Consider the following reaction:
2 B5H9 + 12 O2 => 5 B2O3 + 9 H2O
How many grams of O2 are needed to make 432.7 g of H2O?
mols H2O = grams/molar mass = ?
Use the coefficients to convert mols H2O to mols O2.
Now convert mols O2 to grams O2. g O2 = mols O2 x molar mass O2
To determine the number of grams of O2 needed to produce 432.7 g of H2O, we need to calculate the stoichiometric ratio between O2 and H2O using the balanced equation.
The balanced equation is:
2 B5H9 + 12 O2 => 5 B2O3 + 9 H2O
From the equation, we can see that for every 12 moles of O2, we produce 9 moles of H2O. We will use this ratio to find the number of moles of O2 needed.
First, we need to convert the given mass of H2O to moles:
Molar mass of H2O = 2 * atomic mass of H + atomic mass of O
= 2 * 1.00784 g/mol + 15.999 g/mol
= 2.01568 g/mol + 15.999 g/mol
= 18.014 g/mol
Now, let's calculate the number of moles of H2O:
moles of H2O = mass of H2O / molar mass of H2O
= 432.7 g / 18.014 g/mol
≈ 24.026 mol
Based on the stoichiometry of the balanced equation, we know that 9 moles of H2O require 12 moles of O2. Therefore, let's set up a ratio:
12 mol O2 / 9 mol H2O = x mol O2 / 24.026 mol H2O
To find the value of x, we can solve the proportion:
(12/9) = (x/24.026)
Multiply both sides by 24.026:
x = (12/9) * 24.026
x ≈ 32.035 mol
Now, for the final step, let's calculate the mass of O2 needed:
mass of O2 = moles of O2 * molar mass of O2
= 32.035 mol * (32 g/mol)
≈ 1025.12 g
Therefore, approximately 1025.12 grams of O2 are needed to produce 432.7 grams of H2O.
To determine the number of grams of O2 needed to produce 432.7 g of H2O, we need to use stoichiometry. Stoichiometry allows us to relate the amounts of reactants and products in a chemical equation.
First, we need to determine the molar mass of H2O. The molar mass of H2O is the sum of the molar masses of hydrogen (H) and oxygen (O). The molar mass of H is approximately 1 g/mol, and the molar mass of O is approximately 16 g/mol. Therefore, the molar mass of H2O is 18 g/mol.
Next, we need to set up a ratio using the balanced chemical equation. From the equation, we know that 2 moles of B5H9 react with 12 moles of O2 to produce 9 moles of H2O. Therefore, the ratio of O2 to H2O is 12:9.
To calculate the amount of O2 needed to produce 432.7 g of H2O, we can follow these steps:
1. Convert the given mass of H2O to moles by dividing by the molar mass of H2O:
Moles of H2O = 432.7 g / 18 g/mol = 24.04 mol
2. Set up a ratio using the mole ratio from the balanced chemical equation:
Moles of O2 / Moles of H2O = 12 / 9
3. Solve for the moles of O2:
Moles of O2 = (24.04 mol H2O) * (12 mol O2 / 9 mol H2O) ≈ 32.05 mol O2
4. Finally, convert the moles of O2 to grams by multiplying by the molar mass of O2:
Grams of O2 = (32.05 mol O2) * (32 g/mol O2) ≈ 1026.4 g O2
Therefore, approximately 1026.4 grams of O2 are needed to produce 432.7 grams of H2O.