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Let's solve this step by step:

### Given:
- Mass of a hydrogen atom = \( 1.67 \times 10^{-24} \, \text{g} \)
- Mass of a carbon atom = \( 1.99 \times 10^{-23} \, \text{g} \)
- Methane molecule consists of 4 hydrogen atoms and 1 carbon atom.

### Part (a): Calculate the mass of one molecule of methane.

To find the mass of one methane molecule, sum up the masses of the 4 hydrogen atoms and 1 carbon atom:

\[
\text{Mass of methane} = (4 \times \text{mass of hydrogen}) + (1 \times \text{mass of carbon})
\]
\[
\text{Mass of methane} = (4 \times 1.67 \times 10^{-24}) + (1.99 \times 10^{-23})
\]

Let me calculate that for you.The mass of one methane molecule is \( 2.658 \times 10^{-23} \, \text{grams} \).

### Part (b): Calculate the number of methane molecules in 1 gram of methane.

The number of molecules can be found using:

\[
\text{Number of molecules} = \frac{1 \, \text{gram}}{\text{mass of one molecule}}
\]

Substituting the mass of one methane molecule:

\[
\text{Number of molecules} = \frac{1}{2.658 \times 10^{-23}}
\]

Let me compute that for you.The number of methane molecules in 1 gram of methane is approximately \( 3.76 \times 10^{22} \).

Would you like further details or clarification?

### Related Questions:
1. What is the molecular formula of methane and why does it have 4 hydrogen atoms?
2. How would the mass of a larger hydrocarbon like ethane compare to methane?
3. What is the process for converting from mass to number of molecules in other elements or compounds?
4. How do Avogadro’s number and the mole concept relate to calculations like these?
5. How would the result change if the molecular composition of methane were different?

### Tip:
When solving for the number of molecules from mass, ensure that the units of mass match (grams, kilograms, etc.) to avoid calculation errors.

The mass of a hydrogen atom is 1.67 × 10^-24 grams. The mass of a carbon atom is 1.99 × 10^-23 grams. A molecule of methane contains 4 atoms of hydrogen and 1 atom of carbon. a) Calculate the mass of one molecule of methane, giving your exact answer in standard form. b) Calculate the number of molecules in 1 gram of methane, giving your answer in standard form to 3 significant figures.

Learn how to calculate the mass of one methane molecule and the number of molecules in 1 gram of methane using standard form. This problem involves key concepts like atomic mass, stoichiometry, and unit conversion. Ideal for students in Grades 10-12.

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