The rate of a chemical reaction doubles for every $$10^\circ \text{C}$$ rise of temperature. If the temperature is raised by $$50^\circ \text{C}$$, the rate of the reaction increases by about:

The empirical rule for many reactions states: for every $$10^\circ \text{C}$$ rise in temperature, the rate constant (and hence the rate) becomes twice its previous value.

Given a total temperature rise of $$50^\circ \text{C}$$, we can divide this rise into five successive $$10^\circ \text{C}$$ steps:

Number of steps $$= \frac{50^\circ \text{C}}{10^\circ \text{C}} = 5$$.

If the rate after one step is multiplied by $$2$$, then after $$n$$ identical steps the overall multiplication factor is $$2^n$$.

Thus, for $$n = 5$$ steps:

Overall rate increase factor $$= 2^5 = 32$$.

Hence the rate of the reaction becomes $$32$$ times its original value when the temperature is raised by $$50^\circ \text{C}$$.

Option B which is: $$32$$ times