The reaction between M\(_2\)CO\(_3\) and HCl is: \[ \text{M}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{MCl} + \text{H}_2\text{O} + \text{CO}_2. \] From the principle of atomic conservation, 1 mole of M\(_2\)CO\(_3\) produces 1 mole of CO\(_2\). Given: \[ \text{Moles of CO}_2 = 0.01 \, \text{mol}. \] \[ \text{Moles of M}_2\text{CO}_3 = 0.01 \, \text{mol}. \] The mass of M\(_2\)CO\(_3\) is 1 g, so: \[ \text{Molar mass of M}_2\text{CO}_3 = \frac{\text{Mass}}{\text{Moles}} = \frac{1}{0.01} = 100 \, \text{g mol}^{-1}. \]
Final Answer: \( \boxed{100} \, \text{g mol}^{-1} \).
At STP \(x\) g of a metal hydrogen carbonate (MHCO$_3$) (molar mass \(84 \, {g/mol}\)) on heating gives CO$_2$, which can completely react with \(0.02 \, {moles}\) of MOH (molar mass \(40 \, {g/mol}\)) to give MHCO$_3$. The value of \(x\) is:
Let \( A = \{-3, -2, -1, 0, 1, 2, 3\} \). A relation \( R \) is defined such that \( xRy \) if \( y = \max(x, 1) \). The number of elements required to make it reflexive is \( l \), the number of elements required to make it symmetric is \( m \), and the number of elements in the relation \( R \) is \( n \). Then the value of \( l + m + n \) is equal to: