Question

When solutions containing silver ions and chloride ions are mixed, silver chloride precipitates: $$ \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q)-\longrightarrow \mathrm{AgCl}(s) \quad \Delta H=-65.5 \mathrm{~kJ} $$ (a) Calculate \(\Delta H\) for production of \(0.200 \mathrm{~mol}\) of \(\mathrm{AgCl}\) by this reaction. (b) Calculate \(\Delta H\) for the production of \(2.50 \mathrm{~g}\) of \(\mathrm{AgCl}\). (c) Calculate \(\Delta \mathrm{H}\) when \(0.150 \mathrm{mmol}\) of AgCl dissolves in water.

Short answer

(a) The enthalpy change for producing 0.200 mol of AgCl is -13.1 kJ. (b) The enthalpy change for producing 2.50 g of AgCl is -1.141 kJ. (c) The enthalpy change when 0.150 mmol of AgCl dissolves in water is 9.825 x 10⁻³ kJ.

Step-by-step solution

Identify the given values

We are given the \(\Delta H\) value for the reaction as -65.5 kJ per mole of AgCl produced. We are also given the amount of AgCl as 0.200 mol.

Calculate the enthalpy change

To find the enthalpy change for the production of 0.200 mol of AgCl, we can use the formula: \(\Delta H_\text{reaction} = (n \times \Delta H_\text{per mole})\) Where \(n\) is the amount of AgCl produced in moles and \(\Delta H_\text{per mole}\) is the enthalpy change per mole. \(\Delta H_\text{reaction} = (0.200 \: \text{mol}) \times (-65.5 \: \text{kJ/mol}) = -13.1 \: \text{kJ}\) The enthalpy change for producing 0.200 mol of AgCl is -13.1 kJ. #Case(b): Calculate \(\Delta H\) for the production of 2.50 g of \(\mathrm{AgCl}\)#

Find the moles of AgCl

We are given the mass of AgCl as 2.50 g. First, we need to convert the mass into moles using the molar mass of AgCl (Ag = 107.87 g/mol, Cl = 35.45 g/mol): Molar mass of AgCl = 107.87 + 35.45 = 143.32 g/mol Moles of AgCl = \( \frac{2.50 \: \text{g}}{143.32 \: \text{g/mol}} = 0.01744 \: \text{mol}\)

Calculate the enthalpy change

Now that we have the amount of AgCl produced in moles, we can use the same formula as in case (a): \(\Delta H_\text{reaction} = (n \times \Delta H_\text{per mole})\) \(\Delta H_\text{reaction} = (0.01744 \: \text{mol}) \times (-65.5 \: \text{kJ/mol}) = -1.141 \: \text{kJ}\) The enthalpy change for producing 2.50 g of AgCl is -1.141 kJ. #Case(c): Calculate \(\Delta \mathrm{H}\) when \(0.150 \mathrm{mmol}\) of AgCl dissolves in water#

Convert mmol to mol and find the reverse reaction enthalpy change

We are given that 0.150 mmol of AgCl dissolves in water. First, let's convert mmol to mol: Moles of AgCl = \(\frac{0.150 \: \text{mmol}}{1000} = 1.5 \times 10^{-4} \: \text{mol}\) Since dissolving AgCl in water is the reverse reaction of its precipitation, the enthalpy change for this reaction will have the opposite sign: \(\Delta H_\text{reverse reaction} = +65.5 \: \text{kJ/mol}\)

Calculate the enthalpy change

Now that we have the moles of AgCl dissolved and the correct enthalpy change, we can follow the same equation as before: \(\Delta H_\text{reaction} = (n \times \Delta H_\text{per mole})\) \(\Delta H_\text{reaction} = (1.5 \times 10^{-4} \: \text{mol}) \times (65.5 \: \text{kJ/mol}) = 9.825 \times 10^{-3} \: \text{kJ}\) The enthalpy change when 0.150 mmol of AgCl dissolves in water is 9.825 x 10⁻³ kJ.

Key concepts

Enthalpy Change

The concept of enthalpy change is essential in thermochemistry and refers to the heat absorbed or released during a chemical reaction at constant pressure. It is denoted by the symbol \( \Delta H \). Understanding enthalpy change helps in predicting whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). For the reaction where silver ions and chloride ions form silver chloride, the enthalpy change is given as -65.5 kJ per mole. This negative sign indicates that the reaction releases energy, which classifies it as exothermic. In any reaction, \( \Delta H \) can be calculated using the formula:

• \( \Delta H_\text{reaction} = n \times \Delta H_\text{per mole} \)

This simply involves multiplying the moles of the substance formed or consumed by the given enthalpy change per mole. For practical problem-solving, it’s important to be able to figure out \( \Delta H \) for different amounts of reactants or products, keeping the relationship proportional.

Reaction Enthalpy

Reaction enthalpy specifically refers to the change in enthalpy associated with a particular chemical reaction. It's a vital indicator of how energy is exchanged in the form of heat during a reaction. Reaction enthalpy allows chemists to understand the energy requirement or energy deliverance of a chemical process. In chemical reactions, like the formation of silver chloride from silver and chloride ions, the reaction enthalpy is -65.5 kJ per mole. This indicates that each mole of AgCl formed releases 65.5 kJ of energy. The calculation involves determining the number of moles involved and applying them to the known enthalpy change per mole of the reactants or products. By understanding this concept, one can make informed predictions about the energetic feasibility of reactions.

Chemical Equations

Chemical equations are symbolic representations showing the reactants and products involved in a chemical reaction. The equation not only highlights which substances are involved but also their respective quantities and phases, such as solid, liquid, gas, or aqueous. For the given exercise, the chemical equation is:

• \( \mathrm{Ag}^{+}(aq) + \mathrm{Cl}^{-}(aq) \rightarrow \mathrm{AgCl}(s) \)

This equation illustrates the formation of solid silver chloride from aqueous silver and chloride ions. It's crucial to interpret these equations accurately to understand how matter is conserved and rearranged during the reaction. Moreover, chemical equations are balanced, highlighting the law of conservation of mass, ensuring that matter is not created nor destroyed during a reaction.

Mole Calculations

Moles are a fundamental unit in chemistry, allowing us to count particles by relating macroscopic amounts to microscopic numbers. This concept is pivotal for calculating quantities in reactions, as chemical equations depict reactants and products in terms of moles.Using moles, we can determine how much of a chemical will react or be produced. To convert grams to moles, the formula is:

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

In the exercise, to find how many moles correspond to a given mass of silver chloride (AgCl), we use its molar mass (143.32 g/mol). For example, when 2.50 g of AgCl is involved, calculating its moles allows for determining the reaction enthalpy with other given data. Such calculations are crucial for experimental planning and efficiency in chemical synthesis.