VIPSolutionsGive answer in 3 steps with explanation at the and of each step and final answer at the end The Dulong - Petit law states that heat capacities for most metals is about 2 4 . 9 J / ( mol K ) . An unknown metal has a heat capacity of 0 . 2 7 3 J / ( g K ) . What is the predicted atomic weight ( g / mol ) ? Round to the nearest whole number.
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Give answer in 3 steps with explanation at the and of each step and final answer at the end The Dulong - Petit law states that heat capacities for most metals is about 2 4 . 9 J / ( mol K ) . An unknown metal has a heat capacity of 0 . 2 7 3 J / ( g K ) . What is the predicted atomic weight ( g / mol ) ? Round to the nearest whole number.
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Asked by: Test User 100162
Created at: 2025-05-07 08:57:24
Asked by: Test User 100162
Created at: 2025-05-07 08:57:24
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**Step 1: Recall the Dulong-Petit Law and relate the given values.**
The Dulong-Petit Law states that the molar heat capacity for most metals is about **24.9 J/(mol·K)**. You are given the **specific heat capacity** (per gram) of the unknown metal:
\( c = 0.273\ \text{J/(g·K)} \)
**Step 2: Set up the relationship between specific heat and molar heat capacity.**
Molar heat capacity (\( C_m \)) relates to specific heat (\( c \)) and molar mass (\( M \)) as:
\( C_m = c \times M \)
Given \( C_m = 24.9\ \text{J/(mol·K)} \) and \( c = 0.273\ \text{J/(g·K)} \), solve for \( M \):
\( 24.9 = 0.273 \times M \)
**Step 3: Solve for the atomic weight (molar mass) and round to the nearest whole number.**
\( M = \frac{24.9}{0.273} \approx 91.2 \)
**Final Answer:**
**The predicted atomic weight is 91 g/mol.**
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