Question

question 1
1 pts

what is the molecular formula of a compound given the molar mass of the compound is \\(186.5\text{ gram}\\) and the empirical formula is \\(\text{c}_2\text{h}_7\\)?

none of these
\\(\text{c}_3\text{h}_{21}\\)
\\(\text{c}_4\text{h}_{14}\\)
\\(\text{c}_2\text{h}_{14}\\)
\\(\text{c}_2\text{h}_7\\)

Explanation:

🆕 New Concept Discovered: Empirical to Molecular Formula Conversion
Scaling up the simplest ratio to match the actual mass

Step 1: Calculate the empirical formula mass

The empirical formula is \(\text{C}_2\text{H}_7\). We find its mass using the average atomic masses of carbon (\(\approx 12.011\text{ g/mol}\)) and hydrogen (\(\approx 1.008\text{ g/mol}\)):

$$ \text{Empirical Mass} = 2 \times 12.011\text{ g/mol} + 7 \times 1.008\text{ g/mol} $$

$$ \text{Empirical Mass} = 24.022 + 7.056 = 31.078\text{ g/mol} $$

Step 2: Determine the scaling factor

To find how many times larger the actual molecule is compared to its empirical formula, we divide the given molar mass of the compound by the empirical formula mass:

$$ n = \frac{\text{Molar Mass}}{\text{Empirical Mass}} = \frac{186.5\text{ g/mol}}{31.078\text{ g/mol}} \approx 6 $$

Step 3: Multiply the empirical subscripts

Multiply the subscripts in the empirical formula \(\text{C}_2\text{H}_7\) by the scaling factor \(n = 6\):

$$ \text{C}_{2 \times 6}\text{H}_{7 \times 6} = \text{C}_{12}\text{H}_{42} $$

Since \(\text{C}_{12}\text{H}_{42}\) is not listed among the multiple-choice options, the correct choice is "none of these".

Answer:

none of these