Question #66e6d

1 Answer
Jun 27, 2016

Answer:

The answer is (3) #27#

Explanation:

The idea here is that the temperature coefficient, which you'll sometimes see referred to as the #Q_(10)# coefficient, relates the change in the rate of a reaction to a #10^@"C"# increase in the temperature of the reaction.

Simply put, the #Q_(10)# coefficient tells you how increasing the temperature of the reaction by #10^@"C"# will affect its rate.

The equation that allows you to calculate the #Q_(10)# coefficient looks like this

#color(blue)(|bar(ul(color(white)(a/a)Q_(10) = ("rate"_2/"rate"_1)^(10/(T_2 - T_1))color(white)(a/a)|)))#

Here

#T_1# - the initial absolute temperature of the reaction
#T_2# - the new absolute temperature of the reaction
#"rate"_1# - the rate at #T_1#
#"rate"_2# - the rate at #T_2#

Now, a #Q_(10)# coefficient of #3# means that with every #10^@"C"# increase in temperature, the rate of the reaction increases by a factor of #3#.

https://en.wikipedia.org/wiki/Q10_(temperature_coefficient)

It's important to notice that because you're dealing with change in temperature, you can skip the conversion to Kelvin.

That is the case because an increase by #1^@"C"# is equal to an increase by #"1 K"#.

So in the case of a #10^@"C"# increase, you would have

#T_2 - T_1 = "10 K"#

and

#Q_(10) = ("rate"_2/"rate"_1)^(10/10) = "rate"_2/"rate"_1#

In your case,

#3 = "rate"_2/"rate"_1 implies color(purple)(|bar(ul(color(white)(a/a)color(black)("rate"_2 = 3 xx "rate"_1)color(white)(a/a)|)))#

For your reaction, the temperature goes from #35^@"C"# to #65^@"C"#. This is equivalent to

#DeltaT = 65^@"C" - 35^@"C" = 30^@"C"#

So, if the rate of the reaction increases by factor of #3# with every #10^@"C"# increase in temperature, it follows that a

#30^@"C" = 3 xx 10^@"C"#

increase will cause the rate to go up by

#"rate"_2 = overbrace(color(white)(aaa)3color(white)(aaa))^(color(darkgreen)("for a 10"^@"C increase")) xx overbrace(color(white)(aaa)3color(white)(aaa))^(color(darkgreen)("for a 10"^@"C increase")) xx overbrace(color(white)(aaa)3color(white)(aaa))^(color(darkgreen)("for a 10"^@"C increase")) xx "rate"_1#

#"rate"_2 = 27 xx "rate"_1#

Therefore, the rate of the reaction will increase by a factor of #27#.