Question

What is the mass change in \(\mathrm{g} / \mathrm{mol}\) of \(\mathrm{NaCl}\) for the reaction of sodium metal with chlorine gas \(\left(\mathrm{Cl}_{2}\right)\) to give sodium chloride? $$ 2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NaCl}(s) \quad \Delta E=-820 \mathrm{~kJ} $$

Short answer

The mass change is 0 g/mol.

Step-by-step solution

Identify the Reactants and Products

The chemical reaction given is \( 2 \text{Na}(s) + \text{Cl}_2(g) \to 2 \text{NaCl}(s) \). The reactants are sodium metal (\( \text{Na} \)) and chlorine gas (\( \text{Cl}_2 \)), and the product is sodium chloride (\( \text{NaCl} \)).

Determine Molar Masses

Calculate the molar masses of the reactants and products. The molar mass of \( \text{Na} \) is approximately 23 g/mol, \( \text{Cl}_2 \) is approximately 71 g/mol, and \( \text{NaCl} \) is approximately 58.5 g/mol.

Calculate Total Molar Mass of Reactants

In the reaction, 2 moles of \( \text{Na} \) are used, each with a molar mass of 23 g/mol, totaling \( 2 \times 23 = 46 \) g/mol. The molar mass of \( \text{Cl}_2 \) is 71 g/mol. Therefore, the total molar mass of reactants is \( 46 + 71 = 117 \) g/mol.

Calculate Total Molar Mass of Products

The reaction produces 2 moles of \( \text{NaCl} \), with each mole having a molar mass of 58.5 g/mol. Therefore, the total molar mass of the products is \( 2 \times 58.5 = 117 \) g/mol.

Determine Mass Change

The total molar mass of the reactants and products are both 117 g/mol. Therefore, the mass change in \( \mathrm{g/mol} \) for the reaction is \( 117 - 117 = 0 \).

Conclusion

The reaction of sodium metal with chlorine gas to produce sodium chloride results in no change in mass per mole.

Key concepts

Molar Mass Calculation

Understanding the concept of molar mass is crucial for analyzing any chemical reaction. Each element has a specific molar mass, which is the mass of one mole of its atoms. It's usually expressed in grams per mole (g/mol).
In the context of the reaction where sodium (\(\text{Na}\)) reacts with chlorine gas (\(\text{Cl}_2\)) to form sodium chloride (\(\text{NaCl}\)), molar mass allows us to quantify the reactants and products involved.

• Sodium (\(\text{Na}\)) has a molar mass of approximately 23 g/mol.
• Chlorine as a diatomic gas (\(\text{Cl}_2\)) has a molar mass of approximately 71 g/mol.
• Sodium chloride (\(\text{NaCl}\)) has a molar mass of approximately 58.5 g/mol.

Calculating these values helps us understand the scale of chemical reactions by knowing exactly how much of each substance is involved in a mole-to-mole interaction.

Mass Change in Reactions

In chemical reactions, the principle of conservation of mass implies that the total mass of reactants should equal the total mass of products. This principle helps us determine if there is any mass change during a reaction.
In the specific reaction between sodium and chlorine to form sodium chloride, we start by calculating the total molar mass of the reactants:

• 2 moles of sodium: \[2 \times 23 = 46 \text{ g/mol}\]
• 1 mole of chlorine gas: \[71 \text{ g/mol}\]

Thus, the total molar mass of reactants is \(46 + 71 = 117 \text{ g/mol}\).
For the products:

• 2 moles of sodium chloride: \[2 \times 58.5 = 117 \text{ g/mol}\]

Hence, the total molar mass of products is also 117 g/mol.
The mass change is calculated as follows:
\[ \text{Mass change} = 117 - 117 = 0 \text{ g/mol} \]
This means there is no mass change, confirming the conservation of mass in this reaction.

Enthalpy Change

In addition to examining mass changes, chemical reactions are often analyzed for enthalpy change, which reflects the energy change during the reaction. Enthalpy change is typically represented by the symbol \(\Delta E\).
In our reaction of sodium with chlorine gas, the enthalpy change is given as \(-820 \text{ kJ}\). This negative value indicates that the reaction is exothermic, meaning it releases energy to the surroundings. In this case, 820 kJ of energy is released per mole of reaction as heat when sodium chloride forms.
Understanding enthalpy change is crucial for:

• Predicting the energy requirements or output of chemical processes.
• Evaluating reaction safety, especially in industrial processes.
• Designing chemical reactions for energy efficiency.

Thus, recognizing the enthalpy change helps in understanding the broader implications of a chemical reaction beyond just the transformation of reactants to products.