Problem 9 - General Chemistry: Principles and Modern Applications

Question

In one experiment, 2.18 g sodium was allowed to react with \(16.12 \mathrm{g}\) chlorine. All the sodium was used up, and 5.54 g sodium chloride (salt) was produced. In a second experiment, 2.10 g chlorine was allowed to react with \(10.00 \mathrm{g}\) sodium. All the chlorine was used up, and 3.46 g sodium chloride was produced.Show that these results are consistent with the law of constant composition.

Step-by-Step Solution

Answer

The percentages by mass of sodium and chlorine in sodium chloride for Experiment 1 are approximately 39.35% and 60.65%, respectively. For Experiment 2, these values are approximately 39.31% and 60.69% respectively. This shows that the results are consistent with the law of constant composition.

Step 1: Calculating the mass of Chlorine in Experiment 1

From Experiment 1, the mass of sodium chloride produced is 5.54 g and the mass of sodium used up is 2.18 g. To get the mass of chlorine, subtract the mass of sodium from the total mass of sodium chloride, i.e., \(5.54 - 2.18 = 3.36\) g.

Step 2: Calculating the percentages of Sodium and Chlorine in Experiment 1

The percentage of sodium (by mass) in the compound is given as \(\frac{2.18}{5.54} \times 100 = 39.35 \% \). The percentage of chlorine (by mass) in the compound is \(\frac{3.36}{5.54} \times 100 = 60.65 \% \).

Step 3: Calculating the mass of Sodium in Experiment 2

From Experiment 2, the mass of sodium chloride produced is 3.46 g and the mass of chlorine used up is 2.10 g. The mass of sodium is found by subtracting the mass of chlorine from the total mass of sodium chloride, i.e., \(3.46 - 2.10 = 1.36\) g.

Step 4: Calculating the percentages of Sodium and Chlorine in Experiment 2

The percentage of sodium (by mass) in the compound is \(\frac{1.36}{3.46} \times 100 = 39.31 \% \). The percentage of chlorine (by mass) in the compound is \(\frac{2.10}{3.46} \times 100 = 60.69 \% \).

Step 5: Comparing the Results

The percentages by mass of sodium and chlorine in sodium chloride are approximately the same in both experiments. This shows that the results are consistent with the law of constant composition.

Key Concepts

Chemical Reactions

Chemical reactions are processes where substances, called reactants, transform into new substances, known as products. During a chemical reaction, the atoms are rearranged to form new compounds. This is what happened in our sodium and chlorine experiments, where they reacted to form sodium chloride. Here are some key points:

• Nature of Reactants: Sodium and chlorine, both highly reactive elements, were the starting materials.
• Formation of Products: The combination of sodium and chlorine atoms resulted in the formation of sodium chloride, a stable compound.
• Mass Conservation: According to the law of conservation of mass, the total mass of reactants equals the mass of the products. This principle was evident as all the sodium and chlorine were accounted for in sodium chloride formation.

Understanding chemical reactions helps us predict the quantities and identities of the products we can expect from given reactants.

Sodium Chloride

Sodium chloride, often known as table salt, is the compound formed when sodium and chlorine react. It exemplifies the specific ratio in which these elements combine and follows the law of constant composition. Here are some insights into sodium chloride:

• Composition: It consists of equal numbers of sodium ions (Na⁺) and chloride ions (Cl^-) in a lattice structure.
• Physical Properties: Sodium chloride is known for its white, crystalline appearance and solubility in water.
• Stability: The ionic bond between sodium and chlorine makes it stable and ubiquitous in our daily lives, from seasoning food to use in industry.

This compound shows how individual elements lose their properties and form a completely new substance with its set of characteristics.

Percentage Composition Analysis

Percentage composition analysis involves calculating the percent by mass of each element in a compound, providing insight into the formula and makeup. In the experiments, we used this technique to verify the law of constant composition through the following steps:

• Calculation: We determined the mass of each element in the total compound mass. For example, in experiment one, sodium's percentage was calculated as \(\frac{2.18}{5.54} \times 100\) which equals 39.35%.
• Comparison: By comparing the results from both experiments, despite different starting amounts, the percentage composition remained consistent. Sodium was about 39% and chlorine about 61%.
• Significance: This reveals that no matter the amount of each element used initially, the resulting compound maintains the same element ratio, reinforcing the law of constant composition.

Applying percentage composition analysis certifies that compounds are formed in definite proportions by mass, vital in chemistry for understanding substance formation.