Find the mass of `7 xx 10^(20)` molecules of `H_2`gas.

Answer

To find the mass of \( 7 \times 10^{20} \) molecules of \( H_2 \) gas, we can follow these steps:

### Step 1: Calculate the number of moles
To find the number of moles of \( H_2 \) gas, we use Avogadro's number, which is \( N_A = 6.022 \times 10^{23} \) molecules/mole. The formula to calculate moles (\( n \)) from the number of molecules (\( N \)) is:

\[ n = \frac{N}{N_A} \]

Substituting the values:

\[ n = \frac{7 \times 10^{20}}{6.022 \times 10^{23}} \]

### Step 2: Perform the calculation
Calculating the above expression:

\[ n \approx \frac{7}{6.022} \times 10^{20 - 23} = \frac{7}{6.022} \times 10^{-3} \approx 1.16 \times 10^{-2} \text{ moles} \]

### Step 3: Find the molar mass of \( H_2 \)
The molar mass of hydrogen gas (\( H_2 \)) is calculated as follows:

- The atomic mass of hydrogen (H) is approximately \( 1 \, \text{g/mol} \).
- Since \( H_2 \) consists of 2 hydrogen atoms, the molar mass of \( H_2 \) is:

\[ \text{Molar mass of } H_2 = 2 \times 1 \, \text{g/mol} = 2 \, \text{g/mol} \]

### Step 4: Calculate the mass
Now, we can calculate the mass (\( m \)) using the formula:

\[ m = n \times \text{Molar mass} \]

Substituting the values we found:

\[ m = 1.16 \times 10^{-2} \, \text{moles} \times 2 \, \text{g/mol} = 2.32 \times 10^{-2} \, \text{grams} \]

### Final Answer
The mass of \( 7 \times 10^{20} \) molecules of \( H_2 \) gas is approximately:

\[ \text{Mass} \approx 2.32 \times 10^{-2} \, \text{grams} \text{ or } 0.0232 \, \text{grams} \]

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