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 

• $\frac{1}{2^{\mathrm{m} + \mathrm{n}}}$

• (m + n)

• (n - m)

• 2^{(n - m)}

What is the half-life of ₆C¹⁴, if its disintegration constant is 2.31× 10^-4 year^-1?

• 0.3 × 10⁴ year

• 0.3 × 10³ year

• 0.3 × 10⁸ year

• 0.3 × 10² year

For the reaction system,

2NO (g) + O₂ (g) → 2NO₂ (g)

volume is suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to O₂ and second order with respect to NO; the rate of reaction will

• diminish to one-fourth of its initial value

• diminish to one-eighth of its initial value

• increase to eight times of its initial value

• increase to four times of its initial value

The radioisotope, tritium (${}_1{}^3$H) has a half-life of 12.3 yr. If the initial amount of tritium is 32 mg, how many milligrams of it would remain after 49.2 yr ?

• 4 mg

• 8 mg

• 1 mg

• 2 mg

The activity of a radioactive substance falls to 87.5% of the initial value in 5 years. What is the half-life of the element ?

• 52 years

• 104 years

• 26 years

• 13 years

A reaction proceeds by first order, 75% of this reaction was completed in 32 min. The time required for 50% completion is

• 8 min

• 16 min

• 20 min

• 24 min

Time period of a wave is 5 × 10^-3 s, what is the frequency?

• 5 × 10^-3 s^-1

• 2 × 10² s^-1

• 2.3 × 10³ s^-1

• 5 × 10² s^-1

For the decomposition reaction of lime stone, the correct expression for rate constant, K_P is

• ${\mathrm{K}}_{\mathrm{p}} = \frac{{\mathrm{p}}_{\mathrm{CaO}}.{\mathrm{p}}_{{\mathrm{CO}}_2}}{{\mathrm{p}}_{{\mathrm{CaCO}}_3}}$

• ${\mathrm{K}}_{\mathrm{p}} = \frac{\left[\mathrm{CaO}\right]\left[{\mathrm{CO}}_2\right]}{\left[{\mathrm{CaCO}}_3\right]}$

• ${\mathrm{K}}_{\mathrm{p}} = \frac{{\mathrm{p}}_{\mathrm{CaO}} + {\mathrm{p}}_{{\mathrm{CO}}_2}}{{\mathrm{p}}_{{\mathrm{CaCO}}_3}}$

• K_p = p_CO2

Decomposition of H₂O₂ is a first order reaction. Initially, solution of H₂O₂ having half-life time 15 min is 16 volume. When solution becomes 1 volume

• 4 min

• 15 min

• 30 min

• 60 min

What is the two third life of a first order reaction having k = 5.48 × 10^-14s^-1?

• 1 × 10¹³ s

• 2 × 10¹³ s

• 8 × 10¹³ s

• 5 × 10¹⁴ s