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

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 :

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

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

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

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

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

$\mathrm\pink{f = 1.99 × 10^{-9}}$

$\mathrm\pink{f = 2.0 × 10^{-9}}$

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