The number of hydrogen atoms in 60 u of ethane is____________

Answer

To find the number of hydrogen atoms in 60 u of ethane (C2H6), we can follow these steps:

### Step 1: Determine the Molar Mass of Ethane
The molecular formula of ethane is C2H6. To calculate its molar mass:
- Carbon (C) has an atomic mass of approximately 12 u.
- Hydrogen (H) has an atomic mass of approximately 1 u.

Calculating the molar mass:
\[ \text{Molar mass of ethane} = (2 \times 12) + (6 \times 1) = 24 + 6 = 30 \text{ u} \]

### Step 2: Calculate the Number of Moles of Ethane in 60 u
To find the number of moles of ethane in 60 u, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{60 \text{ u}}{30 \text{ u}} = 2 \text{ moles} \]

### Step 3: Determine the Number of Hydrogen Atoms in 2 Moles of Ethane
From the molecular formula C2H6, we see that each mole of ethane contains 6 hydrogen atoms. Therefore, in 1 mole of ethane, there are:
\[ 6 \text{ hydrogen atoms} \]
For 2 moles of ethane:
\[ \text{Number of hydrogen atoms} = 2 \text{ moles} \times 6 \text{ hydrogen atoms/mole} = 12 \text{ hydrogen atoms} \]

### Step 4: Convert Hydrogen Atoms to Actual Number of Atoms
To find the actual number of hydrogen atoms, we multiply by Avogadro's number (\(N_A = 6.022 \times 10^{23}\)):
\[ \text{Total hydrogen atoms} = 12 \times N_A = 12 \times 6.022 \times 10^{23} \]
Calculating this gives:
\[ \text{Total hydrogen atoms} = 72.264 \times 10^{23} \approx 7.2264 \times 10^{24} \text{ hydrogen atoms} \]

### Final Answer
The number of hydrogen atoms in 60 u of ethane is approximately \(7.224 \times 10^{24}\).

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