Advertisement

Advertisement

Advertisement

Sum

**Solve**

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

Advertisement

#### Solution

**Given:**

Activation energy (E_{a}) = 50 kJ mol^{-1} = 50 × 10^{3} J mol^{-1}

Temperature (T) = 300 K

**To find: **

Fraction of molecule (f) with energy equal to E_{a}

**Formula:**

f = `"e"^((-"E"_"a")/("RT"))`

**Calculation: **

Substituting the given value above

f = `"e"^(((-50 xx 10^3 "J" "mol"^-1)/(8.314 "J" "K"^-1 "mol"^-1 xx 300 "K")))`

log_{10}f = `((-50 xx 10^3)/(8.314 xx 300 xx 2.303))`

log_{10}f = -8.70

f = antilog (-8.70)

f = 1.99 × 10^{-9} ≈ 2.0 × 10^{-9}

Fraction of molecules having energy equal to activation energy is 2.0 × 10^{-9}.

Concept: Temperature Dependence of Reaction Rates

Is there an error in this question or solution?