Can you use melting point to determine the identity of an unknown solid?
The metal is observed to begin to melt when the temperature of its container is approximately $29^{\circ} C$. The metal is most likely:
copper
lead
mercury
tin
gallium
| Substance | Melting Point |
|---|---|
| copper | $1,085^{\circ} C$ |
| lead | $327.5^{\circ} C$ |
| mercury | $-38.6^{\circ} C$ |
| tin | $232^{\circ} C$ |
| gallium | $29.78^{\circ} C$
Answer (2)
Compare the observed melting point ( 2 9 ∘ C ) with the melting points of the given metals.
Calculate the absolute differences between the observed melting point and each metal's melting point.
Identify the metal with the smallest absolute difference.
The metal with the melting point closest to 2 9 ∘ C is gallium, with a melting point of 29.7 8 ∘ C , so the answer is g a ll i u m .
Explanation
Problem Analysis We are given the melting point of an unknown metal as approximately 2 9 ∘ C . We need to identify the metal from the given options: copper, lead, mercury, tin, and gallium, using their respective melting points.
Listing Melting Points We have the following melting points for the given metals:
Copper: 108 5 ∘ C
Lead: 327. 5 ∘ C
Mercury: − 38. 6 ∘ C
Tin: 23 2 ∘ C
Gallium: 29.7 8 ∘ C We need to find the metal whose melting point is closest to the observed melting point of 2 9 ∘ C .
Calculating Differences Let's calculate the absolute differences between the observed melting point and the melting points of each metal:
Copper: ∣29 − 1085∣ = 1056
Lead: ∣29 − 327.5∣ = 298.5
Mercury: ∣29 − ( − 38.6 ) ∣ = ∣29 + 38.6∣ = 67.6
Tin: ∣29 − 232∣ = 203
Gallium: ∣29 − 29.78∣ = 0.78
Identifying the Metal Comparing the absolute differences, we see that the smallest difference is 0.78 , which corresponds to gallium. Therefore, the unknown metal is most likely gallium.
Examples
Melting points are crucial in various real-world applications. For example, in metallurgy, knowing the melting points of different metals helps in designing alloys with specific properties. In electronics, soldering involves using metals with low melting points to create electrical connections. Also, in geology, the melting points of rocks and minerals are important in understanding volcanic activity and the formation of the Earth's crust.
The unknown metal is most likely gallium, as its melting point of 29.7 8 ° C is closest to the observed melting point of 2 9 ° C . The calculations show that gallium has the smallest absolute difference in melting points compared to the other metals listed. Therefore, the answer is gallium.
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