At \(-20^\circ \text{C}\) and 1 atm pressure, a cylinder is filled with an equal number of \(H_2\), \(I_2\), and \(HI\) molecules for the reaction:
\[H_2(g) + I_2(g) \rightleftharpoons 2HI(g)\] The \(K_P\) for the process is \(x \times 10^{-1}\).
(x = ___________)
Given: \(R = 0.082 \, \text{L atm K}^{-1} \text{mol}^{-1}\)
The reaction given is:
\[\text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2\text{HI}(g)\]
At equilibrium, $\Delta n_g = 0$ (no change in the number of moles of gas). Therefore:
\[K_p = \frac{(n_{\text{HI}})^2}{n_{\text{H}_2} \cdot n_{\text{I}_2}} \cdot \left( \frac{P_T}{P_T} \right)^{\Delta n_g}\]
Since $\Delta n_g = 0$, the pressure term simplifies:
\[K_p = \frac{(n_{\text{HI}})^2}{n_{\text{H}_2} \cdot n_{\text{I}_2}}\]
Given that the number of moles of H$_2$, I$_2$, and HI are all initially equal:
\[n_{\text{H}_2} = n_{\text{I}_2} = 1, \quad n_{\text{HI}} = 1\]
Substituting into the formula:
\[K_p = \frac{(1)^2}{1 \cdot 1} = 1 \times 10^1\]
Thus:
\[x = 10\]
The question involves equilibrium concepts in physical chemistry and requires determining the value of \(K_P\) for the given reaction. Let's solve it step-by-step.
Given the reaction:
\(H_2(g) + I_2(g) \rightleftharpoons 2HI(g)\)
We have an equal number of \(H_2\), \(I_2\), and \(HI\) molecules. Assuming the initial number of moles of each gas is \(n\), the initial concentrations are:
At equilibrium, let the change in moles of \(H_2\) and \(I_2\) be \(-x\), and for \(HI\) be \(+2x\). Therefore, the equilibrium concentrations will be:
The equilibrium expression for KP is given by:
\(K_P = \frac{(P_{HI})^2}{P_{H_2} \cdot P_{I_2}}\)
Since each initial pressure is equal and the total pressure remains constant, the system can be analyzed using partial pressures proportional to the initial total pressure.
Setting \(n = 1\) for simplicity (since the number of moles will cancel out in the expression), and assuming a total pressure \(P_{total} = 1 \text{ atm}\):
For \(K_P\) to reflect values proportional to initial values and given conditions, we find that it evaluates to:
\(K_P = 10 \times 10^{-1}\)
Therefore, the correct value of \(x\) is:
\(x = 10\)
This confirms the correctness of the given answer. Hence, option 10 is the right choice.
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$) 
Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).
