of H2O = 15.0 g / 18.015 g/mol ≈ 0.832 mol
2. Determine the limiting reactant:
From the balanced equation, we can see that 4 moles of H3PO4 are produced for every mole of P4 reacted. This means that the moles of H3PO4 that can be formed will be limited by the moles of P4.
3. Calculate the maximum moles of H3PO4 formed:
Maximum moles of H3PO4 = moles of P4 × (4 moles of H3PO4 / 1 mole of P4)
Maximum moles of H3PO4 = 0.161 mol × 4 ≈ 0.644 mol
4. Calculate the maximum mass of H3PO4 formed:
Maximum mass of H3PO4 = maximum moles of H3PO4 × molar mass of H3PO4
Molar mass of H3PO4 = (1 x molar mass of H) + (3 x molar mass of P) + (4 x molar mass of O)
Molar mass of H3PO4 = (1 x 1.008 g/mol) + (3 x 30.973 g/mol) + (4 x 16.00 g/mol)
Molar mass of H3PO4 = 97.994 g/mol
Substituting the values:
Maximum mass of H3PO4 = 0.644 mol × 97.994 g/mol ≈ 63.14 g
Therefore, the maximum mass of phosphoric acid (H3PO4) that can be formed is approximately 63.14 grams.
To determine the maximum mass of phosphoric acid that can be formed, we need to identify the limiting reactant in the chemical reaction. The limiting reactant is the reactant that is completely consumed first and determines the maximum amount of product that can be formed.
First, let's write the balanced chemical equation for the reaction between phosphorus and oxygen gas to form phosphoric acid:
4P + 5O₂ → 2P₂O₅
Now, let's calculate the number of moles for each reactant:
Phosphorus (P):
Mass of phosphorus = 20.0g
Molar mass of phosphorus (P) = 31.0g/mol
Number of moles of phosphorus = mass / molar mass
Number of moles of phosphorus = 20.0g / 31.0g/mol
Oxygen gas (O₂):
Mass of oxygen gas = 30.0g
Molar mass of oxygen (O₂) = 32.0g/mol
Number of moles of oxygen gas = mass / molar mass
Number of moles of oxygen gas = 30.0g / 32.0g/mol
Water (H₂O):
Mass of water = 15.0g
Molar mass of water (H₂O) = 18.0g/mol
Number of moles of water = mass / molar mass
Number of moles of water = 15.0g / 18.0g/mol
Now, we will compare the moles of the reactants according to the stoichiometry of the balanced equation. The stoichiometric ratio is given by the coefficients in the balanced equation and tells us the proportion of reactants used in the reaction.
Looking at the balanced equation, we see that 4 moles of phosphorus react with 5 moles of oxygen gas to produce 2 moles of phosphoric acid. Therefore, the stoichiometric ratio of phosphorus to oxygen gas is 4:5, and the stoichiometric ratio of phosphorus to phosphoric acid is 4:2.
Let's compare the ratios of phosphorus to phosphoric acid and oxygen gas to phosphoric acid:
Phosphorus ratio:
Number of moles of phosphorus divided by its stoichiometric coefficient = (20.0g / 31.0g/mol) / 4
Oxygen gas ratio:
Number of moles of oxygen gas divided by its stoichiometric coefficient = (30.0g / 32.0g/mol) / 5
Comparing these ratios, the smaller value represents the limiting reactant. The reactant with the smaller ratio will be completely consumed, while the other reactant will be in excess.
Once we determine the limiting reactant, we can calculate the maximum mass of phosphoric acid formed by using its stoichiometric coefficient and the number of moles of the limiting reactant.
So, let's calculate the ratios:
Phosphorus ratio = (20.0g / 31.0g/mol) / 4 = 0.161 mol
Oxygen gas ratio = (30.0g / 32.0g/mol) / 5 = 0.1875 mol
Comparing the ratios, we find that the smaller ratio comes from phosphorus, so phosphorus is the limiting reactant.
To find the maximum mass of phosphoric acid that can be formed, we need to calculate the number of moles of phosphoric acid that can be produced using the stoichiometric coefficient:
Number of moles of phosphoric acid = number of moles of limiting reactant * stoichiometric coefficient (P₂O₅)
Number of moles of phosphoric acid = 0.161 mol * 2
Finally, we can calculate the maximum mass of phosphoric acid formed by multiplying the number of moles by the molar mass:
Maximum mass of phosphoric acid = number of moles of phosphoric acid * molar mass of phosphoric acid (P₂O₅)
Molar mass of phosphoric acid (P₂O₅) = 141.9g/mol
Maximum mass of phosphoric acid = (0.161 mol * 2) * 141.9g/mol
Therefore, the maximum mass of phosphoric acid that can be formed is approximately 45.9g.
This is a limiting reagent problem. There are other ways to do this but I like this method.
Basically you work three stoichiometry problems. I will assume you will use P for phosphorus (and not P4) and P2O5 for the oxide (and not P4L10) You will need to adjust the equation if yo use something other than what I use. I am rounding the atomic masses and molar masses; you should use better numbers and recalculate all.
4P + 5O2 + 6H2O ==> 4H3PO4
mols P = g/atomic mass P = 20.0/31 = 0.645
mols O2 = 30.0/32 = 0.937
mols H2O = 15.0/18 = 0.833
Now convert each of these mole amounts to mols H3PO4.
P is first.
0.645 mols P x (4 mols H3PO4/4 mols P) = 0.645 x 4/4 = 0.645 mols H3PO4.
Next is O2.
0.937 mols O2 x (4 mols H3PO4/5 mols O2) = 0.937 x 4/5 = 0.75 mols H3PO4.
Next is H2O.
0.833 mols H2O x (4 mols H3PO4/6 mols H2O) = 0.833 x 4/6 = 0.555 mols H3PO4.
In limiting reagent problems the correct for mols H3PO4 formed is the smallest value and that looks like 0.555 mol H3PO4.
Convert that number to grams. g = mols x molar mass.