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Let's go through the given problem step by step.

We are provided:
- The mass of a hydrogen atom: \( 1.67 \times 10^{-24} \) grams.
- The mass of an oxygen atom: \( 2.66 \times 10^{-23} \) grams.
- A water molecule contains 2 hydrogen atoms and 1 oxygen atom.

### Part a) Calculate the mass of one molecule of water.

The mass of one water molecule is the sum of the masses of its atoms:
\[
\text{Mass of H}_2\text{O} = (2 \times \text{mass of hydrogen}) + (1 \times \text{mass of oxygen})
\]
Substituting the given values:
\[
\text{Mass of H}_2\text{O} = (2 \times 1.67 \times 10^{-24}) + (2.66 \times 10^{-23})
\]
\[
\text{Mass of H}_2\text{O} = 3.34 \times 10^{-24} + 2.66 \times 10^{-23}
\]
To add these, we rewrite them with the same exponent:
\[
3.34 \times 10^{-24} = 0.334 \times 10^{-23}
\]
\[
\text{Mass of H}_2\text{O} = 0.334 \times 10^{-23} + 2.66 \times 10^{-23}
\]
\[
\text{Mass of H}_2\text{O} = 2.994 \times 10^{-23} \text{ grams.}
\]

### Part b) Calculate the number of molecules in 1 gram of water.

To find the number of water molecules in 1 gram of water:
\[
\text{Number of molecules} = \frac{1 \text{ gram}}{\text{mass of one water molecule}}
\]
Using the mass of one water molecule from part a):
\[
\text{Number of molecules} = \frac{1}{2.994 \times 10^{-23}}
\]
\[
\text{Number of molecules} \approx 3.34 \times 10^{22}.
\]

### Final answers:
- a) The mass of one water molecule is \( 2.994 \times 10^{-23} \) grams.
- b) The number of water molecules in 1 gram of water is approximately \( 3.34 \times 10^{22} \).

Would you like further details on any part of the solution?

### Follow-up questions:
1. How does the mass of hydrogen compare to that of oxygen in water?
2. What is the mass of 10 grams of water in terms of the number of molecules?
3. How does the calculation change if we consider the isotope deuterium instead of hydrogen?
4. What is the significance of standard form in scientific calculations?
5. Can we relate the number of molecules to Avogadro’s number?

### Tip:
When adding or subtracting numbers in scientific notation, ensure they have the same exponent for easier calculations.

The mass of a hydrogen atom is 1.67 × 10^(-24) grams. The mass of an oxygen atom is 2.66 × 10^(-23) grams. A molecule of water contains 2 atoms of hydrogen and 1 atom of oxygen. a) Calculate the mass of one molecule of water, giving your exact answer in standard form. b) Calculate the number of molecules in 1 gram of water, giving your answer in standard form to 3 significant figures.

Learn how to calculate the mass of one water molecule using scientific notation. This detailed solution covers basic arithmetic with exponents and explains how to find the number of molecules in 1 gram of water. Perfect for high school students studying chemistry and physics.

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