Consider the following equilibrium, $$ \text{CO(g)} + \text{H}_2\text{(g)} \rightleftharpoons \text{CH}_3\text{OH(g)} $$ 0.1 mol of CO along with a catalyst is present in a 2 dm$^3$ flask maintained at 500 K. Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of CH$_3$OH is formed. The $ K_p $ is ...... x $ 10^7 $ (nearest integer).
Given: $ R = 0.08 \, \text{dm}^3 \, \text{bar} \, \text{K}^{-1} \, \text{mol}^{-1} $
Assume only methanol is formed as the product and the system follows ideal gas behavior.
The pH of a 0.01 M weak acid $\mathrm{HX}\left(\mathrm{K}_{\mathrm{a}}=4 \times 10^{-10}\right)$ is found to be 5 . Now the acid solution is diluted with excess of water so that the pH of the solution changes to 6 . The new concentration of the diluted weak acid is given as $\mathrm{x} \times 10^{-4} \mathrm{M}$. The value of x is _______ (nearest integer).
A body of mass $m$ is suspended by two strings making angles $\theta_{1}$ and $\theta_{2}$ with the horizontal ceiling with tensions $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ simultaneously. $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ are related by $\mathrm{T}_{1}=\sqrt{3} \mathrm{~T}_{2}$. the angles $\theta_{1}$ and $\theta_{2}$ are
A block of certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are 0.4 and 0.25 respectively. A constant horizontal force \( F = 20 \, \text{N} \) acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take \( g = 10 \, \text{m/s}^2 \)):
A wooden block of mass M lies on a rough floor. Another wooden block of the same mass is hanging from the point O through strings as shown in the figure. To achieve equilibrium, the coefficient of static friction between the block on the floor and the floor itself is
The circuit shown in the figure contains two ideal diodes \( D_1 \) and \( D_2 \). If a cell of emf 3V and negligible internal resistance is connected as shown, then the current through \( 70 \, \Omega \) resistance (in amperes) is: