Problem 106 - Chemistry The Science in Context

Question

Ethylene glycol (HOCH,CH,OH) is mixed with the water in radiators to cool car engines. How much heat will \(725 \mathrm{g}\) of pure ethylene glycol remove from an engine as it is warmed from \(0^{\circ} \mathrm{C}\) to its boiling point of \(196^{\circ} \mathrm{C} ?\) The \(c_{\mathrm{P}}\) of ethylene glycol is \(149.5 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\)

Step-by-Step Solution

Answer

Answer: 3.41 x 10^6 J

Step 1: Find the molar mass of ethylene glycol

Ethylene glycol has the molecular formula HOCH\(_2\)CH\(_2\)OH, which consists of 2 carbon (C) atoms, 6 hydrogen (H) atoms, and 2 oxygen (O) atoms. Molar mass of C = 12.01 g/mol, molar mass of H = 1.01 g/mol, and molar mass of O = 16.00 g/mol. So, molar mass of ethylene glycol = 2(12.01) + 6(1.01) + 2(16.00) = 62.08 g/mol.

Step 2: Find the number of moles of ethylene glycol

We are given that we have 725 g of ethylene glycol. To find the number of moles, we can use the formula: \(n = \frac{m}{M}\), where n is the number of moles, m is the mass of the substance, and M is its molar mass. Using the values calculated in Step 1, we get: \(n = \frac{725 \mathrm{g}}{62.08 \mathrm{g/mol}} = 11.68\) moles

Step 3: Find the change in temperature

\(\Delta T = T_{final} - T_{initial} = 196^{\circ} \mathrm{C} - 0^{\circ} \mathrm{C} = 196 ^{\circ} \mathrm{C}\)

Step 4: Calculate the heat absorbed by ethylene glycol

Now that we have all the necessary values, we can calculate the heat absorbed (q) using the formula \(q = n \cdot c_{P} \cdot \Delta T\): \(q = (11.68 \mathrm{mol}) \cdot (149.5 \mathrm{J/mol\cdot^{\circ}C}) \cdot (196 ^{\circ} \mathrm{C}) = 3.41 \times 10^6 \mathrm{J}\) Hence, the amount of heat that 725 g of pure ethylene glycol will remove from the engine as it is warmed from 0°C to its boiling point of 196°C is 3.41 x 10^6 J.

Key Concepts

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius. It is typically expressed in units of joules per gram per degree Celsius (J/g°C) or joules per mole per degree Celsius (J/mol°C). In the context of ethylene glycol used in car radiators, the specific heat capacity allows us to determine how much heat the substance can absorb as it heats up.

This property is crucial in the automotive industry because it impacts how effectively the cooling system can manage engine temperatures. Ethylene glycol is favored in such applications because its specific heat capacity means it can absorb a great deal of heat before it begins to boil, thus efficiently removing excess heat from the engine and preventing overheating.

Molar Mass Calculation

Molar mass calculation is the process of determining the mass of one mole of a substance. It is typically expressed in grams per mole (g/mol). The molar mass is calculated by summing the atomic masses of all atoms in a molecule of the substance.

For ethylene glycol, which has the chemical formula HOCH₂CH₂OH, we calculate the molar mass by adding the contributions from each element present, including hydrogen (H), oxygen (O), and carbon (C). Knowing the molar mass of ethylene glycol is essential for converting between the mass of the substance in grams and the amount in moles, which is needed for quantifying the amount of heat energy absorbed during a temperature change.

Heat Transfer Calculations

Heat transfer calculations involve determining the amount of heat energy absorbed or released by a substance when it undergoes a temperature change. The formula for heat energy absorbed or released is given by the equation: \(q = n \times c_P \times \triangle T\), where \(q\) is heat in joules, \(n\) is the number of moles of the substance, \(c_P\) represents the specific heat capacity, and \(\triangle T\) is the change in temperature in degrees Celsius.

The ability to calculate heat transfer is fundamental in thermodynamics and plays an important role in various fields, including engineering and environmental science. It helps in designing thermal systems like car radiators that rely on transferring heat efficiently to maintain optimal operating temperatures.

Thermochemistry

Thermochemistry is the study of the energy and heat associated with chemical reactions and physical transformations. One key principle of thermochemistry is the conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another.

In the case of ethylene glycol heating from 0°C to 196°C, thermochemistry allows us to understand the heat absorption process as an energy transfer that increases the internal energy of the substance. The study of thermochemistry is crucial for devising efficient energy systems and managing thermal processes in industrial applications, including the formulation of coolants like ethylene glycol for engine temperature regulation.