JEE Chemistry - MCQ Practice Questions

According to Coulomb's law, lattice energy is proportional to the product of the ionic charges divided by the distance between ions:

Step 1: Consider the ionic charges.

$\text{MgO}$ consists of ${\text{Mg}}^{2+}$ and ${\text{O}}^{2-}$ ions, giving a charge product of $|+2|\times |-2|=4$, which is larger than that of singly charged ion pairs.

Step 2: Consider the ionic radii.

The ions ${\text{Mg}}^{2+}$ and ${\text{O}}^{2-}$ have relatively small ionic radii, so the interionic distance $r$ is small. A smaller $r$ leads to a larger lattice energy.

Step 3: Combine both factors.

Since $\text{MgO}$ has both a high charge product and a small interionic distance,

this results in a stronger electrostatic attraction and therefore the highest lattice energy among the given options.

Conclusion:

Vapour pressure depends on the following factors:

Step 1: Effect of Temperature

As temperature increases, more molecules have sufficient kinetic energy to escape the liquid phase, so vapour pressure increases. In general,

Step 2: Effect of Intermolecular Forces

The nature of intermolecular forces in the liquid determines how easily molecules can escape into the vapour phase. Liquids with weaker intermolecular forces have higher vapour pressures, and those with stronger intermolecular forces have lower vapour pressures:

Step 3: Factors That Do NOT Affect Vapour Pressure

Surface area and volume of the liquid do not affect the vapour pressure:

Conclusion

Vapour pressure depends only on:

Boiling point elevation depends only on the number of solute particles (expressed as molality $m$), not on their chemical nature. The relationship is given by

where $K_b$ is the ebullioscopic (boiling point elevation) constant of the solvent and $m$ is the molality of the solution. Since $\Delta T_b$ depends solely on $m$ (the number of solute particles per kilogram of solvent) and $K_b$ (a property of the solvent alone), it is completely independent of the chemical nature of the solute.

At constant temperature and pressure, the criterion for spontaneity is

where the Gibbs free energy change is defined as

A process is spontaneous when the enthalpy and entropy contributions combine such that $\Delta H-T\Delta S<0$, meaning the system lowers its Gibbs free energy. The final condition is therefore

Step 1: Identify the property type.

A property is extensive if it depends on the amount (or size) of the system, and intensive if it does not.

Step 2: Classify each property.

Step 3: Conclusion.

Entropy $S$ scales with the size of the system — doubling the amount of substance doubles the entropy. The remaining properties (refractive index, surface tension, and density) are independent of the amount of substance, making them intensive.

Osmotic Pressure

The osmotic pressure of a solution is given by:

where:

Osmotic pressure is a colligative property, meaning it depends on the number of solute particles present in the solution, not on their chemical identity.

Both the larger atomic radius and the greater shielding effect in sodium make the valence electron easier to remove compared to hydrogen's single electron.

Step 1: Effective Nuclear Charge

The effective nuclear charge $Z_{\text{eff}}$ experienced by the valence electron is approximated by Slater's rules:

where $Z$ is the atomic number and $\sigma$ is the shielding constant.

However, despite sodium having a higher $Z_{\text{eff}}$ than hydrogen's $Z_{\text{eff}}=1$ in absolute terms, the valence electron in sodium resides in the $n=3$ shell, which is much farther from the nucleus.

Step 2: Distance and Ionization Energy

The ionization energy scales approximately as:

Since the atomic radius of sodium ($r_{\text{Na}}\approx 186\text{pm}$) is far larger than that of hydrogen ($r_{\text{H}}\approx 53\text{pm}$), the combined effect gives:

Step 3: Conclusion

Therefore, the first ionization energies compare as:

The larger atomic radius and greater electron shielding in sodium reduce the attraction between the nucleus and the $3s$ valence electron, making it significantly easier to remove than hydrogen's $1s$ electron.

Step 1: Write the dissolution equilibrium

For the dissolution of AgCl in pure water:

**Step 2: Set up the expression for $K_{sp}$

Let $s$ be the molar solubility of AgCl. Then $[{\text{Ag}}^{+}]=s$ and $[{\text{Cl}}^{-}]=s$, so:

**Step 3: Solve for $s$

Result:

The pH changes most steeply at the equivalence point in an acid-base titration because the buffer capacity is at a minimum at this point.

