Can a reaction have negative activation energy?

Explanation

According to Arrhenius eqn., `k="A e"^(-E_(a)//RT)`. If `E_(a)` were negative, the exponential factor can be written as `e^(x)` where `x=E_(a)//RT`. If `xltlt1`, we have
`e^(x)=1+x+(x^(2))/(2!)+(x^(3))/(3!)+…=1+x" "("Neglecting higher powers of x")`
`=1+E_(a)//RT`
`:." "k=A(1+E_(a)//RT)`, i.e., `kgtgtA` which is impossible. Hence, `E_(a)` cannot be negative.