80
Graphical Representation
of ///o against C (as abscissa), where C is the concentration expressed in mg
of Mn per 100 ml of solution
C
///o
1 00
0418
200
0 149
3 00
0058
400
0026
(b) Replot the given data on semilog paper, again plotting concentration along
the abscissa, but plotting /<,// along the ordmate
(c) From the graph made in (b), find the mathematical equation for the relationship between /„// and C
*(d) (;) Using the method of least squares, find the equation of the best-fit line
for the data as plotted in (b) above (/;) Find the correlation coefficient
and the 95% confidence interval for the slope of the best fit equation (in) On the plot made in (b), draw the line that corresponds to the
best-fit equation.
When radioactive isotopes disintegrate, they obey a rate law that may be
expressed as log N = -kt + K, where t is time, and N is the number of
radioactive atoms (or something proportional to it) present at time / A common way to describe the number of radioactive atoms present in a given
sample is in terms of the number of disintegrations observed per minute on a
Geiger counter (this is referred to as "the number of counts per minute," or
simply as cpm)
(a) The following cpm are obtained for a sample of an unknown isotope at
10-mmute intervals (beginning with t = 0) 10,000 8166, 7583, 6464, 5381,
5023,4466,3622,2981,2690,2239 2141, 1775, 1603, 1348, 1114, 1048 Plot
these data, using semilog graph paper
(b) Construct a graph on the plot made in part (a), and from this graph evaluate the constants k and K to give the equation of the rate law
*(c) (i) Using the method of least squares, find the rate-law equation of the
best-fit line for the data as plotted in (a) above (//) Find the correlation
coefficient and the 95% confidence intervals for both the slope and the y
intercept of the best-fit equation (in) On the plot made in (a), draw the
line that corresponds to the best-fit equation
(d) What is the physical significance ot K"
1
i When the rates of chemical reaction are studied, it is common to determine
the "rate constant" k, which is characteristic of a given reaction at a given
temperature Still further information can be obtained by determining the
value of k at several different temperatures, because these values of A are
related to the Kelvin temperature (T) at which they were measured according
to the equation
In this equation A// d is the so-called "energy of activation," Q is a constant
characteristic of the reaction, andR is the gas constant of 1 987 cal mole ' K '
(a) The following data are obtained for the reaction
Graphical Representation
of ///o against C (as abscissa), where C is the concentration expressed in mg
of Mn per 100 ml of solution
C
///o
1 00
0418
200
0 149
3 00
0058
400
0026
(b) Replot the given data on semilog paper, again plotting concentration along
the abscissa, but plotting /<,// along the ordmate
(c) From the graph made in (b), find the mathematical equation for the relationship between /„// and C
*(d) (;) Using the method of least squares, find the equation of the best-fit line
for the data as plotted in (b) above (/;) Find the correlation coefficient
and the 95% confidence interval for the slope of the best fit equation (in) On the plot made in (b), draw the line that corresponds to the
best-fit equation.
When radioactive isotopes disintegrate, they obey a rate law that may be
expressed as log N = -kt + K, where t is time, and N is the number of
radioactive atoms (or something proportional to it) present at time / A common way to describe the number of radioactive atoms present in a given
sample is in terms of the number of disintegrations observed per minute on a
Geiger counter (this is referred to as "the number of counts per minute," or
simply as cpm)
(a) The following cpm are obtained for a sample of an unknown isotope at
10-mmute intervals (beginning with t = 0) 10,000 8166, 7583, 6464, 5381,
5023,4466,3622,2981,2690,2239 2141, 1775, 1603, 1348, 1114, 1048 Plot
these data, using semilog graph paper
(b) Construct a graph on the plot made in part (a), and from this graph evaluate the constants k and K to give the equation of the rate law
*(c) (i) Using the method of least squares, find the rate-law equation of the
best-fit line for the data as plotted in (a) above (//) Find the correlation
coefficient and the 95% confidence intervals for both the slope and the y
intercept of the best-fit equation (in) On the plot made in (a), draw the
line that corresponds to the best-fit equation
(d) What is the physical significance ot K"
1
i When the rates of chemical reaction are studied, it is common to determine
the "rate constant" k, which is characteristic of a given reaction at a given
temperature Still further information can be obtained by determining the
value of k at several different temperatures, because these values of A are
related to the Kelvin temperature (T) at which they were measured according
to the equation
In this equation A// d is the so-called "energy of activation," Q is a constant
characteristic of the reaction, andR is the gas constant of 1 987 cal mole ' K '
(a) The following data are obtained for the reaction