Step 1: Neutralization Reaction

The reaction between $\text{HCl}$ and $\text{NaOH}$ is:

Step 2: Equivalence Point Condition

The equivalence point is reached when the moles of $\text{NaOH}$ added exactly equal the moles of $\text{HCl}$ present:

For equal concentrations, this occurs when equal volumes have been mixed:

Step 3: pH at the Equivalence Point

At the equivalence point, the solution contains only $\text{NaCl}$ (a neutral salt), so:

Step 4: Rate of pH Change

The rate of change of pH with respect to volume of $\text{NaOH}$ added, $\frac{d(\text{pH})}{dV}$, is greatest at the equivalence point. This is because the buffer capacity $\beta$ is defined as:

and $\beta$ reaches its minimum at the equivalence point, meaning the smallest addition of $\text{NaOH}$ produces the largest change in pH.

Conclusion

Step 1: State Henry's Law

Henry's Law relates the solubility of a gas to its partial pressure:

where $S$ is the solubility, $K_H$ is the Henry's law constant, and $P$ is the partial pressure of the gas.

Step 2: Substitute the given values

Given $K_H=1.67\times 10^{-3}\text{mol/(L⋅atm)}$ and $P=0.8\text{atm}$:

Result

Boiling point elevation depends only on the number of solute particles, not their identity, making it a colligative property.

Formally, the boiling point elevation is given by

where:

Since $\Delta T_b$ depends on $i\cdot m$ (a measure of the total number of solute particles) and not on the chemical identity of the solute, boiling point elevation is classified as a colligative property.

According to the second law of thermodynamics, the entropy of an isolated system increases or remains constant:

At equilibrium, the reaction quotient equals the equilibrium constant:

For a system not at equilibrium, two cases arise:

Therefore, a non-equilibrium condition is characterised by $Q_c\ne K_c$, and the direction of shift is given by:

In a galvanic cell, the following conventions hold:

Step 1: Electrode Polarity

The anode carries a negative charge, while the cathode carries a positive charge:

Step 2: Reaction at the Anode

Oxidation occurs at the anode:

Step 3: Direction of Electron Flow

Electrons flow from the anode to the cathode through the external circuit:

Conclusion:

The correct statement is:

Step 1: Recall the definition of pH

The pH of a solution is defined as

Step 2: Substitute the given concentration

We are given $[{\text{H}}^{+}]=2.5\times 10^{-5}\text{M}$, so

Result

The color of the reaction vessel has no effect on the rate of a chemical reaction. The major factors that influence reaction kinetics are temperature, pressure, and concentration — none of which are related to vessel color.

**Spontaneity Criterion at Constant $T$ and $P$

The Gibbs free energy change $\Delta G$ governs whether a process is spontaneous at constant temperature and pressure. The fundamental criterion is:

That is, a process is spontaneous if and only if the Gibbs free energy of the system decreases. More completely, the three cases are:

Thus, for any spontaneous process at constant $T$ and $P$, it is always true that $\Delta G<0$.

Step 1: Calculate the pOH

Step 2: Calculate the pH

Step 3: Classify the solution

Since $\text{pH}=6<7$, the solution is acidic.

Step 1: Identify the rate law

The given rate law is:

Step 2: Determine the order with respect to each reactant

Step 3: Calculate the overall order

The overall reaction order is the sum of all the exponents in the rate law:

This is a third-order reaction.

> Note: The reaction order is determined experimentally and need not match the stoichiometric coefficients. Here, the stoichiometric coefficient of $A$ is $2$ and of $B$ is $1$, which happen to equal the exponents in the rate law, but this is not always the case.

The coordination number is the number of ligands attached to the central metal ion.

Step 1: Identify the central metal ion and the ligands present.

In $[{\text{Cu(NH}}_3{)}_4{]}^{2+}$, the central metal ion is ${\text{Cu}}^{2+}$, and the ligands are ${\text{NH}}_3$ molecules.

Step 2: Count the number of ligands bonded to the central metal ion.

There are $4$ ammonia (${\text{NH}}_3$) ligands directly bonded to ${\text{Cu}}^{2+}$, so the coordination number is: