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A plot of ΔG (in units of kJ/mol) vs. T (K) yields a straight line with the equation: y = -10.195x + 171.674. What is the value of ΔH (kJ/mol) for the reaction, based on this data?

User Amit Patil
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Final answer:

The value of ΔH (kJ/mol) for the reaction can be determined using the equation ΔG° = ΔH° - TΔS°, where ΔG° is the standard free energy change, ΔH° is the standard enthalpy change, ΔS° is the standard entropy change, and T is the temperature in Kelvin. From the given equation of the straight line, y = -10.195x + 171.674, where y represents ΔG (in kJ/mol) and x represents T (in K), we can identify that the slope of the line (-10.195) represents -ΔH°, as ΔH° is the negative of the slope. Therefore, the value of ΔH° for the reaction is 10.195 kJ/mol.

Step-by-step explanation:

The value of ΔH (kJ/mol) for the reaction can be determined using the equation ΔG° = ΔH° - TΔS°, where ΔG° is the standard free energy change, ΔH° is the standard enthalpy change, ΔS° is the standard entropy change, and T is the temperature in Kelvin.

From the given equation of the straight line, y = -10.195x + 171.674, where y represents ΔG (in kJ/mol) and x represents T (in K), we can identify that the slope of the line (-10.195) represents -ΔH°, as ΔH° is the negative of the slope.

Therefore, the value of ΔH° for the reaction is 10.195 kJ/mol.

User Alex Fish
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5 votes

The value of
\( \Delta H \) is approximately -10.195 kJ/mol based on the given equation. So, based on the equation of the plot, the enthalpy change
(\( \Delta H \)) for the reaction is approximately -10.195 kJ/mol.

The equation you provided for the plot is in the form
\( y = mx + b \), where:


  • y is the dependent variable (in this case,
    \( \Delta G \)),

  • x is the independent variable (in this case,
    \( T \),

  • \( m \) is the slope of the line, and

  • \( b \) is the y-intercept.

In thermodynamics, the relationship between Gibbs free energy change
(\( \Delta G \), enthalpy change
(\( \Delta H \)), temperature
(\( T \)), and entropy change
(\( \Delta S \)) is given by:


\[ \Delta G = \Delta H - T \Delta S \]

Comparing this with the equation of the line
\( y = mx + b \), you can see that
\( \Delta G \) corresponds to
\( y \), \( \Delta H \) corresponds to the slope
\( m \), and
\( -T \Delta S \) corresponds to the y-intercept
\( b \).

So, the slope
(\( m \)) of the line is equal to
\( \Delta H \).

Therefore, based on the provided equation
\( y = -10.195x + 171.674 \), the value of
\( \Delta H \) is approximately
\( -10.195 \) kJ/mol.

User Daiki
by
7.9k points

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