To determine the initial amount of water, we can use the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. The reaction is:
\[ 2H_2O \rightarrow 2H_2 + O_2 \]
From the equation, we can see that 2 moles of water yield 2 moles of hydrogen gas and 1 mole of oxygen gas.
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Calculate the moles of H2 and O2 produced:
- Molar mass of H2 = 2 g/mol \( \Rightarrow \) Moles of H2 from 112g = \( \frac{112g}{2g/mol} = 56 \) moles
- Molar mass of O2 = 32 g/mol \( \Rightarrow \) Moles of O2 from 888g = \( \frac{888g}{32g/mol} = 27.75 \) moles
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From the balanced equation, 2 moles of H2O produce 2 moles of H2 and 1 mole of O2. This means:
- The ratio of H2 to O2 in the reaction is 2:1.
- Therefore, for every 2 moles of H2 produced, 1 mole of O2 is produced.
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The number of moles of H2 suggests twice the number of moles of O2 should be produced. Hence, for 56 moles of H2, we should have:
- \( \text{Expected moles of O2} = \frac{56}{2} = 28 \)
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We have calculated through the mass of oxygen that we obtained \( 27.75 \) moles, which is very close to what we would expect if we started with water.
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Using the overall stoichiometry:
- From 2 moles of H2O, we produce \( 2 \times 2 = 112 \) grams of H2 (which is correct)
- From the same 2 moles of H2O, we produce \( 32 \) grams of O2
To find the total mass of the water, we add:
- \( 112g \) of H2 + \( 888g \) of O2 = \( 1000g \)
Thus, the initial amount of water must have been \( 1000g \).
Therefore, the correct answer is:
Student B, because of the law of conservation of matter.
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