The specific heat of octane, C 8 H 18 (l), is 2.22 J•g/K. (b) Which will require more heat, increasing the temperature of 1 mol of C 8 H 18 (l), by a certain amount or increasing the temperature of 1 mol of H 2 O(l) by the same amount?

Hi everyone here we have a question asking us to identify which between one mole of water or one mole of acetic acid will cries more heat to increase the temperature by one degree. At the specific heat of acetic acid is 2.043 jules. Programs kelvin. So first we're going to convert to moles Using the more mass, the more mass of acetic acid is 60 0.6 grams Permal. The molar mass of water is 18 .02 g per mole. And now we can convert to moles. So for acetic acid, we're going to take our heat capacity to point 043 jules, her grams times kelvin. We're going to multiply by the molar mass. So 60.6 grams per mole And that equals 0.7 jules Permal times kelvin. Next we're going to do the same for water. So its specific heat is for .184 jules per grams times killed in Are going to multiply by its molar mass, which is 18.02 grams per mole. And that equals 0.40 jules Permal times kelvin. So acetic acid Is going to require more heat to increase the temperature by 1° because it is our larger number. So our answer is acetic acid. Thank you for watching. Bye.

Ch.5 - Thermochemistry

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Brown 14th Edition

Ch.5 - Thermochemistry

Problem 53b

Chapter 5, Problem 53b

The specific heat of octane, C₈H₁₈(l), is 2.22 J•g/K. (b) Which will require more heat, increasing the temperature of 1 mol of C₈H₁₈(l), by a certain amount or increasing the temperature of 1 mol of H₂O(l) by the same amount?

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First, determine the molar mass of octane, C₈H₁₈. The molar mass is calculated by adding the atomic masses of all the atoms in the molecule: 8 carbons (C) and 18 hydrogens (H).

Calculate the total heat required to increase the temperature of 1 mol of octane by a certain temperature change, \(\Delta T\). Use the formula: \(q = m \cdot c \cdot \Delta T\), where \(m\) is the mass of the substance, \(c\) is the specific heat, and \(\Delta T\) is the temperature change.

Next, find the specific heat of water, which is typically 4.18 J/g/K. Calculate the total heat required to increase the temperature of 1 mol of water by the same temperature change, \(\Delta T\), using the same heat formula.

Compare the total heat required for octane and water. The substance requiring more heat to achieve the same temperature change will have a higher product of its mass and specific heat.

Conclude which substance, octane or water, requires more heat to increase the temperature by the same amount based on the calculations from the previous steps.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius (or Kelvin). It is a crucial property that varies between different substances, influencing how much energy is needed to change their temperature. In this question, the specific heat of octane is given, which allows for comparison with water's specific heat to determine which substance requires more heat for the same temperature change.

Molar Mass and Moles

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). Understanding moles is essential in chemistry as it allows for the conversion between mass and the number of particles. In this question, both octane and water are considered in terms of moles, which helps in calculating the total heat required for temperature changes based on their specific heat capacities.

Heat Transfer and Energy Calculations

Heat transfer refers to the movement of thermal energy from one object or substance to another, often quantified using the formula Q = mcΔT, where Q is the heat added, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. This concept is fundamental in determining how much heat is needed to raise the temperature of a substance, allowing for a direct comparison between octane and water in the context of the question.