To determine the mass of water that was separated into hydrogen and oxygen, we need to use the given amounts of collected gases and the stoichiometry of the reaction:
The balanced equation is: \[ 2H_2O \rightarrow 2H_2 + O_2 \]
From the equation:
- 2 moles of water (H2O) produce 2 moles of hydrogen gas (H2) and 1 mole of oxygen gas (O2).
We can convert the collected gases (hydrogen and oxygen) into grams and then use their molar masses:
The molar masses are approximately:
- Hydrogen (H2) = 2 g/mol
- Oxygen (O2) = 32 g/mol
- Water (H2O) = 18 g/mol
Now we convert the collected gases:
For hydrogen (96 g): \[ \text{Moles of } H_2 = \frac{96 , \text{g}}{2 , \text{g/mol}} = 48 , \text{moles} \]
For oxygen (404 g): \[ \text{Moles of } O_2 = \frac{404 , \text{g}}{32 , \text{g/mol}} = 12.625 , \text{moles} \]
According to the balanced equation, to produce 2 moles of H2, we need 2 moles of H2O, and to produce 1 mole of O2, we need 2 moles of H2O. This means the ratio of moles of water needed to produce the collected gases is:
- For hydrogen: 48 moles of H2 require 48 moles of H2O (since 2 moles of H2 are produced from 2 moles of H2O).
- For oxygen: 12.625 moles of O2 require 25.25 moles of H2O (since 1 mole of O2 is produced from 2 moles of H2O).
Now we take the maximum of the two moles of water calculated:
- The moles required for hydrogen (48 moles of H2O) and for oxygen (25.25 moles of H2O). Hence we can calculate the corresponding mass of water:
Using the moles of water for oxygen since it produces a smaller value (25.25 moles): \[ \text{Mass of } H_2O = 25.25 , \text{moles} \times 18 , \text{g/mol} = 454.5 , \text{g} \]
However, we need it for hydrogen: Mass calculated from hydrogen: \[ \text{Mass of } H_2O = 48 , \text{moles} \times 18 , \text{g/mol} = 864 , \text{g} \]
By mass game, it suggests that one of the statements is correct since the actual starting water after the calculation must be between reasonable expectations.
If we consider the conservation of mass and both gases collected indicate we could yield a similar check enforcement would require substantial additional measures established for accurative assessment.
In this scenario, both students have limitations in rationalizing their statements based upon gas collected.
Correct Answer:
Neither are correct. It would have been 454.5 g for calculations relative to oxygen. However, if measured from hydrogen, we see derivation flaw. Yet can assert based on total volumetric mortals metrics align none conclusively secured at 500g absolute.
Therefore the larger statement of conservation should emphasize process engineering methods over razor thin matured factual wherein each student's reasoning falters verification of measures.