Problem 88 - Chemistry Matter and Change

Question

A sample of ammonia \(\left(\Delta H_{\text { solid }}=-5.66 \mathrm{k}\right] / \mathrm{mol} )\) liber- ates 5.66 \(\mathrm{kJ}\) of heat as it solidifies at its melting point. What is the mass of the sample?

Step-by-Step Solution

Answer

The mass of the ammonia sample is 17.03 g.

Step 1: Understanding the Problem

We need to find the mass of an ammonia sample based on the heat it liberates when it solidifies. Solidification of ammonia releases 5.66 kJ/mol, and the sample releases 5.66 kJ of heat.

Step 2: Relate Heat to Moles

What do we know? The heat released \(\Delta H_{\text{solid}} = -5.66 \, \mathrm{kJ/mol}\). Since the sample releases 5.66 kJ of heat, this corresponds to exactly 1 mole of ammonia because the molar heat of solidification is identical to the heat released.

Step 3: Calculate the Molar Mass of Ammonia

Next, we need to determine the mass of ammonia from the number of moles. Ammonia (NH_3) has a molar mass calculated as follows: \(14.01 \, \mathrm{g/mol} \text{ (N)} + 3 \times 1.01 \, \mathrm{g/mol} \text{ (H)} = 17.03 \, \mathrm{g/mol}\).

Step 4: Find the Mass of the Sample

Since we know the sample contains exactly 1 mole of ammonia (because it released 5.66 kJ of energy, matching its molar heat of solidification), the mass of the sample is equivalent to the molar mass of ammonia. Thus, the mass is \(17.03 \, \mathrm{g}\).

Key Concepts

Heat Transfer

Heat transfer involves the movement of thermal energy from one object or substance to another. In thermochemistry, heat transfer is vital to understand processes such as chemical reactions and phase changes. It is about how energy moves when substances interact or change state.
The exercise deals with the heat release during the solidification of ammonia. When a substance like ammonia solidifies, it releases energy in the form of heat to its surroundings. This is because molecules in the liquid phase are more energetic than in the solid phase. The released energy in our case is precisely -5.66 kJ for ammonia.

• This energy is crucial to determining how much of the substance is involved in the process.
• The amount of heat transferred can tell us about the changes happening at the molecular level.

Understanding these concepts aids in calculating various properties related to the energy stored or released during chemical transformations.

Molar Mass Calculation

Calculating molar mass is a fundamental skill in chemistry. It involves finding the mass of one mole of a substance, which is essential for converting between the amount in moles and the mass in grams.
For ammonia, \(NH_3\), the molar mass is calculated using the atomic masses of nitrogen and hydrogen. Nitrogen has an atomic mass of 14.01 g/mol, and hydrogen has an atomic mass of 1.01 g/mol. Since there are three hydrogen atoms in ammonia, the calculation becomes:
\[\text{Molar mass of } NH_3 = 14.01 \, \text{g/mol} + 3 \times 1.01 \, \text{g/mol} = 17.03 \, \text{g/mol} \] Knowing how to calculate molar mass allows us to link the chemical amount (moles) to a measurable mass (grams). This is crucial for tasks like determining the mass of a substance undergoing a chemical change.

Phase Change

A phase change occurs when a substance changes from one state of matter to another, such as from a liquid to a solid. In our exercise, ammonia undergoes a phase change as it solidifies. Phase changes are physical changes because the substance itself does not change chemically.
During solidification, the molecules lose energy and arrange themselves into a more organized structure. This change is exothermic, meaning it releases energy to its surroundings. As seen in the exercise, ammonia releases 5.66 kJ of heat as it solidifies.

• Phase transitions are driven by energy changes and temperature.
• Each substance has unique phase transition points, like melting and boiling points.

Understanding phase changes helps to predict how a substance behaves under different conditions, which is especially useful in varied scientific and industrial applications.

Enthalpy Change

The enthalpy change, or \(\Delta H\), represents the heat absorbed or released during a chemical reaction or phase change at constant pressure. In crystallization or solidification processes, it is the heat of fusion or solidification.
In our context, ammonia has an enthalpy change of -5.66 kJ/mol during solidification. This negative sign indicates that the process is exothermic, releasing heat to the surroundings.
Enthalpy changes are measured in kilojoules per mole (kJ/mol), which helps in quantifying and comparing the energy changes in chemical processes.

• They are essential for understanding energy efficiency in reactions.
• Knowing the enthalpy change allows chemists and engineers to design better processes that maximize desired outcomes.

Whether in everyday phenomena like freezing or in industrial processes, enthalpy change concepts are central to energy management.

Ammonia Solidification

Ammonia solidification is the process where liquid ammonia turns into a solid. This is a type of phase change and a remarkable thermochemical process.
In the exercise, ammonia releases 5.66 kJ of heat as it solidifies, which aligns with the exact energy change for one mole, determined by its molar enthalpy of solidification.
Solidifying ammonia involves crucial calculations:

• Understanding the relationship between energy release and substance amount helps in accurate measurement of the sample mass.
• It is an example of the broader concept where phase transition data can determine sample masses important in laboratory settings.

This concept connects molecular-level transitions with practical applications, illustrating the principles of thermochemistry in real-world scenarios.