(a)
Interpretation:
The rate constant for the growth in the number of transistor on an integrated circuit has to be determined using the given plot ln N versus year.
Concept introduction:
Rate of the reaction is the change in the concentration of reactant or a product with time.
The rate law expresses the relationship of the rate of a reaction to the rate constant.
Rate equation for the general reaction
Order of a reaction: The sum of exponents of the concentrations in the rate law for the reaction is said to be order of a reaction.
For first order reaction,
Moore’s law states that the number of transistors per square inch on integrated circuits had doubled every year since their invention (1958).
(a)
Explanation of Solution
Given plot of ln N versus t (year) is shown below,
Figure 1
The plot of ln N versus t is linear for a process which follows first order kinetics. And so the given process follows first order kinetics.
The rate can be described using the equation,
Where N is the number of transistor on an integrated circuit, which is roughly doubles every 1.5 year according to the Moore’s law.
For first order reaction,
For this case, the equation can be rearranged as follows,
Comparing this equation to the straight line equation (
(b)
Interpretation:
The time required for
Concept introduction:
The rate law expresses the relationship of the rate of a reaction to the rate constant.
Rate equation for the general reaction
Order of a reaction: The sum of exponents of the concentrations in the rate law for the reaction is said to be order of a reaction.
For first order reaction,
Moore’s law states that the number of transistors per square inch on integrated circuits had doubled every year since their invention (1958).
(b)
Explanation of Solution
Given plot of ln N versus t (year) is shown below,
Figure 1
The time required for
For first order reaction,
This value is very close to the value mentioned in Moore’s law.
(c)
Interpretation:
The number of transistors on an integrated circuit
Concept introduction:
The rate law expresses the relationship of the rate of a reaction to the rate constant.
Rate equation for the general reaction
Order of a reaction: The sum of exponents of the concentrations in the rate law for the reaction is said to be order of a reaction.
For first order reaction,
Moore’s law states that the number of transistors per square inch on integrated circuits had doubled every year since their invention (1958).
(c)
Explanation of Solution
Given plot of ln N versus t (year) is shown below,
Figure 1
The time required for
For first order reaction,
For this case, the equation can be rearranged as follows,
Assume the year 1960 as
The year 2100 would corresponds to
Substituting known values in the above mentioned equation,
Thus, there will be
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Chapter 13 Solutions
Chemistry
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