Answer:
1. Heat capacity: 24J/ºC. This is the full heat capacity. See below for explanation and the specific heat capacity.
2. The approximate molar mass is 25g/mol and the element is magnesium.
3. Tha calculations are limited to two significant figures for two reasons:
- i) the temperature difference 22.7ºC - 20.5ºC = 2.2ºC contains two significant figures, and
- ii) Dulong & Petit's Law is an approximation.
Step-by-step explanation:
1. Heat capacity
Assuming that the two metals are isolated from the surroundings, by the law of conservation of energy, the heat released by the hotter substance is equal to the heat absorbed by the colder substance:
- Heat released by the metal = Heat absorbed by water
Heat = mass × specific heat × change in temperature
Call Sh the specific heat:
93.3g × Sh × (98.6°C - 22.7°C) = 200.0g × 4.18 J/g°C × ( 22.7°C - 20.5°C)
Compute and clear Sh:
- Sh = 0.2597 g/J`C ≈ 0.26J/gºC
Notice that the temperature difference 22.7 - 20.5 = 2.2 only contains two significant figures which makes that your final calculation is limited to two significant figures.
The full heat capacity is the product of the specific heat capacity by the mass:
- Full heat capacity = 0.2597J/gºC × 93.3g ≈ 24 J/ºC ← answer
Note that the question is the heat capacity, not the specific heat capacity.
2. Approximate molar mass of the metal
Dulong & Petit's Law states an approximate form to estimate the molar mass of a solid by relating the specifig heat capacity and the molar mass:
- Specific heat capacity × molar mass ≈ 6.4
Then:
- Molar mass ≈ 6.4 / specific heat
- Molar mass ≈ 6.4 / 0.26 ≈ 24.6
Dulong&Petit's Law is just an approximation.
From a periodic table, the metal element whose atomic mass (the same as molar mass for elements) is closer to 25g/mol is magnesium, with an atomic mass of 24.3g/mol. Thus, your element most likely is magnesium.