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Mass analysis of a common drying agent of organic molecules reveals that it has the empirical formula P2O5. If the molar mass is 283.89 g/mol, which molecular formula is correct?

Mass analysis of a common drying agent of organic molecules reveals that it has the empirical formula P2O5. If the molar mass is 283.89 g/mol, which molecular formula is correct?

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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### Determining the Molecular Formula from Empirical Formula and Molar Mass Mass analysis of a common drying agent of organic molecules reveals that it has the empirical formula \( P_2O_5 \). If the molar mass is 283.89 g/mol, which molecular formula is correct? - \(\quad\) \( P_2O_5 \) - \(\quad\) \( P_4O_{10} \) - \(\quad\) \( P_6H_{15} \) - \(\quad\) \( P_5O_6 \) - \(\quad\) \( P_3O_4 \) #### Explanation To determine the correct molecular formula, you divide the given molar mass by the molar mass of the empirical formula \( P_2O_5 \) and then use the resulting factor to scale the subscripts in the empirical formula. * **Step 1:** Calculate the molar mass of the empirical formula \( P_2O_5 \): - Phosphorus (P): \( 2 \times 30.97 \) g/mol - Oxygen (O): \( 5 \times 16.00 \) g/mol Molar mass of \( P_2O_5 \) = \( 2 \times 30.97 \) + \( 5 \times 16.00 \) = \( 61.94 \) + \( 80.00 \) = \( 141.94 \) g/mol * **Step 2:** Divide the given molar mass by the molar mass of the empirical formula: Scaling factor = \( \frac{283.89\ g/mol}{141.94\ g/mol} \approx 2 \) * **Step 3:** Multiply the subscripts in the empirical formula by this factor to get the molecular formula: Molecular formula = \( P_{2 \times 2}O_{5 \times 2} \) = \( P_4O_{10} \) Therefore, the correct molecular formula is **\( P_4O_{10} \)**.
Transcribed Image Text:### Determining the Molecular Formula from Empirical Formula and Molar Mass Mass analysis of a common drying agent of organic molecules reveals that it has the empirical formula \( P_2O_5 \). If the molar mass is 283.89 g/mol, which molecular formula is correct? - \(\quad\) \( P_2O_5 \) - \(\quad\) \( P_4O_{10} \) - \(\quad\) \( P_6H_{15} \) - \(\quad\) \( P_5O_6 \) - \(\quad\) \( P_3O_4 \) #### Explanation To determine the correct molecular formula, you divide the given molar mass by the molar mass of the empirical formula \( P_2O_5 \) and then use the resulting factor to scale the subscripts in the empirical formula. * **Step 1:** Calculate the molar mass of the empirical formula \( P_2O_5 \): - Phosphorus (P): \( 2 \times 30.97 \) g/mol - Oxygen (O): \( 5 \times 16.00 \) g/mol Molar mass of \( P_2O_5 \) = \( 2 \times 30.97 \) + \( 5 \times 16.00 \) = \( 61.94 \) + \( 80.00 \) = \( 141.94 \) g/mol * **Step 2:** Divide the given molar mass by the molar mass of the empirical formula: Scaling factor = \( \frac{283.89\ g/mol}{141.94\ g/mol} \approx 2 \) * **Step 3:** Multiply the subscripts in the empirical formula by this factor to get the molecular formula: Molecular formula = \( P_{2 \times 2}O_{5 \times 2} \) = \( P_4O_{10} \) Therefore, the correct molecular formula is **\( P_4O_{10} \)**.
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