A student proposes the following hypothesis regarding the thermal stability of Group 2 met… — ACT

A student proposes the following hypothesis regarding the thermal stability of Group 2 metal carbonates:

*Hypothesis*: The decomposition temperature of a Group 2 metal carbonate is directly proportional to the charge density of its metal cation. Because charge density decreases as ionic radius increases, metal carbonates with larger metal cations will decompose at lower temperatures.

A chemist conducts an experiment to test this hypothesis by measuring the decomposition temperature ( $T_d$ , the temperature at which the carbonate decomposes into a metal oxide and carbon dioxide) of four Group 2 metal carbonates. The results are shown in Table 1.

### Table 1

Metal Carbonate	Metal Cation	Cation Ionic Radius ( $\text{pm}$ )	Decomposition Temperature ( $^\circ\text{C}$ )
$\text{MgCO}_3$	$\text{Mg}^{2+}$	72	350
$\text{CaCO}_3$	$\text{Ca}^{2+}$	100	825
$\text{SrCO}_3$	$\text{Sr}^{2+}$	118	1,100
$\text{BaCO}_3$	$\text{Ba}^{2+}$	135	1,360

Based on Table 1, is the student's hypothesis supported by the experimental results, and how should the hypothesis be modified?

A
Yes; the data show that as the ionic radius of the metal cation increases, the decomposition temperature also increases.
No; the hypothesis should be modified to state that as the ionic radius of the metal cation increases, the decomposition temperature increases.Answer
C
No; the hypothesis should be modified to state that the decomposition temperature of a Group 2 metal carbonate is independent of the metal cation's ionic radius.
D
Yes; the data show that $\text{MgCO}_3$ , which contains the metal cation with the highest charge density, decomposes at the lowest temperature.

Answer

The student's hypothesis is not supported because the experimental data show that as the ionic radius of the metal cation increases, the decomposition temperature increases. Therefore, the hypothesis should be modified to state that as the ionic radius of the metal cation increases, the decomposition temperature increases.

The experimental results show that as the ionic radius increases, the decomposition temperature increases. This trend is the opposite of the student's prediction that larger cations would decompose at lower temperatures. Thus, the hypothesis is not supported and must be modified to state that as the ionic radius of the metal cation increases, the decomposition temperature increases.

Step-by-Step Solution

Determine the prediction made by the student's hypothesis.

The student predicted that since charge density decreases as ionic radius increases, larger metal cations would lead to lower decomposition temperatures (an inverse relationship between ionic radius and decomposition temperature).

To evaluate a hypothesis, we must first clearly define the relationship it predicts.

Analyze the experimental data in Table 1 to identify the actual trend.

As the ionic radius of the cation increases from

72\text{ pm}

(

\text{Mg}^{2+}

) to

135\text{ pm}

(

\text{Ba}^{2+}

), the decomposition temperature increases from

350\ ^\circ\text{C}

1,360\ ^\circ\text{C}

(a direct relationship).

This establishes the empirical relationship demonstrated by the experiment.

Compare the predicted trend with the observed trend.

The observed direct relationship is the opposite of the predicted inverse relationship, meaning the hypothesis is not supported.

Comparing predictions with actual data determines whether the hypothesis is supported or refuted.

Formulate the correct modification to the hypothesis.

The hypothesis should be modified to state that as the ionic radius of the metal cation increases, the decomposition temperature increases.

Modifying a refuted hypothesis requires aligning it with the experimental evidence.

Key Concept

Evaluating and modifying a hypothesis based on empirical data trends

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