- Identify the atomic masses of Na (\(22.99 \text{ g/mol}\)), O (\(16.00 \text{ g/mol}\)), and H (\(1.01 \text{ g/mol}\)).
- Calculate the molar mass of NaOH: \(M = 22.99 + 16.00 + 1.01 = 40.00 \text{ g/mol}\).
- Use the formula \(m = n \times M\) with \(n = 2.75 \times 10^{-4} \text{ mol}\) to find the mass: \(m = 2.75 \times 10^{-4} \times 40 = 1.10 \times 10^{-2} \text{ g}\).
- Conclude that the correct answer is \(d\), corresponding to \(\boxed{1.10 \times 10^{-2} \text{ g } NaOH}\).
Explanation
- Analysis of the Problem
To determine the mass of \(2.75 \times 10^{-4}\) moles of sodium hydroxide (NaOH), we need to relate the number of moles to the mass using the molar mass. The formula for mass is \(m = n \times M\), where \(n\) is the number of moles and \(M\) is the molar mass in grams per mole. The molar mass of a compound is the sum of the atomic masses of its constituent elements. For NaOH, the elements are sodium (Na), oxygen (O), and hydrogen (H). Using the standard atomic masses (Na: \(22.99 \text{ g/mol}\), O: \(16.00 \text{ g/mol}\), H: \(1.01 \text{ g/mol}\)), we can determine the molar mass of NaOH.
- Calculating Molar Mass of NaOH
The molar mass \(M\) of NaOH is calculated by summing the atomic masses of sodium, oxygen, and hydrogen:
\[M = 22.99 \text{ g/mol} + 16.00 \text{ g/mol} + 1.01 \text{ g/mol} = 40.00 \text{ g/mol}.\]
With the molar mass determined to be \(40.00 \text{ g/mol}\), we can proceed to calculate the total mass of the given substance.
- Calculating Mass and Selecting the Correct Option
Given the number of moles \(n = 2.75 \times 10^{-4} \text{ mol}\), we use the mass formula \(m = n \times M\):
\[m = (2.75 \times 10^{-4} \text{ mol}) \times (40.00 \text{ g/mol})\]
\[m = 2.75 \times 40.00 \times 10^{-4} \text{ g}\]
\[m = 110.00 \times 10^{-4} \text{ g} = 1.10 \times 10^{-2} \text{ g}.\]
The calculated mass is \(1.10 \times 10^{-2} \text{ g}\), which matches option (d).
Examples
In a chemical laboratory, knowing the exact mass of a substance is critical for experiments. For instance, when preparing a buffer solution, chemists often weigh precise amounts of bases like sodium hydroxide. By converting moles, which are used to represent chemical quantities, into grams, which can be measured on a balance, scientists ensure the accuracy and safety of their chemical reactions. Understanding this conversion is a fundamental skill in chemistry for preparing reagents for medical research or industrial processing.