Rate of Chemical Reaction

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JEE Advanced 2026

For a reversible reaction $R ⇌ P$ , at constant temperature, both the forward and the backward reactions are first order elementary reaction with rate constant $k_{f}$ and $k_{b}$ , respectively. At time zero, the concentration of $R$ is $[R]_{0}$ and the concentration of $P$ is zero. At any given time $[R]$ and $[P]$ are the concentration of $R$ and $P$ , respectively. If $k_{b} = 4 k_{f}$ , the correct graphical representation of the reaction is

JEE Advanced 2026

For a first-order reaction R $⟶$ P at a given temperature, $k$ is the rate constant. For this reaction, at the given temperature, the concentrations of R and P at a time $t$ are [R] and [P], respectively. The correct graphical representation(s) for this reaction is(are)

* Multiple Correct Options

JEE Advanced 2020

Which of the following plots is(are) correct for the given reaction? ( $[P]_{0}$ is the initial concentration of P)

* Multiple Correct Options

LEVELJEE Advanced

For the following reaction $2 X + Y k P$ the rate of reaction is $\frac{d [ P ]}{d t} = k [X]$ . Two moles of X are mixed with one mole of Y to make 1.0 L of solution. At 50 s, 0.5 mole of Y is left in the reaction mixture. The correct statement(s) about the reaction is(are) (Use: $ln 2 = 0.693$ )

* Multiple Correct Options

The rate constant,

k

, of the reaction is

13.86 \times 1 0^{- 4} s^{- 1}

Half-life of X is 50s.

- \frac{d [ X ]}{d t} = 13.86 \times 1 0^{- 3} mol L^{- 1} s^{- 1}

- \frac{d [ Y ]}{d t} = 3.46 \times 1 0^{- 3} mol L^{- 1} s^{- 1}

JEE Advanced 2019

In the decay sequence : $_{92}^{238} U - x_{1}_{90}^{234} Th - x_{2}_{91}^{234} Pa - x_{3}^{234} Z - x_{4}_{90}^{230} Th$ $x_{1}$ , $x_{2}$ , $x_{3}$ and $x_{4}$ are particles/ radiation emitted by the respective isotopes. The correct option(s) is/are-

* Multiple Correct Options

Z is an isotope of uranium

x_{2}

β^{-}

x_{1}

will deflect towards negatively charged plate

x_{3}

γ

During the nuclear explosion, one of the products is $^{90} Sr$ with half-life of $6.93 years$ . If $1 μ g$ of $^{90} Sr$ was absorbed in the bones of a newly born baby in place of Ca, how much time, in years, is required to reduce it by $90%$ if it is not lost metabolically ......... .

For a first order reaction, $A ⟶ products$ the concentration of $A$ changes from $0.1 M$ to $0.025 M$ in $40 min$ . The rate of reaction when the concentration of $A$ is $0.01 M$ is

1.73 \times 1 0^{- 5} M / min

3.47 \times 1 0^{- 4} M / min

3.47 \times 1 0^{- 5} M / min

1.73 \times 1 0^{- 4} M / min

For an elementary chemical reaction, $A_{2} k_{- 1} ⇌ k_{1} 2 A$ , the expression for $\frac{d [ A ]}{d t}$ is

2 k_{1} [A_{2}] - k_{- 1} [A]^{2}

k_{1} [A_{2}] - k_{- 1} [A]^{2}

2 k_{1} [A_{2}] - 2 k_{- 1} [A]^{2}

k_{1} [A_{2}] + k_{- 1} [A]^{2}

For the reaction $2 A + 3 B + \frac{3}{2} C \to 3 P$ , which statement is correct?

\frac{d n _{A}}{d t} = \frac{2}{3} \frac{d n _{B}}{d t} = \frac{3}{4} \frac{d n _{C}}{d t}

\frac{d n _{A}}{d t} = \frac{3}{2} \frac{d n _{B}}{d t} = \frac{3}{4} \frac{d n _{C}}{d t}

\frac{d n _{A}}{d t} = \frac{d n _{B}}{d t} = \frac{d n _{C}}{d t}

\frac{d n _{A}}{d t} = \frac{2}{3} \frac{d n _{B}}{d t} = \frac{4}{3} \frac{d n _{C}}{d t}

For the reaction $2 H_{2} (g) + 2 NO (g) \to N_{2} (g) + 2 H_{2} O (g)$ the observed rate expression is, $rate = K_{f} [NO]^{2} [H_{2}]$ . The rate expression for the reverse reaction is

K_{b} [N_{2}] [H_{2} O]^{2} / [H_{2}]

K_{b} [N_{2}] [H_{2} O]

K_{b} [N_{2}] [H_{2} O]^{2} / [NO]

K_{b} [N_{2}] [H_{2} O]^{2}

For the non-stoichiometric reaction, $2 A + B \to C + D$ , the following kinetic data were obtained in three separate experiments, all at $298 K$ . $Initial concentration (A) 0.1 M 0.1 M 0.2 M Initial concentration (B) 0.1 M 0.2 M 0.1 M Initial rate of formation of C (mol L^{- 1} s^{- 1}) 1.2 \times 1 0^{- 3} 1.2 \times 1 0^{- 3} 2.4 \times 1 0^{- 3}$ The rate law for the formation of C is

\frac{d c}{d t} = k [A] [B]

\frac{d c}{d t} = k [A]^{2} [B]

\frac{d c}{d t} = k [A] [B]^{2}

\frac{d c}{d t} = k [A]

For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is ........... (Integer answer)

