Calculate the electrochemical equivalent of the lightest element .

Answer

To calculate the electrochemical equivalent (E) of the lightest element, which is hydrogen (H2), we can follow these steps:

### Step 1: Identify the lightest element
The lightest element is hydrogen (H), and in its molecular form, it exists as H2.

### Step 2: Determine the atomic weight of hydrogen
The atomic weight of hydrogen (H) is approximately 1 g/mol. Since H2 consists of two hydrogen atoms, the molecular weight of H2 is:
\[ \text{Molecular weight of H2} = 2 \times 1 = 2 \text{ g/mol} \]

### Step 3: Determine the number of electrons involved in the reaction
The half-reaction for the reduction of hydrogen ions (H⁺) to hydrogen gas (H2) is:
\[ 2 \text{H}^+ + 2 \text{e}^- \rightarrow \text{H2} \]
From this reaction, we can see that 2 moles of electrons (n = 2) are involved in the formation of 1 mole of H2.

### Step 4: Calculate the electrochemical equivalent (E)
The electrochemical equivalent (E) is calculated using the formula:
\[ E = \frac{\text{Atomic weight}}{n} \]
Substituting the values we have:
\[ E = \frac{2 \text{ g/mol}}{2} = 1 \text{ g/equiv} \]

### Step 5: Calculate the electrochemical equivalent in terms of grams per coulomb
The electrochemical equivalent (W) can also be calculated using the formula:
\[ W = \frac{E \times Q}{96500} \]
Where Q is the charge in coulombs. For 1 coulomb of charge:
\[ W = \frac{1 \text{ g/equiv} \times 1 \text{ C}}{96500} = \frac{1}{96500} \text{ g/C} \]

### Step 6: Calculate the value of W
Calculating the value:
\[ W = \frac{1}{96500} \approx 1.036 \times 10^{-5} \text{ g/C} \]

### Final Answer
Thus, the electrochemical equivalent of hydrogen (H2) is approximately:
\[ W \approx 1.036 \times 10^{-5} \text{ g/C} \]

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