Verified Answer :
- Determine the mass of the water sample using the given volume and density: \(m = 45.0 \text{ g}\).
- Calculate the number of moles of water using its molar mass: \(n \approx 2.4979 \text{ mol}\).
- Determine the number of water molecules by multiplying the moles by Avogadro's number: \(N_{\text{molecules}} \approx 1.5042 \times 10^{24}\).
- Multiply by 2 to find the total number of hydrogen atoms: \(\boxed{3.01 \times 10^{24}}\).
Explanation
- Mass and Molar Mass Calculation
To find the total number of hydrogen atoms in 45.0 mL of liquid water, we first determine the mass of the water sample using its density. Given a volume \(V = 45.0 \text{ mL}\) and a density \(\rho = 1.00 \text{ g/mL}\), the mass \(m\) is:
\[m = \rho \times V = 1.00 \text{ g/mL} \times 45.0 \text{ mL} = 45.0 \text{ g}\]
The molar mass \(M\) of water (\(H_2O\)) is the sum of the atomic masses of two hydrogen atoms and one oxygen atom:
\[M = 2 \times 1.008 \text{ g/mol} + 15.999 \text{ g/mol} = 18.015 \text{ g/mol}\]
Thus, the mass is 45.0 grams of water.
- Calculating Moles and Molecules
Next, we calculate the number of moles \(n\) of water present in the sample by dividing the total mass by the molar mass:
\[n = \frac{m}{M} = \frac{45.0 \text{ g}}{18.015 \text{ g/mol}} \approx 2.4979 \text{ mol}\]
Using Avogadro's constant \(N_A \approx 6.022 \times 10^{23} \text{ molecules/mol}\), we find the total number of water molecules \(N_{\text{molecules}}\):
\[N_{\text{molecules}} = n \times N_A = \left( \frac{45.0}{18.015} \right) \times 6.022 \times 10^{23} \text{ molecules} \approx 1.5042 \times 10^{24} \text{ molecules}\]
- Calculating Hydrogen Atoms and Conclusion
Since each molecule of water (\(H_2O\)) contains exactly 2 hydrogen atoms, we multiply the total number of water molecules by 2 to get the total number of hydrogen atoms (\(N_H\)):
\[N_H = N_{\text{molecules}} \times 2 \approx 1.5042 \times 10^{24} \times 2 \approx 3.0084 \times 10^{24}\]
Rounding to three significant figures (consistent with the initial volume of 45.0 mL), the total number of hydrogen atoms is approximately \(3.01 \times 10^{24}\).
\[\boxed{3.01 \times 10^{24}}\]
Examples
In chemistry, understanding the relationship between macroscopic measurements like volume and microscopic counts like atoms is fundamental. For example, when creating a chemical reaction, calculating the precise number of atoms allows scientists to balance equations perfectly and predict the amount of product formed. This skill is vital for everything from manufacturing pharmaceuticals to refining materials for electronics and understanding the composition of the universe.