Dinitrogen pentoxide, N 2 O 5 , N2O5, decomposes by first‑order kinetics with a rate constant of 3.7 × 10 − 5 s − 1 3.7×10−5 s−1 at 298 K . 298 K. What is the half‑life, in hours, of N 2 O 5 N2O5 at 298 K ? 298 K? half‑life: h h If [ N 2 O 5 ] 0 = 0.0603 mol ⋅ L − 1 , [N2O5]0=0.0603 mol⋅L−1, what will be the concentration of N 2 O 5 N2O5 after 3.2 h ?

The half-life of the given reaction is 5.2 hours

The concentration of N₂O₅ after 3.2 hours is 3 × 10⁻² molL⁻¹

Explanation:

The value of rate constant, k is  3.7  ×  10⁻⁵  s⁻¹.

Temperature is  298  K  

The initial concentration of N₂O₅ is 6.03  × 10 ⁻²  m ol/L.

Time is 3.2 hours.

The formula for half-life of the first order reaction is given below:

t1/2 = 0.693 /k

Where,  t 1/2 is the half-life of first order reaction.

k  is the rate constant of the first order reaction.

Substitute the given values in the equation (I).

t1/2 =  0.693  / 3.7  ×  10⁻⁵  s⁻¹

t1/2 =  1.87  ×  10⁴ s

Converting to hours; (1.87  ×  10⁴ s  / 3600 s) * 1 hour = 5.2 hours

Therefore, the half-life of the given reaction is 5.2 hours

 The formula for first order reaction is shown as:

k  =  1 /t * ㏑([X]₀ / [X]ₙ)

Where,  k  is rate constant for first order reaction.

t  is time.

[X]₀ is initial concentration of the reactant.

[X]ₙ is concentration of the reactant at time t.

Converting 3.2 hours to seconds  3.2 * 60 * 60 = 11520 seconds

Substitute the given values in equation for the rate constant

3.7  ×  10⁻⁵  s⁻¹ = 1/11520 * ㏑(6.03  × 10 ⁻²  / [X]ₙ)

㏑(6.03  × 10 ⁻²  / [X]ₙ) =  3.7  ×  10⁻⁵  s⁻¹ * 11520

㏑(6.03  × 10 ⁻²  / [X]ₙ) = 0.426

6.03  × 10 ⁻²  / [X]ₙ = e ⁰°⁴²⁶

6.03  × 10 ⁻²  / [X]ₙ = 1.531

[X]ₙ = 6.03  × 10 ⁻² / 1.531

[X]ₙ = 3 × 10⁻² molL⁻¹

Therefore the concentration of N₂O₅ after 3.2 hours is 3 × 10⁻² molL⁻¹

considering the question as per the attachment

here we can see that the radon nuclide has 222 as the atomic mass number and 86 as the atomic number.

when it undergoes nuclear fission it gives polonium which has atomic mass number as 218 and atomic number will be 84 along with a helium nucleus which has 4 atomic mass number and 2 as its atomic number.

222 = 218 + 4 (atomic mass number)

86 = ? + 2; therefore ? = 86-2 = 84.

the atomic mass number of polonium will be 84.