The osmotic pressure (\( \pi \)) for a solution is given by the formula:
\[ \pi = \frac{nRT}{V} \] where:
\( n \) is the number of moles of solute,
\( R \) is the gas constant,
\( T \) is the temperature,
\( V \) is the volume of the solution.
For non-electrolyte (A) and glucose, the osmotic pressures are the same, so we can equate the osmotic pressures: \[ \frac{12 / M_A}{1} = 0.05 \times 1 \] where \( M_A \) is the molar mass of A, and 12 g is the mass of A. Simplifying the equation: \[ \frac{12}{M_A} = 0.05 \quad \Rightarrow \quad M_A = \frac{12}{0.05} = 240 \, \text{g/mol}. \] Thus, the molecular mass of A is 240 g/mol.
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: