if there are n molecules in 10.0g of hydrogen gas, how many molecules are there in 110g of carbon dioxide gas? 

A: 0.25n
B: 0.5n
C: 2n
D: 4n 

which option is correct? show workings and explain

To solve this problem, we need to compare the number of molecules in two different samples of gases: hydrogen gas (\(\text{H}_2\)) and carbon dioxide (\(\text{CO}_2\)).

### Step 1: Determine the number of moles in 10.0 g of hydrogen gas

1. **Molar mass of hydrogen gas (\(\text{H}_2\)):**
   - Hydrogen (\(\text{H}\)) has a molar mass of approximately \(1.0 \, \text{g/mol}\).
   - Therefore, the molar mass of \(\text{H}_2\) is \(2.0 \, \text{g/mol}\).

2. **Calculate the number of moles in 10.0 g of \(\text{H}_2\):**
   \[
   \text{Number of moles of } \text{H}_2 = \frac{10.0 \, \text{g}}{2.0 \, \text{g/mol}} = 5.0 \, \text{mol}
   \]

3. **Number of molecules:**
   If there are \(n\) molecules in 10.0 g of hydrogen gas, this corresponds to 5.0 moles of \(\text{H}_2\).

### Step 2: Determine the number of moles in 110 g of carbon dioxide gas

1. **Molar mass of carbon dioxide (\(\text{CO}_2\)):**
   - Carbon (\(\text{C}\)) has a molar mass of approximately \(12.0 \, \text{g/mol}\).
   - Oxygen (\(\text{O}\)) has a molar mass of approximately \(16.0 \, \text{g/mol}\).
   - Therefore, the molar mass of \(\text{CO}_2\) is:
     \[
     \text{Molar mass of } \text{CO}_2 = 12.0 \, \text{g/mol} + 2 \times 16.0 \, \text{g/mol} = 44.0 \, \text{g/mol}
     \]

2. **Calculate the number of moles in 110 g of \(\text{CO}_2\):**
   \[
   \text{Number of moles of } \text{CO}_2 = \frac{110 \, \text{g}}{44.0 \, \text{g/mol}} = 2.5 \, \text{mol}
   \]

### Step 3: Compare the number of molecules
- The number of molecules is directly proportional to the number of moles. 

- The ratio of moles of \(\text{CO}_2\) to moles of \(\text{H}_2\) is:
  \[
  \text{Ratio} = \frac{2.5 \, \text{mol}}{5.0 \, \text{mol}} = 0.5
  \]

Thus, the number of molecules in 110 g of \(\text{CO}_2\) is \(0.5n\).

### Final Answer
The correct option is **B: 0.5n**.

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### Related Questions:
1. What would be the number of molecules in 220 g of \(\text{CO}_2\)?
2. How would the number of molecules change if we had 20 g of \(\text{H}_2\) instead?
3. What is the significance of Avogadro's number in these calculations?
4. How would you calculate the number of atoms in 10 g of \(\text{H}_2\)?
5. If the mass of \(\text{H}_2\) was reduced to 5 g, how many molecules would be present?

**Tip:** Remember that the number of molecules is directly proportional to the number of moles, which in turn is proportional to the mass divided by the molar mass.

Explore how to calculate the number of molecules in 110 grams of carbon dioxide compared to 10.0 grams of hydrogen gas. This problem involves using the mole concept and stoichiometry in chemistry. Learn step-by-step with formulas and calculations. Suitable for advanced high school students.

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