Question

15 sep interpret data the table shows the atomic radii and boiling points of five halogens that experience intermolecular dispersion forces. plot the boiling point vs. the atomic radius and use the resulting pattern to predict the boiling point of astatine.
atomic radius and boiling point
fluorine (f₂): atomic radius (pm) 72, boiling point (k) 85
chlorine (cl₂): atomic radius (pm) 99, boiling point (k) 238
bromine (br₂): atomic radius (pm) 114, boiling point (k) 332
iodine (i₂): atomic radius (pm) 133, boiling point (k) 457
astatine (at₂): atomic radius (pm) 150, boiling point (k)

Explanation:

Step1: Plot the data points

Plot the points \((72,85)\) for \(F_2\), \((99,238)\) for \(Cl_2\), \((114,332)\) for \(Br_2\), \((133,457)\) for \(I_2\) on a graph with atomic radius (pm) on the x - axis and boiling point (K) on the y - axis.

Step2: Analyze the trend

As the atomic radius increases, the boiling point also increases. The relationship appears to be approximately linear. We can calculate the slope between consecutive points.

• Between \(F_2\) and \(Cl_2\): Slope \(m_1=\frac{238 - 85}{99 - 72}=\frac{153}{27}\approx5.67\)
• Between \(Cl_2\) and \(Br_2\): Slope \(m_2=\frac{332 - 238}{114 - 99}=\frac{94}{15}\approx6.27\)
• Between \(Br_2\) and \(I_2\): Slope \(m_3=\frac{457 - 332}{133 - 114}=\frac{125}{19}\approx6.58\)

The slopes are increasing slightly, but for a rough prediction, we can use a linear regression - like approach. Using the two - point formula \(y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)\). Let's use the points \((133,457)\) (for \(I_2\)) and assume a similar rate of change.

Let \(x_1 = 133\), \(y_1=457\), \(x = 150\)

The average of the slopes \(m=\frac{5.67+6.27 + 6.58}{3}\approx6.17\)

Using the point - slope form \(y-457=6.17(x - 133)\)

Substitute \(x = 150\)

\(y-457=6.17\times(150 - 133)\)

\(y-457=6.17\times17\)

\(y-457 = 104.89\)

\(y=457+104.89=561.89\approx562\)

Answer:

The predicted boiling point of \(At_2\) is approximately \(562\) K.