Chapter 13: Problem 60

A calculation shows that a salt will have a negative \(\Delta H\) and a positive \(\Delta S\) when it dissolves. Is it actually soluble?

Short Answer

Expert verified

Yes, the salt is soluble. This conclusion is made on the basis that when \(\Delta H\) is negative and \(\Delta S\) is positive, \(\Delta G = \Delta H - T\Delta S\) becomes negative. According to thermodynamic principles, if \(\Delta G\) is negative, the process is spontaneous.

Step by step solution

Understand given values

\(\Delta H\) value is given to be negative and \(\Delta S\) is positive when the salt is dissolved.

Applying Gibbs Free Energy Equation

Gibbs free energy (\(\Delta G\)) is computed using the following equation: \(\Delta G = \Delta H - T\Delta S\). Therefore, the \(\Delta G\) value will be the difference between the \(\Delta H\) value and the product of temperature, \(T\) (assumed to be positive because temperature is measured in Kelvin), and \(\Delta S\).

Analyzing the result

If \(\Delta H\) is negative and \(\Delta S\) is positive, \(\Delta H - T\Delta S\) will be a negative value minus another positive value, thereby making \(\Delta G\) negative. As per the rules of thermodynamics, if \(\Delta G\) is negative, the process will be spontaneous. Therefore, the salt would indeed be soluble.

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A calculation shows that a salt will have a negative \(\Delta H\) and a positive \(\Delta S\) when it dissolves. Is it actually soluble?

Short Answer

Step by step solution

Understand given values

Applying Gibbs Free Energy Equation

Analyzing the result

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