Question

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?

Answer 1

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.

Answer 2

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.