\(2\) \(mol\) of \(Hg(g)\) is combusted in a fixed volume bomb calorimeter with excess of \(O_2\) at 298K and 1 atm into \(HgO(s)\) During the reaction, temperature increases from \(2980\) \(K\) to \(3128\) \(K\). If heat capacity of the bomb calorimeter and enthalpy of formation of \(Hg(g)\) are \(2000\) \(kJ \;K^{-1}\) and \(6132\) \(kJ \;mol^{-1}\) at \(298\) \(K\), respectively, the calculated standard molar enthalpy of formation of \(HgO(s)\) at \(298\) \(K\) is \(X\) \(kJ \;mol^{-1}\) The value of | \(X\) | is [Given : Gas constant \(R\) =\(83\) \(J\) \(K^{-1}\) \(mol^{-1}\)]
Correct Answer: 90.39
Solution and Explanation
The value of \(|X|\) is \(\underline{90.39}\).
Explanation:
Evaluating the given values we get,
\(\triangle H^{\degree}_{combustion}\) = \(\triangle H^{\degree}_{f}(HgO)-\triangle H^{\degree}_{Hg(l)}+\frac{1}{2} \triangle H^{\degree}_{f}O_2\)
\(\triangle H^{\degree}_{f}(HgO) = -151.710+61.32\)
\(\triangle H^{\degree}_{f}=90.39\)
Top Questions on Thermodynamics
- An ideal gas goes from an initial state to final state. During the process, the pressure of the gas increases linearly with temperature.
A. The work done by gas during the process is zero.
B. The heat added to the gas is different from the change in its internal energy.
C. The volume of the gas is increased.
D. The internal energy of the gas is increased.
E. The process is isochoric (constant volume process).
Choose the correct answer from the options given below:- JEE Main - 2025
- Physics
- Thermodynamics
- For a diatomic gas, if \( \gamma_1 = \frac{C_P}{C_V} \) for rigid molecules and \( \gamma_2 = \frac{C_P}{C_V} \) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (where \( C_P \) and \( C_V \) are specific heats of the gas at constant pressure and volume)
- JEE Main - 2025
- Physics
- Thermodynamics
- Given are statements for certain thermodynamic variables: \begin{itemize} \item[(A)] Internal energy, volume \( V \), and mass \( M \) are extensive variables. \item[(B)] Pressure \( P \), temperature \( T \), and density \( \rho \) are intensive variables. \item[(C)] Volume \( V \), temperature \( T \), and density \( \rho \) are intensive variables. \item[(D)] Mass \( M \), temperature \( T \), and internal energy are extensive variables. \end{itemize} Choose the correct answer from the options given below:
- JEE Main - 2025
- Physics
- Thermodynamics
- A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of the gas should be raised to °C.
- JEE Main - 2025
- Physics
- Thermodynamics
- The work done in an adiabatic change in an ideal gas depends upon:
- JEE Main - 2025
- Physics
- Thermodynamics
Questions Asked in JEE Advanced exam
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity):
- JEE Advanced - 2025
- Waves and Oscillations
- Consider the vectors $$ \vec{x} = \hat{i} + 2\hat{j} + 3\hat{k},\quad \vec{y} = 2\hat{i} + 3\hat{j} + \hat{k},\quad \vec{z} = 3\hat{i} + \hat{j} + 2\hat{k}. $$ For two distinct positive real numbers $ \alpha $ and $ \beta $, define $$ \vec{X} = \alpha \vec{x} + \beta \vec{y} - \vec{z},\quad \vec{Y} = \alpha \vec{y} + \beta \vec{z} - \vec{x},\quad \vec{Z} = \alpha \vec{z} + \beta \vec{x} - \vec{y}. $$ If the vectors $ \vec{X}, \vec{Y}, \vec{Z} $ lie in a plane, then the value of $ \alpha + \beta - 3 $ is ________.
- If $$ \alpha = \int_{\frac{1}{2}}^{2} \frac{\tan^{-1} x}{2x^2 - 3x + 2} \, dx, $$ then the value of $ \sqrt{7} \tan \left( \frac{2\alpha \sqrt{7}}{\pi} \right) $ is.
(Here, the inverse trigonometric function $ \tan^{-1} x $ assumes values in $ \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) $.)- JEE Advanced - 2025
- Integral Calculus
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
- JEE Advanced - 2025
- binomial expansion formula
- The total number of real solutions of the equation $$ \theta = \tan^{-1}(2 \tan \theta) - \frac{1}{2} \sin^{-1} \left( \frac{6 \tan \theta}{9 + \tan^2 \theta} \right) $$ is
(Here, the inverse trigonometric functions $ \sin^{-1} x $ and $ \tan^{-1} x $ assume values in $[-\frac{\pi}{2}, \frac{\pi}{2}]$ and $(-\frac{\pi}{2}, \frac{\pi}{2})$, respectively.)- JEE Advanced - 2025
- Inverse Trigonometric Functions
Concepts Used:
Electrochemical Cells
An electrochemical cell is a device that is used to create electrical energy through the chemical reactions which are involved in it. The electrical energy supplied to electrochemical cells is used to smooth the chemical reactions. In the electrochemical cell, the involved devices have the ability to convert the chemical energy to electrical energy or vice-versa.
Classification of Electrochemical Cell:
Cathode
- Denoted by a positive sign since electrons are consumed here
- A reduction reaction occurs in the cathode of an electrochemical cell
- Electrons move into the cathode
Anode
- Denoted by a negative sign since electrons are liberated here
- An oxidation reaction occurs here
- Electrons move out of the anode
Types of Electrochemical Cells:
Galvanic cells (also known as Voltaic cells)
- Chemical energy is transformed into electrical energy.
- The redox reactions are spontaneous in nature.
- The anode is negatively charged and the cathode is positively charged.
- The electrons originate from the species that undergo oxidation.
Electrolytic cells
- Electrical energy is transformed into chemical energy.
- The redox reactions are non-spontaneous.
- These cells are positively charged anode and negatively charged cathode.
- Electrons originate from an external source.