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Question
Solve
What fraction of molecules in a gas at 300 K collide with an energy equal to the activation energy of 50 kJ/mol?
Solution
Given:
Activation energy (Ea) = 50 kJ mol-1 = 50 × 103 J mol-1
Temperature (T) = 300 K
To find:
Fraction of molecule (f) with energy equal to Ea
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")))`
log10f = `((-50 xx 10^3)/(8.314 xx 300 xx 2.303))`
log10f = -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.
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