Question

How much heat in kilojoules is evolved or absorbed in the reaction of \(1.00 \mathrm{~g}\) of \(\mathrm{Na}\) with \(\mathrm{H}_{2} \mathrm{O}\) ? Is the reaction exothermic or endothermic? $$\begin{aligned}2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g) \\ \Delta H^{\circ} &=-368.4 \mathrm{~kJ}\end{aligned}$$

Short answer

The reaction releases 8.01 kJ of heat and is exothermic.

Step-by-step solution

Determine Moles of Na

First, find out how many moles of sodium (\(\mathrm{Na}\)) are in \(1.00\, \mathrm{g}\) of Na. Use the formula: \[ \text{Moles of Na} = \frac{\text{Mass}}{\text{Molar mass}} \] The molar mass of Na is \(22.99\, \mathrm{g/mol}\). So, the moles of Na are: \[ \text{Moles of Na} = \frac{1.00 \text{ g}}{22.99 \text{ g/mol}} \approx 0.0435 \text{ mol} \]

Calculate Heat Evolved or Absorbed

Next, calculate the heat change for the moles of \(\mathrm{Na}\) calculated in Step 1. The given enthalpy change is for the reaction of 2 moles of Na: \(\Delta H = -368.4 \text{ kJ} \) for 2 moles of Na. Therefore, for 1 mole of Na, the enthalpy change is: \(\Delta H = \frac{-368.4 \text{ kJ}}{2} = -184.2 \text{ kJ/mol} \). So for \(0.0435 \) moles: \[ \text{Heat change} = -184.2 \text{ kJ/mol} \times 0.0435 \text{ mol} = -8.01 \text{ kJ} \]

Determine Reaction Nature

Since the heat change is negative, \(-8.01 \text{ kJ}\), heat is released. Therefore, the reaction is exothermic.

Key concepts

Exothermic Reaction

In chemistry, reactions can either release or absorb energy, and these are termed exothermic or endothermic, respectively. An exothermic reaction is one that releases heat to its surroundings. This happens because the energy required to break bonds in the reactants is less than the energy released when new bonds form in the products.

When a reaction is exothermic, the temperature of the surroundings increases as heat is released. In the given exercise, the reaction of sodium (\(\mathrm{Na}\)) with water results in a release of energy, indicated by a negative change in enthalpy (\(\Delta H\)).

The enthalpy change for the reaction is given as \(-368.4 \mathrm{~kJ}\). This means 368.4 kilojoules of energy are released for every 2 moles of sodium that react.

• In an exothermic reaction such as this, we often observe the formation of gases, increase in temperature, and sometimes even light or flames due to the energy released.
• For experiments or applications, knowing a reaction is exothermic helps in predicting its behavior and necessary precautions if handling large quantities.

Enthalpy Change

Enthalpy change (\(\Delta H\)) is a measure of the total heat content in a system and indicates how much heat is absorbed or released during a reaction at constant pressure. It is expressed in kilojoules per mole (kJ/mol).

For a particular reaction, the enthalpy change tells us whether the process is exothermic or endothermic. In the exercise, \(\Delta H\) is given as \(-184.2 \text{ kJ/mol}\) for one mole of sodium, calculated from the reaction’s stoichiometry. The negative sign indicates heat is being released.

• To find the enthalpy change per mole for a given amount, you divide the total \(\Delta H\) by the number of moles the enthalpy change corresponds to, which allows you to scale the measurement to any quantity of reactant.
• This process helps us to determine exactly how much energy will be released or absorbed when a specific amount of reactants is used, making it a key calculation in chemistry for understanding reaction energetics.
• In endothermic reactions, the enthalpy change would be positive, indicating the system absorbs heat from the surroundings.

Molar Mass Calculations

Molar mass is an essential concept for converting between grams of a substance and moles, which is necessary to understand chemical reactions quantitatively. The molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol).

To find the number of moles in a given mass, you use the formula:

• Moles = \(\frac{\text{Mass}}{\text{Molar mass}}\)

In the exercise, the molar mass of sodium (\(\mathrm{Na}\)) is given as \(22.99 \mathrm{~g/mol}\). This allows you to calculate the number of moles in 1 gram of sodium as follows:

• The calculation: \(\frac{1.00 \text{ g}}{22.99 \text{ g/mol}} \approx 0.0435 \text{ mol}\) determines how many moles are present in the sample.
• Understanding molar mass and being able to calculate moles is vital in chemistry as it connects the macroscopic world of grams and kilograms with the microscopic world of atoms and molecules.

Molar mass calculations are fundamental for scaling reactions, predicting the quantity of products formed, and determining the reactant amounts needed, which are critical in both laboratory settings and industrial applications.