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is $2 K_{2} C r_{2} O_{7} + 8 H_{2} S O_{4} + 3 C_{2} H_{6} O \to 2 C r_{2} (S O_{4})_{3} + 3 C_{2} H_{4} O_{2} + 2 K_{2} S O_{4} + 11 H_{2} O$ If the rate of appearance of $C r_{2} (S O_{4})_{3}$ is $2.67 mol min^{- 1}$ at a particular time, the rate of disappearance of $C_{2} H_{6} O$ at the same time is ......... $mol min^{- 1}$ . (Nearest integer)

For a chemical reaction $A ⟶ B$ , it was found that concentration of $B$ is increased by $0.2 mol L^{- 1}$ in $30 min$ . The average rate of the reaction is $\dots \times 1 0^{- 1} mol L^{- 1} h^{- 1}$ . (Nearest integer)

LEVELJEE Advanced

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of $3.33 h$ at $2 5^{\circ} C$ . After $9 h$ , the fraction of sucrose remaining is $f$ . The value of $lo g_{10} (\frac{1}{f})$ is ...... $\times 1 0^{- 2}$ (Rounded off to the nearest integer). [Assume, $ln 10 = 2.303$ , $ln 2 = 0.693$ ]

For the reaction, $H_{2} + I_{2} ⟶ 2 H I$ , the differential rate law is

- \frac{d [ H _{2} ]}{d t} = - \frac{d [ I _{2} ]}{d t} = 2 \frac{d [ H I ]}{d t}

- 2 \frac{d [ H _{2} ]}{d t} = - 2 \frac{d [ I _{2} ]}{d t} = \frac{d [ H I ]}{d t}

- \frac{d [ H _{2} ]}{d t} = - \frac{d [ I _{2} ]}{d t} = \frac{d [ H I ]}{d t}

- \frac{d [ H _{2} ]}{2 d t} = - \frac{d [ I _{2} ]}{2 d t} = \frac{d [ H I ]}{d t}

A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?

For a reaction $\frac{1}{2} A ⟶ 2 B$ , rate of disappearance of 'A' is related to the rate of appearance of 'B' by the expression

- \frac{d [ A ]}{d t} = \frac{1}{2} \frac{d [ B ]}{d t}

- \frac{d [ A ]}{d t} = \frac{1}{4} \frac{d [ B ]}{d t}

- \frac{d [ A ]}{d t} = \frac{d [ B ]}{d t}

- \frac{d [ A ]}{d t} = 4 \frac{d [ B ]}{d t}

The reaction $N_{2} O_{5} (g) ⟶ 2 N O_{2} (g) + \frac{1}{2} O_{2} (g)$ is a first order reaction. The initial concentration of $N_{2} O_{5}$ is $2.40 \times 1 0^{- 2} mol L^{- 1}$ at $318 K$ . The concentration of $N_{2} O_{5}$ after $1 hour$ was $1.60 \times 1 0^{- 2} mol L^{- 1}$ . The rate constant of the reaction at $318 K$ is ...... $\times 1 0^{- 3} min^{- 1}$ . (Nearest integer) [Given : $lo g 3 = 0.477, lo g 5 = 0.699$ ]

Consider the reaction, $Cl_{2} (a q) + H_{2} S (a q) ⟶ S (s) + 2 H^{+} (a q) + 2 Cl^{-} (a q)$ The rate equation for this reaction is, $rate = k [Cl_{2}] [H_{2} S]$ Which of these mechanisms is/are consistent with this rate equation? (I) $Cl_{2} + H_{2} S ⟶ H^{+} + Cl^{-} + Cl^{+} + HS^{-}$ (slow) $Cl^{+} + HS^{-} ⟶ H^{+} + Cl^{-} + S$ (fast) (II) $H_{2} S ⇌ H^{+} + HS^{-}$ (fast) $Cl_{2} + HS^{-} ⟶ 2 Cl^{-} + H^{+} + S$ (slow)

Both (I) and (II)

Neither (I) nor (II)

In the following reaction; $x A \to y B$ $lo g_{10} [- \frac{d [ A ]}{d t}] = lo g_{10} [\frac{d [ B ]}{d t}] + 0.3010$ $A$ and $B$ respectively can be

n

i so

C_{2} H_{2}

C_{6} H_{6}

C_{2} H_{4}

C_{4} H_{8}

N_{2} O_{4}

N O_{2}

The rate law for a reaction between the substances $A$ and $B$ is given by $rate = k [A]^{n} [B]^{m}$ . On doubling the concentration of $A$ and halving the concentration of $B$ , the ratio of the new rate to the earlier rate of the reaction will be as

\frac{1}{2 ^{m + n}}

(m + n)

(n - m)

2^{(n - m)}

Rate constant, $k$ of the first order reaction when initial concentration $(C_{0})$ and concentration $(C_{t})$ at time $t$ , is given by equation $k t = lo g C_{0} - lo g C_{t}$ Graph is a straight line if we plot

t

lo g C_{0}

t

lo g C_{t}

t^{- 1}

lo g C_{t}

lo g C_{0}

lo g C_{t}

The reaction $2 A + B_{2} \to 2 A B$ is an elementary reaction. For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of 3, the rate of the reaction increases by a factor of ........... . (Round off to the nearest integer).

Gaseous cyclobutene isomerises to butadiene in a first order process which has a ' $k$ ' value of $3.3 \times 1 0^{- 4} s^{- 1}$ at $15 3^{\circ} C$ . The time in minutes it takes for the isomerisation to proceed $40%$ to completion at this temperature is ....... . (Rounded off to the nearest integer)