On heating 0.220 g of a metallic oxide in presence of hydrogen,0.045 g of water is formed. If the equivalent mass of the metal is E,then what is the value of E/9

Answer

To solve the problem step by step, we will follow the outlined approach:

### Step 1: Understand the Reaction
When a metallic oxide (M₂Oₙ) is heated in the presence of hydrogen, it produces metal (M) and water (H₂O). The reaction can be represented as:
\[ \text{M}_2\text{O}_n + \text{H}_2 \rightarrow 2\text{M} + n\text{H}_2\text{O} \]

### Step 2: Calculate the Number of Moles of Water Produced
We are given that 0.045 g of water is formed. The molar mass of water (H₂O) is approximately 18 g/mol. Thus, the number of moles of water produced can be calculated as:
\[ \text{Number of moles of water} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.045 \, \text{g}}{18 \, \text{g/mol}} = 0.0025 \, \text{mol} \]

### Step 3: Calculate the Number of Equivalents of Water
Since each mole of water contains one equivalent of oxygen, the number of equivalents of water produced is equal to the number of moles:
\[ \text{Number of equivalents of water} = 0.0025 \, \text{mol} \]

### Step 4: Set Up the Equation for the Metallic Oxide
Let the metallic oxide be represented as M₂Oₙ. The molar mass of the metallic oxide can be expressed as:
\[ \text{Molar mass of M}_2\text{O}_n = 2M + 16n \]
where M is the atomic mass of the metal.

### Step 5: Calculate the Number of Moles of the Metallic Oxide
The mass of the metallic oxide is given as 0.220 g. Therefore, the number of moles of the metallic oxide can be expressed as:
\[ \text{Number of moles of M}_2\text{O}_n = \frac{0.220 \, \text{g}}{2M + 16n} \]

### Step 6: Calculate the Number of Equivalents of the Metallic Oxide
The number of equivalents of the metallic oxide is given by:
\[ \text{Number of equivalents of M}_2\text{O}_n = \text{Number of moles} \times n = \frac{0.220}{2M + 16n} \times n \]

### Step 7: Set the Equivalents Equal
Since the equivalents of the metallic oxide and water are equal, we can set up the equation:
\[ \frac{0.220 \times n}{2M + 16n} = 0.0025 \]

### Step 8: Cross Multiply and Simplify
Cross-multiplying gives:
\[ 0.220n = 0.0025(2M + 16n) \]
Expanding and rearranging:
\[ 0.220n = 0.005M + 0.04n \]
\[ 0.220n - 0.04n = 0.005M \]
\[ 0.18n = 0.005M \]
\[ \frac{M}{n} = \frac{0.18n}{0.005} = 36 \]

### Step 9: Calculate the Equivalent Mass
The equivalent mass (E) of the metal is given by:
\[ E = \frac{M}{n} = 36 \]

### Step 10: Find E/9
Finally, we need to find the value of E/9:
\[ \frac{E}{9} = \frac{36}{9} = 4 \]

### Final Answer
Thus, the value of E/9 is **4**.

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