First Order Reaction

Q. For a first order reaction $A\left(g\right)\to 2B\left(g\right)+C\left(g\right)$ at constant volume and 300 K, the total pressure at the beginning (t= 0) and at time t are $P_0$ and $P_t$, respectively. Initially, only A is present with concentration $\left[A_0\right]$, and $t_{\frac{1}{3}}$ is the time required for the partial pressure of A to reach ${\frac{1}{3}}^{rd}$ of its initial vlaue. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

1. 
2. 
3. 
4. 

Q. The rate of a first order reaction has been found to be $2.45\times {10}^{-6}mol{L}^{-1}{s}^{-1}$at concentration $C_1$. The value of $C_1$ is (rate constant = $3.5\times {10}^{-5}$)

1. $7mol{L}^{-1}$
2. $0.7mol{L}^{-1}$
3. $0.07mol{L}^{-1}$
4. $2.1mol{L}^{-1}$

Q. The rate of a first order reaction $R\to P$is $7.5\times {10}^{-4}mol{L}^{-1}{s}^{-1}$ when the concentration of R is 0.5 mol $L^{-1}$.

The rate constant is

1. $4.16\times {10}^{-7}{s}^{-1}$
2. $2.5\times {10}^{-5}{s}^{-1}$
3. $1.5\times {10}^{-5}{s}^{-1}$
4. $1.5\times {10}^{-3}{s}^{-1}$

Q. The reaction : A $\to$ B follows first order kinetics. The time taken for 0.8 mol of A to produce 0.6 mol of B is 1 hour. What is the time taken for conversion of 0.9 mol of A produce 0.675 mol of B?

1. 1 hr
2. 0.5 hr
3. 0.25 hr
4. 2 hr

Q. A reaction $2A+B\stackrel{K}{\to }C+D$ is first order w.r.t. and second order w.r.t. . Initial conc. (t=0) of is $C_0$ while is $2C_0$. If at as 300 minutes the conc. of C is $\frac{C_0}{4}$ then rate expression at t = 300 minutes is

1. $R=7C_0^3\frac{k}{16}$
2. $R=27C_0^3\frac{k}{32}$
3. $R=247C_0^3\frac{k}{64}$
4. $R=49C_0^3\frac{k}{32}$

Q.

In the reaction, P + Q ⟶ R + S

the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

1. 0
2. 1

3. 2

4. 3

Q. The rate constant for a first order reaction is $k=7\times {10}^{-4}{s}^{-1}$. The time taken for the reactant to be reduced to $\frac{1}{4}$ of the initial concentration is

1. 990 s
2. 1980 s
3. 445 s
4. 2970 s

Q. What is the half life period of a radioactive substance if 87.5$\%$ of any given amount of the substance disintegrates in 40 minutes?

1. 160 min
2. 10 min
3. 13.58 min
4. 20 min

Q. 75$\%$ of a first order reaction was completed in 32 minutes. 50$\%$ of the reaction was complete in

1. 4 min
2. 8 min
3. 16 min
4. 24 min

Q. The rate for a first order reaction is $0.639\times {10}^{-2}mold{m}^{-1}mi{n}^{-1}$ and the initial concentration is 0.2 mol $d{m}^{-3}$. The half-life period is

1. 1200 s
2. 20 s
3. 600 s
4. 0.33 s