The balanced reaction between KMnO\(_4\) and ferrous ammonium sulfate in the presence of H\(_2\)SO\(_4\) is:
\[
2 \, \text{KMnO}_4 + 10 \, \text{Fe}^{2+} + 8 \, \text{H}_2\text{SO}_4 \rightarrow 2 \, \text{Mn}^{2+} + 10 \, \text{Fe}^{3+} + 8 \, \text{H}_2\text{O} + \text{K}_2\text{SO}_4 + 2\text{H}_2\text{SO}_4.
\]
This equation shows that for every 2 molecules of KMnO\(_4\), 8 molecules of water are produced.
Thus, for 2 molecules of KMnO\(_4\), the total number of water molecules produced is:
\[
8 \, \text{water molecules}.
\]
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:
What is the kinetic energy (in \( {J/mol} \)) of one mole of an ideal gas (molar mass = \(0.01 \, {kg/mol}\)) if its rms velocity is \(4 \times 10^2 \, {m/s}\)?
Which of the following represents double stranded helix structure of DNA?
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: