Introduction:
In the electrolysis of water, water molecules are broken down into hydrogen gas and oxygen gas through the process of electrolysis. This process involves the passage of an electric current through a water solution, known as an electrolyte, which contains two electrodes: an anode and a cathode. At the anode, oxygen gas is produced, while at the cathode, hydrogen gas is produced.

Explanation:
The value of mc/ma, which is the ratio of the mass of gas collected at the cathode (mc) to the mass of gas collected at the anode (ma), can be determined based on the stoichiometry of the electrolysis reaction.

1. Balanced Electrolysis Reaction:
The balanced equation for the electrolysis of water is as follows:
2H2O(l) → 2H2(g) + O2(g)

2. Molar Ratio:
From the balanced equation, we can see that for every 2 moles of water molecules that are electrolyzed, 2 moles of hydrogen gas and 1 mole of oxygen gas are produced. Therefore, the molar ratio of hydrogen gas to oxygen gas is 2:1.

3. Relationship between moles and mass:
The mass of a substance can be calculated using its molar mass. The molar mass of hydrogen gas (H2) is 2 g/mol, and the molar mass of oxygen gas (O2) is 32 g/mol.

4. Calculation of mass:
To determine the mass of hydrogen gas and oxygen gas produced, we need to know the number of moles of each gas collected at the anode and cathode.

- Let nH2 be the number of moles of hydrogen gas collected at the cathode.
- Let nO2 be the number of moles of oxygen gas collected at the anode.

The mass of hydrogen gas (mH2) collected at the cathode is given by:
mH2 = nH2 x molar mass of H2 = nH2 x 2 g/mol

The mass of oxygen gas (mO2) collected at the anode is given by:
mO2 = nO2 x molar mass of O2 = nO2 x 32 g/mol

5. Relationship between moles of gases:
Since the molar ratio of hydrogen gas to oxygen gas is 2:1, we can write the following relationship between the number of moles of hydrogen gas and oxygen gas:
nH2/nO2 = 2/1

6. Relationship between masses of gases:
Using the relationship between moles and masses, we can write the following relationship between the masses of hydrogen gas and oxygen gas:
mH2/mO2 = (nH2 x 2 g/mol)/(nO2 x 32 g/mol)

7. Ratio of masses:
Finally, substituting the values of mH2 and mO2, we can find the ratio of mc/ma:
mc/ma = (nH2 x 2 g/mol)/(nO2 x 32 g/mol)

Conclusion:
The value of mc/ma, the ratio of the mass of gas collected at the cathode to the mass of gas collected at the anode, can be determined using the stoichiometry of the electrolysis reaction. By understanding the molar ratios and relationships between moles

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