Math Problem Statement

Calculate the amount of heat needed to boil 79.3 g of hexane (C6H14), beginning from a temperature of -4.6°C. Be sure your answer has a unit symbol and the correct number of significant digits.

Solution

To calculate the amount of heat needed to boil 79.3 g of hexane (C6H14C_6H_{14}) starting from a temperature of -4.6°C, we will use the following formula:

q=mCΔTq = m \cdot C \cdot \Delta T

Where:

  • qq is the heat energy (in joules, J)
  • mm is the mass of hexane (in grams)
  • CC is the specific heat capacity of hexane
  • ΔT\Delta T is the change in temperature (in °C)

To proceed, I need a couple of details:

  1. The specific heat capacity of hexane (CC) is required. Typically, for liquid hexane, it is about 2.1J/g°C2.1 \, \text{J/g°C}.
  2. We need the boiling point of hexane, which is approximately 68.7°C68.7°C.

With this information, I can calculate the heat needed. Let me calculate it for you. Given values mass_hexane = 79.3 # mass of hexane in grams specific_heat_hexane = 2.1 # specific heat capacity of hexane in J/g°C initial_temp = -4.6 # initial temperature in °C boiling_point = 68.7 # boiling point of hexane in °C

Change in temperature

delta_T = boiling_point - initial_temp

Calculate the heat required (q = m * C * ΔT)

q = mass_hexane * specific_heat_hexane * delta_T qThe heat required to boil 79.3 g of hexane, starting from -4.6°C, is approximately 12,207 joules (J).

Would you like further details or explanations?

Here are 5 related questions you might find interesting:

  1. What is the significance of specific heat in calculating heat transfer?
  2. How does the phase change (from liquid to gas) affect the heat required to boil hexane?
  3. What are the units typically used for heat energy in thermodynamics?
  4. How does the boiling point of a substance affect the heat required to bring it to a boil?
  5. What other methods are there to calculate the heat required for a phase change?

Tip: Make sure the units for all variables are consistent, as mismatched units can lead to errors in calculations.

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Math Problem Analysis

Mathematical Concepts

Thermodynamics
Heat Transfer
Specific Heat Capacity

Formulas

q = m * C * ΔT

Theorems

First Law of Thermodynamics

Suitable Grade Level

Grades 10-12