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Chapter 12: Q57 E (page 708)

The rate of a certain reaction doubles for every 10°C rise in temperature.

(a) How much faster does the reaction proceed at 45°C than at 25°C?

(b) How much faster does the reaction proceed at 95°C than at 25°C?

Short Answer

Expert verified

The rate increases by four times.

The rate increases by 128 times.

Step by step solution

01

Calculating the difference in temperature

For every10°C rise in temperature the rate is 2 times the original.

Difference in temperature =\({\bf{(45 - 25)^\circ C = 20^\circ C}}\)

02

Step 2: Difference in rate

Thus, for 20°C rise in temperature the rate increases by \({{\bf{(2)}}^{\bf{2}}}{\bf{ = 4}}\)

03

Calculating the difference in temperature

Difference in temperature =\({\bf{(95 - 25)^\circ C = 70^\circ C}}\)

04

Step 4: Difference in rate 

Thus for \(70^\circ C\)rise in temperature the rate increases by \({{\bf{(2)}}^{\bf{7}}}{\bf{ = 128}}\) .

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What is the half-life for the first-order decay of carbon-14?

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