If all the H2O2 in 25mL of a 3% solution of H2O2 decomposed, calculate the
diameter of a sphere that would contain the resulting O2 at 1 atm and 296K.
I understand how to do the problem if I have moles but I am not sure how to get moles. I thought n=0.075moles because 3% solution could mean 3M so 3 moles/ L and 0.025L
I believe this is 3% w/w which means 3g H2O2/100 g solution.
mols H2O2 = 3/molar mass H2O2 in 100 g solution.
2H2O2 ==> 2H2O + O2
Thanks!!
To calculate the number of moles of H2O2 in the given solution, we can use the equation:
moles = concentration x volume
Given:
- Volume of the solution = 25 mL = 0.025 L (since 1 L = 1000 mL)
- Concentration of the solution = 3% (which means 3 g of H2O2 in 100 mL of solution, or 3 g H2O2 / 100 mL solution)
First, let's calculate the mass of H2O2 in the solution:
mass = concentration x volume = 3 g/100 mL x 25 mL = 0.75 g
Next, we need to convert the mass of H2O2 to moles. For this, we need the molar mass of H2O2, which is 34.02 g/mol (2 hydrogen atoms, each with a molar mass of 1.01 g/mol, and 2 oxygen atoms, each with a molar mass of 16.00 g/mol).
moles = mass / molar mass = 0.75 g / 34.02 g/mol ≈ 0.022 moles
Now, with the number of moles of H2O2 calculated, we can proceed to find the volume of O2 gas produced by the decomposition of H2O2 using the ideal gas law equation:
PV = nRT
Given:
- Pressure (P) = 1 atm
- Temperature (T) = 296 K
- Number of moles of O2 (n) = 0.022 moles (since 1 mole of H2O2 decomposes to produce 1 mole of O2)
R is the ideal gas constant, which is 0.0821 L·atm/(mol·K).
Rearranging the equation to solve for volume (V), we get:
V = (nRT) / P = (0.022 moles x 0.0821 L·atm/(mol·K) x 296 K) / 1 atm ≈ 0.568 L
Now, to calculate the diameter of a sphere that could contain this volume of O2, we need to use the formula for the volume of a sphere:
V = (4/3)πr^3
Where V is the volume of the sphere and r is the radius of the sphere.
Rearranging the equation to solve for the radius of the sphere (r), we get:
r = [(3V) / (4π)]^(1/3) = [(3 x 0.568 L) / (4 x π)]^(1/3) ≈ 0.4409 L^(1/3)
Finally, to find the diameter of the sphere, we multiply the radius (r) by 2:
diameter = 2 x r = 2 x 0.4409 L^(1/3) ≈ 0.8818 L^(1/3)
The diameter of the sphere that would contain the resulting O2 gas is approximately 0.8818 times the cubic root of L.