Which one is the correct equation that represents the first law of electrolysis ?

Options

A. `mZ = ct`
B. `m = cZt`
C. `mc = Zt`
D. `c = mZt`

Answer

To solve the question regarding the correct equation that represents the first law of electrolysis, we can follow these steps:

### Step 1: Understand the First Law of Electrolysis
The first law of electrolysis states that the amount of chemical change (deposition) that occurs at an electrode during electrolysis is directly proportional to the quantity of electricity that passes through the electrolyte.

### Step 2: Define the Variables
- Let \( M \) be the mass of the substance deposited.
- Let \( Z \) be the electrochemical equivalent of the substance.
- Let \( Q \) be the total charge passed through the electrolyte.
- The total charge \( Q \) can also be expressed as \( Q = I \times t \), where \( I \) is the current and \( t \) is the time for which the current flows.

### Step 3: Write the Equation
From the first law of electrolysis, we can write the relationship as:
\[ M \propto Q \]
This can be expressed mathematically as:
\[ M = Z \times Q \]

### Step 4: Substitute for Charge
Substituting \( Q \) with \( I \times t \) gives us:
\[ M = Z \times (I \times t) \]
This can be rearranged to:
\[ M = Z \times I \times t \]

### Step 5: Identify the Correct Equation
Now, looking at the options provided, we find that the equation can be represented as:
\[ M = C \times Z \times T \]
where \( C \) represents the charge, \( Z \) is the electrochemical equivalent, and \( T \) is the time.

Thus, the correct equation that represents the first law of electrolysis is:
\[ M = C \times Z \times T \]

### Conclusion
The correct answer is option B: \( M = C \times Z \times T \).

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