A solution contains H2O2 in water. Complete decomposition of the H2O2 in 170 g of this solution yields 5.6 L of O2(g), measured at 0 oC and 101.325 kPa. What is the percentage by mass of H2O2 in this solution? Choose the closest answer.
A 10% B 20% C 5.0% D 3.0% E 1.0%
2H2O2 ==> 2H2O + O2
mols O2 = 5.6 x (1 mol/22.4L) = about 0.26 but that's an estimate and you should work the math and get a better answer.
Convert mols O2 to mols H2O2. That's mols O2 x 2 = mols H2O2.
grams H2O2 = mols H2O2 x molar mass H2O2 = ?
Then %H2O2 = (grams H2O2/mass sample)*100 = ?
To find the percentage by mass of H2O2 in the solution, we need to determine the mass of H2O2 and the total mass of the solution.
First, let's use the ideal gas law to calculate the number of moles of O2 gas produced.
PV = nRT
Where:
P = pressure (101.325 kPa = 1 atm)
V = volume (5.6 L)
n = number of moles (to be determined)
R = ideal gas constant (0.0821 L∙atm/mol∙K)
T = temperature in Kelvin (0 °C = 273.15 K)
Rearranging the equation to solve for n:
n = PV / RT
n = (1 atm)(5.6 L) / (0.0821 L∙atm/mol∙K)(273.15 K)
n ≈ 0.239 moles of O2
Since H2O2 decomposes into O2 with a 1:1 molar ratio, there must also be approximately 0.239 moles of H2O2 in the original solution.
Now, let's calculate the molar mass of H2O2:
H = 1 gram/mol (1 hydrogen atom)
O = 16 grams/mol (1 oxygen atom)
Molar mass of H2O2 = (2*H) + 2*O = 2(1) + 2(16) = 34 grams/mol
Now we can calculate the mass of H2O2 in the solution:
mass of H2O2 = number of moles × molar mass = 0.239 moles × 34 g/mol ≈ 8.126 g
Finally, we can calculate the percentage by mass of H2O2 in the solution:
percentage by mass = (mass of H2O2 / total mass of solution) × 100%
percentage by mass = (8.126 g / 170 g) × 100% ≈ 4.79%
The closest answer is option C, 5.0%.