Prepare a graph of specific heat capacities for metals...

Prepare a graph of specific heat capacities for metals versus their atomic weights. Combine the data in Figure 5.4 and the values in the following table. What is the relationship between specific heat capacity and atomic weight? Use this relationship to predict the specific heat capacity of platinum. The specific heat capacity for platinum is given in the literature as $0.133 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .$ How good is the agreement between the predicted and actual values? $$\begin{aligned} &\begin{array}{|l|c|} \hline & \text { Specific Heat Capacity } \\ \text { Metal } & (\mathrm{J} / \mathrm{g} \cdot \mathrm{K}) \\ \hline \text { Chromium } & 0.450 \\ \text { Lead } & 0.127 \\ \text { Silver } & 0.236 \\ \text { Tin } & 0.227 \\ \text { Titanium } & 0.522 \end{array}\\ &1 \end{aligned}$$

Prepare a graph of specific heat capacities for metals versus their atomic weights. Combine the data in Figure 5.4 and the values in the following table. What is the relationship between specific heat capacity and atomic weight? Use this relationship to predict the specific heat capacity of platinum. The specific heat capacity for platinum is given in the literature as $0.133 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .$ How good is the agreement between the predicted and actual values?
$$\begin{aligned}
&\begin{array}{|l|c|}
\hline & \text { Specific Heat Capacity } \\
\text { Metal } & (\mathrm{J} / \mathrm{g} \cdot \mathrm{K}) \\
\hline \text { Chromium } & 0.450 \\
\text { Lead } & 0.127 \\
\text { Silver } & 0.236 \\
\text { Tin } & 0.227 \\
\text { Titanium } & 0.522
\end{array}\\
&1
\end{aligned}$$

Key Concepts

Specific Heat Capacity

This is a property of materials that measures the amount of heat required to raise the temperature of a unit mass by one degree Kelvin. In the context of the question, it serves as the dependent variable plotted against atomic weight to explore how a metal's intrinsic thermal properties relate to its atomic characteristics.

Atomic Weight

Atomic weight is a measure of the mass of atoms of an element, generally expressed in atomic mass units. It is used in the analysis as the independent variable to see how the mass of individual atoms influences the specific heat capacity in metals.

Graphical Analysis and Trend Identification

Plotting specific heat capacity versus atomic weight allows for visual identification of any trends or relationships between these two variables. Graphical representation is a powerful tool in experimental science for detecting correlations that can hint at underlying physical principles.

Extrapolation and Prediction

Once a relationship between atomic weight and specific heat capacity is established through data plotting, this relationship can be used to predict unknown values. Extrapolation involves extending the established trendline to estimate the specific heat capacity of metals like platinum, based on its atomic weight.

Assessment of Agreement (Validation)

Comparing the predicted specific heat capacity of platinum to literature values is essential for validating the relationship and the model used. This step involves evaluating how closely the predicted value matches the experimentally or literature-determined value, thereby testing the reliability and accuracy of the predictive approach.

Transcript

00:01 So for this question we're asked to make a graph showing the relationship between the specific heat of metals and their atomic weight.

00:10 So we'll make a graph, we have our x -axis and our y -axis.

00:16 On the bottom we'll put our specific heat, which looks like it ranges from 0 .1 to 0 .5.

00:32 So all right, well here this is our zero.

00:36 Let's just go by tenths.

00:42 So we'll have 0 .1, 0 .2, 0 .3, 0 .4, 0 .5.

00:52 Which if you make this graph in excel you can always break it up into much more smaller units right between those.

01:03 Then on the y -axis we'll put the atomic weight or the atomic mass, which if you look these up the smallest one is titanium, which has a molar mass of 47 .88 and the largest one, lead, is 207 .2.

01:26 So we need to make this go up to 207 grams.

01:31 So these units are going to be grams per mole.

01:35 So let's just go by 50s.

01:37 So we have 50, 100, 150, 200.

01:45 So again if have this in excel you can always make it break it down even to further increments.

01:52 So let's plot our metals.

01:54 So we'll start with chromium.

01:59 Chromium has an atomic mass of 0 .45.

02:06 So it's and a molar mass or a specific heat of 0 .45 and a molar mass of 52 grams per mole.

02:15 So it's going to be right about here per chromium.

02:21 Next we have lead.

02:22 It has a specific heat of 0 .125 and weighs 207 .2 grams per mole.