Question

What fraction of molecules in a gas at
300 K collide with an energy equal to
activation energy of 50 kJ/mol ?​

Answer 1

From K=Ae

−Ea/RT

, We know that

K

2

K

1

=

T

2

T

1

(K= number of molecules, T= Temperature)

⇒

25

50

=

T

2

300

⇒T

2

=150K

Answer 2

$\huge\bf\boxed{\boxed{\underline{\orange{Question!!}}}}$

what fraction of molecules in a gas at 300k collides with an energy equal to activation energy of 50KJ/mol

$\huge\bf\boxed{\boxed{\underline{\orange{Answes!!}}}}$

$\huge\bold{Given}$

$\mathrm\red{Activation \:Energy \:Ea = 50KJ/mol^{-1}}$

$\mathrm\red{→ 50 × 10³ J/mol^{-1}}$

$\mathrm\blue{Temperature \:(T) = 300K}$

$\huge\bold{To \:find}$

Fraction of molecules with Energy equal to Ea

We know the formula :

$\huge\mathrm\purple{f = e^\frac{-Ea}{RT}}$

$\huge\mathrm\red{f = e^\frac{-50×10³mol^{-1}}{8.314JK^{-1}mol^{-1}×300K}}$

$\mathrm\pink{log10f = \frac{-50×10³}{8.314×300×2.303}}$

$\mathrm\pink{log10f = -8.70}$

$\mathrm\pink{f = antilog(-8.70)}$

$\mathrm\pink{f = 1.99 × 10^{-9}}$

$\mathrm\pink{f = 2.0 × 10^{-9}}$

Fraction of molecules with Energy equal to Ea = $2.0 × 10^{-9}$

$\huge\bf\boxed{\boxed{\underline{\blue{Ea = 2.0 × 10^{-9}}}}}$