- Identify the given mass \(m = 45.9\text{ g}\) and molar mass \(M = 18.02\text{ g/mol}\).
- Use the formula for moles: \(n = \frac{m}{M}\).
- Perform the calculation: \(n = \frac{45.9}{18.02} \approx 2.547\).
- Round the result to three significant figures to get \(\boxed{2.55}\text{ mol}\).
Explanation
- Problem Analysis and Objective
The objective is to find the number of moles of water present in a given mass of \(45.9\text{ g}\). We are provided with the molar mass of water, which is \(18.02\text{ g/mol}\). In chemistry, the number of moles \(n\) is related to the mass of the substance \(m\) and its molar mass \(M\) by the formula \(n = \frac{m}{M}\). Additionally, we must ensure our final answer respects the rules of significant figures. The mass \(45.9\text{ g}\) has three significant figures, and the molar mass \(18.02\text{ g/mol}\) has four. Therefore, our final result should be rounded to three significant figures.
- Calculating the Number of Moles
To calculate the number of moles of water, we substitute the given mass and molar mass into the formula:
\[n = \frac{45.9\text{ g}}{18.02\text{ g/mol}}\]
Performing the division, we obtain:
\[n \approx 2.5471698\text{ mol}\]
- Rounding and Final Answer
Having obtained the initial result of approximately \(2.5471698\text{ mol}\), we must now round it to the appropriate number of significant figures. As determined in our analysis, the final answer must have three significant figures. Looking at the fourth digit, which is \(7\), we round up the third digit (the \(4\)) to a \(5\). Thus, the number of moles is approximately \(2.55\text{ mol}\). Therefore, the number of moles of water is \(\boxed{2.55}\text{ mol}\).
Examples
Knowing how to calculate the number of moles is essential in chemistry for preparing chemical solutions. For instance, if you are working in a laboratory and need to prepare a specific reaction, you must know how much of a substance to add based on its molar mass. If a protocol requires you to use \(45.9\text{ g}\) of water for a specific reaction, this calculation ensures you know exactly how many moles are involved, allowing you to balance equations and predict product yields accurately. Understanding this conversion is a fundamental skill for anyone experimenting in the sciences.