- Use the formula \(\text{mass} = \text{moles} \times \text{molar mass}\) to calculate the mass.
- Multiply \(1.84 \text{ mol}\) by \(58.44 \text{ g/mol}\) to get \(107.5296 \text{ g}\).
- Identify that the result must have 3 significant figures based on the input \(1.84\).
- Round the result to 3 significant figures to get \(\boxed{108 \text{ g}}\).
Explanation
- Establishing the Relationship and Identifying Given Data
To determine the mass of a substance when the amount in moles and the molar mass are known, we use the fundamental chemical formula relating these quantities:
\[\text{mass (g)} = \text{amount (mol)} \times \text{molar mass (g/mol)}\]
Given the amount of NaCl is \(1.84 \text{ mol}\) and the molar mass of NaCl is \(58.44 \text{ g/mol}\), we can substitute these values into the equation:
\[\text{mass} = 1.84 \text{ mol} \times 58.44 \text{ g/mol}\]
- Performing the Calculation and Applying Significant Figures Rules
Performing the multiplication, we calculate:
\[1.84 \times 58.44 = 107.5296 \text{ g}\]
In scientific measurements, the number of significant figures in the result is determined by the precision of the input data. We are given:
- The amount \(1.84 \text{ mol}\) has 3 significant figures.
- The molar mass \(58.44 \text{ g/mol}\) has 4 significant figures.
According to the rules of significant figures for multiplication, the final result must be reported with the same number of significant figures as the value with the fewest significant figures, which in this case is 3.
- Rounding to Significant Figures and Final Answer
We need to round \(107.5296\) to 3 significant figures.
- The first three digits are 1, 0, and 7.
- The next digit is 5.
Following the rounding convention, because the first digit to be dropped is 5, we round up the preceding digit (7 becomes 8).
Therefore, \(107.5296\) rounded to three significant figures is \(108\).
The mass of \(1.84 \text{ mol NaCl}\) is \(\boxed{108 \text{ g}}\).
Examples
Calculating the mass of a substance is a routine task in laboratories for preparing solutions or performing chemical reactions. For example, if a chemist needs to create a specific concentration of a salt solution, they must calculate the exact mass of salt (NaCl) to weigh out based on the molar amount required for their experimental design. This ensures the accuracy and reproducibility of scientific results.