5.4 grams of a metal is able to produce 0.6 grams of `H_(2)` gas with acid action. What is the equivalent weight of that metal?

Answer

To find the equivalent weight of the metal, we can follow these steps:

### Step 1: Understand the Concept of Equivalent Weight
The equivalent weight of a substance is defined as the mass of that substance that will combine with or displace 1 mole of hydrogen atoms (or 1 mole of electrons in redox reactions).

### Step 2: Use the Relationship Between Metal and Hydrogen
From the question, we know that 5.4 grams of the metal produces 0.6 grams of hydrogen gas (H₂). We can use the concept of gram equivalents to relate the metal to hydrogen.

### Step 3: Calculate the Number of Gram Equivalents of Hydrogen
The equivalent weight of hydrogen (H₂) is 1 gram per equivalent. Therefore, the number of gram equivalents of hydrogen produced can be calculated as:
\[ \text{Number of gram equivalents of H}_2 = \frac{\text{Weight of H}_2}{\text{Equivalent weight of H}_2} = \frac{0.6 \text{ g}}{1 \text{ g/equiv}} = 0.6 \text{ equivalents} \]

### Step 4: Set Up the Equation for the Metal
Since the number of gram equivalents of the metal will be equal to the number of gram equivalents of hydrogen produced, we can write:
\[ \text{Number of gram equivalents of metal} = \text{Number of gram equivalents of H}_2 \]
\[ \frac{\text{Weight of Metal}}{\text{Equivalent weight of Metal}} = 0.6 \]

### Step 5: Substitute the Known Values
We know the weight of the metal is 5.4 grams, so we can substitute this into the equation:
\[ \frac{5.4 \text{ g}}{\text{Equivalent weight of Metal}} = 0.6 \]

### Step 6: Solve for the Equivalent Weight of the Metal
Rearranging the equation to find the equivalent weight of the metal (let's denote it as \( E_m \)):
\[ E_m = \frac{5.4 \text{ g}}{0.6} \]
Calculating this gives:
\[ E_m = 9 \text{ g/equiv} \]

### Conclusion
The equivalent weight of the metal is 9 grams per equivalent.

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