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The specific heat capacities of $\mathrm{Li}(s), \mathrm{Na}(s), \mathrm{K}(s), \mathrm{Rb}(s)$, and $\mathrm{Cs}(s)$ at $25^{\circ} \mathrm{C}$ are $3.57,1.23,0.756,0.363$, and $0.242 \mathrm{~J} \mathrm{~K}^{-1}$ $\mathrm{g}^{-1}$, respectively. Compute the molar heat capacities of these elements and identify any periodic trend. If there is a trend, use it to predict the molar heat capacity of francium, $\operatorname{Fr}(s)$.

    The specific heat capacities of $\mathrm{Li}(s), \mathrm{Na}(s), \mathrm{K}(s), \mathrm{Rb}(s)$, and $\mathrm{Cs}(s)$ at $25^{\circ} \mathrm{C}$ are $3.57,1.23,0.756,0.363$, and $0.242 \mathrm{~J} \mathrm{~K}^{-1}$ $\mathrm{g}^{-1}$, respectively. Compute the molar heat capacities of these elements and identify any periodic trend. If there is a trend, use it to predict the molar heat capacity of francium, $\operatorname{Fr}(s)$.

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Principles of Modern Chemistry

Principles of Modern Chemistry

David W. Oxtoby,… 7th Edition

Chapter 12, Problem 5

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The specific heat capacities at \(25^{\circ} \mathrm{C}\) are: - \(\mathrm{Li}(s): 3.57 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{g}^{-1}\) - \(\mathrm{Na}(s): 1.23 \, \mathrm{J} \, \mathrm{K}^{-1} \, \mathrm{g}^{-1}\) - \(\mathrm{K}(s): 0.756 \, \mathrm{J} \, Show more…

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Transcript

00:04 We're to show that the specific heat of an element is inversely related to its atomic weight.

00:11 So for part a, we're going to use the data from the front cover to plot a straight line graph relating atomic mass and specific heat and showing that this is an inverse relationship.

00:23 We'll pick several elements here.

00:25 Let's create a data table.

00:28 The elements that we'll choose are magnesium, aluminum, iron, copper, mercury, and lead.

00:44 The atomic weight, magnesium is 24 .3.

01:09 Aluminum, it's 26 .98.

01:13 Iron, 55 .84, 63 .55.

01:21 Mercury, 200 .59.

01:25 And lead, 207 .2.

01:28 Now we'll calculate 1 over the inverse of the, the atomic weight.

01:35 So one over the atomic weight.

01:40 This would give me 0 .04115 .0 .03706.

02:00 0 .11791 .1 .17574.

02:16 0 .00499 and 0 .00499 and 0 .00499 and 0 .00499.

02:25 The specific heat for each of these, we'll abbreviate that sh, 1 .023 for magnesium, 897 for aluminum, 0 .449 for iron, 0 .385 for copper, 0 .14 for mercury, and 0 .134 lead.

03:07 Lead.

03:09 Now from this data table, we're going to plot the specific heat versus the inverse of the atomic weight.

03:17 So we're going to plot the specific heat versus one over the inverse of the atomic weight.

03:25 And we're going to show that this is a, that specific heat is inversely related if we get a linear plot.

03:38 And our plot would look like.

03:41 This here.

03:46 So there is our plot of specific heat versus the inverse of atomic weight, and we do get a linear plot.

03:55 The equation of this straight line, using the proper variables, the equation of the line is the specific heat is equal to 24 .909, 1 over 8 .5 .8.

04:19 Aw plus 0 .0131.

04:25 And that would be part a...

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