The empirical mass of C$_6$H$_{12}$O$_6$ is  [H =1, C = 12, O = 16]

1. Analyze the Question

The question asks for the empirical mass of glucose ($C_6H_{12}O_6$). To find this, we must first determine the empirical formula of the compound and then calculate the sum of the atomic masses of the elements in that formula.

2. Explain the Concept

• Empirical Formula: This is the simplest whole-number ratio of atoms of each element in a compound.
• Molecular Formula: This shows the actual number of atoms of each element in a molecule. For glucose, the molecular formula is $C_6H_{12}O_6$.
• Empirical Mass: This is the molar mass calculated using the empirical formula.

3. Show the Solution

Step 1: Find the empirical formula. The molecular formula is $C_6H_{12}O_6$. To get the empirical formula, divide the subscripts by their greatest common divisor (which is 6):

• $C: 6/6 = 1$
• $H: 12/6 = 2$
• $O: 6/6 = 1$

The empirical formula is $CH_2O$.

Step 2: Calculate the empirical mass. Using the provided atomic masses ($C=12, H=1, O=16$):

• Mass of $C = 1 \times 12 = 12$
• Mass of $H = 2 \times 1 = 2$
• Mass of $O = 1 \times 16 = 16$

Total Empirical Mass = $12 + 2 + 16 = 30$

4. Identify the Answer

Comparing our result to the options provided: A. 90 B. 180 C. 45 D. 30

The correct option is D.

5. Tip

When asked for an empirical formula or mass, always look for the simplest ratio first. If you are given a molecular formula like $C_6H_{12}O_6$, just divide all the subscripts by the smallest number present (if possible) to quickly find the empirical unit. Remember: the molecular mass is always a multiple of the empirical mass ($Molecular\ Mass = n \times Empirical\ Mass$). In this case, $180 = 6 \times 30$.