Problem 9 - General Chemistry

Question

A beaker weighed \(50.90 \mathrm{~g}\). To the beaker was added \(5.680 \mathrm{~g}\) of iron pellets and \(53.3 \mathrm{~g}\) of hydrochloric acid. What was the total mass of the beaker and the mixture (before reaction)? Express the answer to the correct number of significant figures.

Step-by-Step Solution

Answer

The total mass is 109.9 g.

Step 1: Identify Given Values

First, note the given masses: the mass of the beaker is \(50.90 \, \text{g}\), the mass of the iron pellets is \(5.680 \, \text{g}\), and the mass of hydrochloric acid is \(53.3 \, \text{g}\).

Step 2: Calculate Total Mass

To find the total mass, we need to sum the mass of the beaker, the mass of the iron pellets, and the mass of the hydrochloric acid. The calculation is:\[ \text{Total mass} = 50.90 \, \text{g} + 5.680 \, \text{g} + 53.3 \, \text{g} \]

Step 3: Perform the Addition

Add the three values together: \(50.90 + 5.680 + 53.3 = 109.88 \, \text{g}\).

Step 4: Determine Significant Figures

The masses are given with different numbers of decimal places: \(50.90\) (3 decimal places), \(5.680\) (3 decimal places), and \(53.3\) (1 decimal place). The result should have as many decimal places as the quantity with the least number of decimal places, which is 1 decimal place.

Step 5: Round to Correct Significant Figures

Round \(109.88 \, \text{g}\) to 1 decimal place, which gives \(109.9 \, \text{g}\).

Key Concepts

Mass Calculation

Understanding how to calculate total mass is crucial in chemistry. When you have multiple components, you simply add their individual masses to find a collective total. In the given exercise, we had three components to consider: the beaker, iron pellets, and hydrochloric acid. Each had a distinct mass as follows: \(50.90 \, \text{g}\) for the beaker, \(5.680 \, \text{g}\) for iron, and \(53.3 \, \text{g}\) for the acid.

To find the total mass of the mixture before the reaction took place, we perform a straightforward addition:

\[ \text{Total mass} = 50.90 \, \text{g} + 5.680 \, \text{g} + 53.3 \, \text{g} = 109.88 \, \text{g} \]

This step ensures you incorporate all components into your calculation. Only with this careful summation can you accurately compute total mass for any process, product, or reaction you're considering in stoichiometry.

Rounding Rules

Rounding to significant figures is a core step when dealing with precise measurements. It ensures that results are reported consistently and without implying too great a level of accuracy.

• The exercise included masses with different levels of precision: \(50.90\) and \(5.680\) with three decimal places, and \(53.3\) with one.


• According to the rounding rule for addition, your final answer should have the same number of decimal places as the least precise measurement.

For this problem, note that 53.3, having a single decimal place, dictates the precision of the final total mass. After calculating the total mass, you must round \(109.88\) to one decimal place. Therefore, the rounded value is \(109.9 \, \text{g}\).

This consistency maintains clarity, especially in stoichiometry, where precise mass values are crucial for reaction calculations.

Stoichiometry

Stoichiometry is the foundation for understanding how ingredients of a chemical reaction relate to one another through their masses. Though the problem at hand did not involve the entirety of a stoichiometric process (like calculating moles or reacting ratios), accurate initial mass calculations are essential.

• By knowing the initial mass, you prepare for further steps in a reaction analysis, such as converting masses into moles using molar masses.
• Accurate total mass calculations help to correctly predict the yield of products or find out limiting reactants.

Despite being a preliminary step, calculating initial mass with proper significant figures is vital for reliability in results. This discipline ensures that any subsequent stoichiometric analyses align correctly with the actual conditions and behaviors observed in lab settings.