10 g of a metal carbonate on heating given 5.6 g of its oxide. The equivalent amount metal 5x. What is x.

Answer

To solve the problem step by step, we will use the information provided about the metal carbonate and its oxide.

### Step 1: Identify the given data
- Weight of metal carbonate (MCO₃) = 10 g
- Weight of metal oxide (MO) = 5.6 g
- Equivalent weight of metal = 5x

### Step 2: Write the formula for equivalent weight
The equivalent weight of a compound is given by the formula:
\[ \text{Equivalent weight} = \frac{\text{Molar mass}}{\text{n-factor}} \]
For the metal carbonate (MCO₃), the n-factor is 2 (since CO₃²⁻ can give 2 moles of ions). The molar mass of CO₃ is 60 g/mol.

### Step 3: Calculate the equivalent weight of the metal carbonate
The equivalent weight of the metal carbonate can be expressed as:
\[ \text{Equivalent weight of MCO₃} = \frac{M + 60}{2} \]
Where M is the molar mass of the metal.

### Step 4: Calculate the equivalent weight of the metal oxide
For the metal oxide (MO), the n-factor is 2 (since O²⁻ can give 2 moles of ions). The molar mass of O is 16 g/mol.
The equivalent weight of the metal oxide can be expressed as:
\[ \text{Equivalent weight of MO} = \frac{M + 16}{2} \]

### Step 5: Set up the equation based on the given data
Using the relationship between the weights and equivalent weights, we have:
\[ \frac{\text{Weight of MCO₃}}{\text{Equivalent weight of MCO₃}} = \frac{\text{Weight of MO}}{\text{Equivalent weight of MO}} \]
Substituting the known values:
\[ \frac{10}{\frac{M + 60}{2}} = \frac{5.6}{\frac{M + 16}{2}} \]

### Step 6: Cross-multiply to solve for M
Cross-multiplying gives:
\[ 10 \cdot \frac{M + 16}{2} = 5.6 \cdot \frac{M + 60}{2} \]
Simplifying this:
\[ 10(M + 16) = 5.6(M + 60) \]
Expanding both sides:
\[ 10M + 160 = 5.6M + 336 \]

### Step 7: Rearranging the equation
Rearranging gives:
\[ 10M - 5.6M = 336 - 160 \]
\[ 4.4M = 176 \]
\[ M = \frac{176}{4.4} = 40 \text{ g/mol} \]

### Step 8: Find the equivalent weight of the metal
The equivalent weight of the metal is given as:
\[ 5x = M = 40 \text{ g/mol} \]

### Step 9: Solve for x
\[ x = \frac{40}{5} = 8 \]

### Conclusion
The value of x is 8 g/equivalent.

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