Question

1.
For the decomposition of dimethyl ether, A in the Arrhenius equation K = Ae-E/RT has a value of
1.26 x 1013 and E, value of 58.5 kcal. Calculate half life period for first order decomposition at
527°C.
1) 525 sec
2) 400 sec
3) 600 sec
4) 800 sec​

Answer 1

Answer:

400 sec

Explanation:

1.

For the decomposition of dimethyl ether, A in the Arrhenius equation K = Ae-E/RT has a value of

1.26 x 1013 and E, value of 58.5 kcal. Calculate half life period for first order decomposition at

527°C.

1) 525 sec

2) 400 sec

3) 600 sec

4) 800 sec

Answer 2

For the decomposition of dimethyl ether, A in the Arrhenius equation K = Ae¯(E/RT) has A value of

1.26 x 10¹³ and E , value of 58.5 kcal/mol

We have to find the half life period for first order decomposition at 527°C.

Temperature, T = 527°C = 527 + 273 = 800K

frequency factor, A = 1.26 × 10¹³

energy of activation, E = 58.5 Kcal/mol

now,

$K=Ae^{-\frac{E}{RT}}$

taking ln both sides we get,

lnK = lnA - E/RT

⇒logK = logA - E/(2.303RT)

R = 1.987 cal/mol/K

so , logK = log(1.26 × 10¹³) - (58.5 × 10³ cal/mol)/(2.303 × 1.987 cal/mol/K × 800K)

= 13.1003 - 15.9799 = -2.8796

⇒logK = -2.8796

⇒K = antilog(-2.8796) = 1.3194 × 10¯³ sec

now, using Half life formula,

$T=\frac{0.693}{K}$

= (0.693)/(1.3194 × 10¯³)

= 693/(1.3194)

= 525 sec

Therefore the half life for first order decomposition at 527°C is 525 sec. hence option (1) is correct.