JEE Chemistry - MCQ Practice Questions

Step 1: Identify the known values

The two rate constants and corresponding temperatures are:

Step 2: Write the two-temperature Arrhenius equation

Step 3: Substitute the known values

Step 4: Evaluate the terms

**Step 5: Solve for $E_a$

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

For a general reaction, the half-life $t_{1/2}$ depends on the initial concentration $[A{]}_0$ according to the reaction order:

where $n$ is the order of reaction.

**Step 1: Zero-order reaction ($n=0$)**

The half-life *increases* with initial concentration, so $t_{1/2}$ is not independent of $[A{]}_0$.

**Step 2: First-order reaction ($n=1$)**

The half-life contains no $[A{]}_0$ term, so $t_{1/2}$ is independent of initial concentration.

**Step 3: Second-order reaction ($n=2$)**

The half-life *decreases* with initial concentration, so $t_{1/2}$ is not independent of $[A{]}_0$.

Conclusion:

Only for a first-order reaction is $t_{1/2}$ independent of the initial concentration $[A{]}_0$. The order of the reaction $2A\to B+C$ is therefore:

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.

**Step 1: Identify the relationship between $\Delta G°$ and $K_c$

The standard Gibbs free energy change is related to the equilibrium constant by:

Step 2: Substitute the known values

Given $R=8.314{\text{J mol}}^{-1}{\text{K}}^{-1}$, $T=298\text{K}$, and $K_c=4$:

**Step 3: Evaluate $\ln (4)$

**Step 4: Calculate $\Delta G°$

Result:

Step 1: Recall the formula for molar conductivity

The molar conductivity ${\Lambda }_m$ is related to the specific conductance $\kappa$ and the molar concentration $C$ by:

where $\kappa$ is in $\text{S/cm}$, $C$ is in $\text{mol/L}$, and ${\Lambda }_m$ is in ${\text{S⋅cm}}^2\text{/mol}$.

Step 2: Substitute the given values

Given $\kappa =0.0141\text{S/cm}$ and $C=0.01\text{mol/L}$:

Step 3: State the final answer

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

Step 1: Identify the Henderson–Hasselbalch equation

The pH of a buffer is given by:

**Step 2: Calculate $p{K}_a$

Step 3: Substitute the concentrations

With $[{\text{A}}^{-}]=0.1\text{M}$ and $[\text{HA}]=0.1\text{M}$:

Result:

Step 1: Recall the entropy change formula for an ideal gas at constant temperature

For an isothermal process involving an ideal gas, the entropy change is given by

Step 2: Substitute the given values

For one mole of gas ($n=1$) with the volume doubled ($V_2=2V,V_1=V$),

Result

The entropy change for one mole of an ideal gas whose volume is doubled at constant temperature is

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:

Step 1: Write the integrated rate law for a first-order reaction.

For a first-order reaction, the concentration at time $t$ is given by

Step 2: Substitute the known values.

With $k=0.05{\text{s}}^{-1}$ and $t=50\text{s}$:

Step 3: Evaluate the exponential.

Therefore:

Step 4: Express as a percentage.

Result:

The percentage of reactant remaining after $50\text{s}$ is

Step 1: Recall the Gibbs free energy equation

The Gibbs free energy change is given by

A reaction is spontaneous when $\Delta G<0$.

**Step 2: Analyze the signs of $\Delta H$ and $\Delta S$

Consider the case where $\Delta H<0$ (exothermic) and $\Delta S>0$ (entropy increases). Substituting these signs into the equation:

Since $T>0$ (temperature in Kelvin is always positive), the term $T\Delta S$ is strictly positive. Therefore:

Step 3: Conclusion

When $\Delta H<0$ and $\Delta S>0$, the Gibbs free energy is always negative regardless of temperature, meaning the reaction is spontaneous at all temperatures.

**Step 1: Find $[{\text{H}}^{+}]$ from the given pH**

Since $\text{pH}=2.5$,

Step 2: Set up the equilibrium expression

For the weak acid dissociation $\text{HA}\rightleftharpoons {\text{H}}^{+}+{\text{A}}^{-}$, the acid dissociation constant is

Step 3: Substitute the values

Result:

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: Relate wavelength to crystal field splitting energy

The crystal field splitting energy $\Delta$ expressed in wavenumbers (${\text{cm}}^{-1}$) is the reciprocal of the wavelength in centimeters:

Step 2: Substitute the given value

Step 3: Convert to nanometers

Result

The wavelength of light absorbed by $[{\text{Fe(CN)}}_6{]}^{4-}$ is:

Step 1: Find the moles of excess HCl

The moles of $\text{HCl}$ and $\text{NaOH}$ present are:

The excess $\text{HCl}$ remaining after neutralisation:

**Step 2: Calculate the concentration of ${\text{H}}^{+}$

The total volume of the solution after mixing is:

Therefore, the concentration of ${\text{H}}^{+}$ is:

Step 3: Calculate the pH

However, with a more careful calculation taking into account significant figures and the precise value of the concentration:

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 $\Delta G<0$.