Problem 93 - Chemistry

Question

Sodium (Na) metal undergoes a chemical reaction with chlorine (Cl) gas to yield sodium chloride, or common table salt. If \(1.00 \mathrm{~g}\) of sodium reacts with \(1.54 \mathrm{~g}\) of chlorine, \(2.54 \mathrm{~g}\) of sodium chloride is formed and \(17.9 \mathrm{~kJ}\) of heat is released. How much sodium and how much chlorine in grams would have to react to release 171 kcal of heat?

Step-by-Step Solution

Answer

To release 171 kcal, 40.05 g of sodium and 61.677 g of chlorine are needed.

Step 1: Understand the Reaction Make-Up

The chemical reaction for forming sodium chloride from sodium metal and chlorine gas is \( 2 \text{Na} + \text{Cl}_2 \rightarrow 2 \text{NaCl} \). This reaction releases heat, and we are given that \( 17.9 \text{ kJ} \) is released when \( 1.00 \text{ g} \) of Na reacts with \( 1.54 \text{ g} \) of Cl, producing \( 2.54 \text{ g} \) of NaCl. We must determine how much of each ingredient is required to release \( 171 \text{ kcal} \).

Step 2: Convert Energy Units

Convert \( 171 \text{ kcal} \) into kilojoules since 1 kcal = 4.184 kJ. Therefore, \( 171 \text{ kcal} \times 4.184 = 716.664 \text{ kJ} \). So, the task is to find the amount of Na and Cl needed to release \( 716.664 \text{ kJ} \).

Step 3: Find the Reaction Scaling Factor

The initial reaction releases \( 17.9 \text{ kJ} \). We need to scale this to match \( 716.664 \text{ kJ} \). Divide \( 716.664 \text{ kJ} \) by \( 17.9 \text{ kJ} \) to find the factor: \( \frac{716.664}{17.9} \approx 40.05 \). Thus, the reaction needs to occur approximately \( 40.05 \) times.

Step 4: Calculate Required Sodium Mass

From the initial reaction, \( 1.00 \text{ g} \) of Na releases \( 17.9 \text{ kJ} \). Multiply the mass of Na by the scaling factor: \( 1.00 \text{ g} \times 40.05 = 40.05 \text{ g} \). Hence, \( 40.05 \text{ g} \) of Na is required.

Step 5: Calculate Required Chlorine Mass

Similarly, for Cl, \( 1.54 \text{ g} \) of Cl releases \( 17.9 \text{ kJ} \). Multiply by the factor: \( 1.54 \text{ g} \times 40.05 \approx 61.677 \text{ g} \). Therefore, \( 61.677 \text{ g} \) of Cl is required.

Step 6: Solution Verification

Calculate the total mass of sodium chloride that will be formed. The masses of the reactants are \( 40.05 \text{ g} \) of Na and \( 61.677 \text{ g} \) of Cl, totaling \( 101.727 \text{ g} \) of NaCl formed. Verify against similar calculations or known energy values if needed.

Key Concepts

Chemical Reactions

Chemical reactions are processes where substances are transformed into different materials, releasing or absorbing energy in the process. In the case of sodium chloride formation, sodium (Na) metal reacts with chlorine gas (Cl\(_2\)) to form sodium chloride (NaCl), a staple in our kitchens.
This specific reaction can be represented by the balanced equation: \[ 2 \text{Na} + \text{Cl}_2 \rightarrow 2 \text{NaCl} \] The balanced equation tells us that two atoms of sodium react with one molecule of chlorine to form two formula units of sodium chloride.
This transformation is not just a new chemical arrangement, but it also involves the release of energy, identifying it as an exothermic process.
Understanding these basics allows us to predict how substances will interact and the type of energy exchange involved.

Energy Conversion

Energy conversion is an essential aspect of understanding chemical reactions, especially in regards to stoichiometry.
In our sodium chloride reaction, we see energy released in the form of heat when sodium and chlorine combine.

• The chemical reaction releases 17.9 kJ of energy for every 1.00 g of Na and 1.54 g of Cl reacting.
• Energy is given in kilojoules (kJ) in the problem, but sometimes it’s necessary to convert energy units for comparison or further calculations.

For instance, in this exercise, 171 kcal needs converting to kJ since 1 kcal is equal to 4.184 kJ. Therefore, we have:
\(171 \text{kcal} \times 4.184 = 716.664 \text{kJ}\).
By understanding energy conversions, we can predict the energy demands or outputs for larger-scale chemical reactions.

Reaction Scaling

Reaction scaling refers to adjusting quantities of reactants and products in a chemical reaction based on a specified condition, such as energy released.
In our sodium chloride problem:

• The initial reaction releases 17.9 kJ with given amounts of Na and Cl.
• To find how much Na and Cl is needed to release 716.664 kJ, we determine a scaling factor.

This scaling factor is calculated by dividing the desired energy by the energy released in the standard reaction:\[\frac{716.664 \text{kJ}}{17.9 \text{kJ}} \approx 40.05\]This means the reaction must happen roughly 40.05 times more to meet the energy requirement.
Scaling reactions helps chemists understand how to manipulate quantities in industrial applications or prepare solutions for different experimental conditions.

Sodium Chloride Formation

Sodium chloride formation is a classic example of a chemical reaction that yields a compound we commonly use.
During this process:

• Sodium (Na), a soft, highly reactive metal, reacts with chlorine (Cl\(_2\)), a toxic yellow-green gas.
• The result is sodium chloride (NaCl), or table salt, a non-toxic crystalline compound.

The reaction can be visually understood as breaking and forming bonds:\[ 2 \text{Na} (s) + \text{Cl}_2 (g) \rightarrow 2 \text{NaCl} (s) \]Here, sodium atoms donate electrons to chlorine, forming ionic bonds. This results in a stable compound that is energetically favorable and releases energy upon formation.
By understanding the formation and scaling of this reaction, we can manipulate conditions to produce desired amounts of NaCl efficiently.